{"group":{"group":{"id":76849,"name":"L3Harris CODESgiving Challenge ","lockable":false,"created_at":"2023-10-11T20:23:40.000Z","updated_at":"2026-06-05T00:10:21.000Z","description":"Calling all coding enthusiasts and MATLAB aficionados! Get ready to showcase your programming prowess, challenge your skills, and compete against L3Harris colleagues in an exciting coding contest running from 11/20 to 12/8. 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with resistance (R), create a function that will return the voltage (V) across the resistor.\r\n","description_html":"\u003cp\u003e\u003cb\u003eBACKGROUND / MOTIVATION:\u003c/b\u003e\u003c/p\u003e\u003cp\u003eMany important observations in math and science can be described by short, but powerful, equations:\u003c/p\u003e\u003cpre\u003e * The Pythagorean Theorem (c^2 = a^2 + b^2)\r\n * Newton's Second Law of Motion (F = ma)\r\n * Einstein's Mass-Energy Equivalence (E = mc^2)\u003c/pre\u003e\u003cp\u003eFor electrical circuits, one of the most useful and important equations is:\u003c/p\u003e\u003cpre\u003e * Ohm's Law (V = IR)\u003c/pre\u003e\u003cp\u003eOhm's Law describes the relationship between voltage (V), current (I), and resistance (R) in electrical circuits.\u003c/p\u003e\u003cp\u003eFor more information, check out: \u003ca href = \"https://www.build-electronic-circuits.com/ohms-law/\"\u003ehttps://www.build-electronic-circuits.com/ohms-law/\u003c/a\u003e\u003c/p\u003e\u003cp\u003e\u003cb\u003ePROBLEM DESCRIPTION:\u003c/b\u003e\u003c/p\u003e\u003cp\u003eGiven the current (I) through a resistor with resistance (R), create a function that will return the voltage (V) across the resistor.\u003c/p\u003e","function_template":"function V = OhmsLaw(I,R)\r\n  V = 0; % modify this equation to use Ohm's Law\r\nend","test_suite":"%%\r\nI = 0.09; %90mA current\r\nR = 100; %100 Ohm resistor\r\nV_correct = 9; %9V voltage\r\nassert(isequal(OhmsLaw(I,R),V_correct))\r\n\r\n%%\r\nI = 0.012; %12mA current\r\nR = 1000; %1kOhm resistor\r\nV_correct = 12; %12V voltage\r\nassert(isequal(OhmsLaw(I,R),V_correct))","published":true,"deleted":false,"likes_count":12,"comments_count":1,"created_by":377536,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":1936,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2019-11-20T14:14:50.000Z","updated_at":"2026-06-11T17:30:10.000Z","published_at":"2019-11-21T02:54:28.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eBACKGROUND / MOTIVATION:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eMany important observations in math and science can be described by short, but powerful, equations:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ * The Pythagorean Theorem (c^2 = a^2 + b^2)\\n * Newton's Second Law of Motion (F = ma)\\n * Einstein's Mass-Energy Equivalence (E = mc^2)]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor electrical circuits, one of the most useful and important equations is:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ * Ohm's Law (V = IR)]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eOhm's Law describes the relationship between voltage (V), current (I), and resistance (R) in electrical circuits.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor more information, check out:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.build-electronic-circuits.com/ohms-law/\\\"\u003e\u003cw:r\u003e\u003cw:t\u003e\u0026lt;https://www.build-electronic-circuits.com/ohms-law/\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e\u0026gt;\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ePROBLEM DESCRIPTION:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven the current (I) through a resistor with resistance (R), create a function that will return the voltage (V) across the resistor.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":2383,"title":"Kepler's Equation","description":"Solve \u003chttp://en.wikipedia.org/wiki/Kepler's_equation Kepler's Equation\u003e. \r\n\r\nNote that the solution is rounded down to 5 decimal places at the test suite.\r\n\r\nInputs:\r\n\r\n* M    mean anomaly [rad]\r\n* e    eccentricity [1]\r\n\r\nOutputs:\r\n\r\n* E    eccentric anomaly [rad]","description_html":"\u003cp\u003eSolve \u003ca href = \"http://en.wikipedia.org/wiki/Kepler's_equation\"\u003eKepler's Equation\u003c/a\u003e.\u003c/p\u003e\u003cp\u003eNote that the solution is rounded down to 5 decimal places at the test suite.\u003c/p\u003e\u003cp\u003eInputs:\u003c/p\u003e\u003cul\u003e\u003cli\u003eM    mean anomaly [rad]\u003c/li\u003e\u003cli\u003ee    eccentricity [1]\u003c/li\u003e\u003c/ul\u003e\u003cp\u003eOutputs:\u003c/p\u003e\u003cul\u003e\u003cli\u003eE    eccentric anomaly [rad]\u003c/li\u003e\u003c/ul\u003e","function_template":"function E = kepler(M, e)\r\n    E = M;\r\nend","test_suite":"%%\r\nM = pi/2;\r\ne = 0;\r\nassert(isequal(round(kepler(M, e)*1e5)/1e5, 1.5708))\r\n%%\r\nM = pi/2;\r\ne = 0.8;\r\nassert(isequal(round(kepler(M, e)*1e5)/1e5, 2.21193))\r\n%%\r\nM = pi/3;\r\ne = 0.1;\r\nassert(isequal(round(kepler(M, e)*1e5)/1e5, 1.13798))\r\n%%\r\nM = 0.1;\r\ne = 0.2;\r\nassert(isequal(round(kepler(M, e)*1e5)/1e5, 0.12492))","published":true,"deleted":false,"likes_count":8,"comments_count":0,"created_by":20319,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":172,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":25,"created_at":"2014-06-23T15:06:25.000Z","updated_at":"2026-05-08T07:46:54.000Z","published_at":"2014-06-23T15:08:37.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eSolve\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://en.wikipedia.org/wiki/Kepler's_equation\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eKepler's Equation\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eNote that the solution is rounded down to 5 decimal places at the test suite.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle 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w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eE eccentric anomaly [rad]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":45493,"title":"SatCom #2: Gain of a circular 'dish' antenna","description":"Satellite and Space Engineering - Problem #2\r\nThis is part of a series of problems looking at topics in satellite and space communications and systems engineering.\r\nDetermine the gain (in dBi) of a circular 'dish' antenna.\r\nYou are given the diameter of the antenna (in m), the frequency of operation (in Hz) and the antenna efficiency (as a %). Calculate the gain of the antenna (in dBi).\r\nYou should take the speed of light to be 299,792,458 m/s.\r\nHint: See \u003chttps://en.wikipedia.org/wiki/Parabolic_antenna#Gain\u003e - but don't forget to convert to dBi!\r\nExample: The gain of a typical direct-to-home 60cm TV receiving antenna at 12 GHz is around 36 dBi.\r\nSome future problems in this series will build on work done in previous problems, so if you get a working solution I suggest you hang onto the code!","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 273px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 136.5px; transform-origin: 407px 136.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 157.5px 8px; transform-origin: 157.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eSatellite and Space Engineering - Problem #2\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 366.5px 8px; transform-origin: 366.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eThis is part of a series of problems looking at topics in satellite and space communications and systems engineering.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 171.5px 8px; transform-origin: 171.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eDetermine the gain (in dBi) of a circular 'dish' antenna.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 380.5px 8px; transform-origin: 380.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eYou are given the diameter of the antenna (in m), the frequency of operation (in Hz) and the antenna efficiency (as a %). Calculate the gain of the antenna (in dBi).\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 182px 8px; transform-origin: 182px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eYou should take the speed of light to be 299,792,458 m/s.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 28.5px 8px; transform-origin: 28.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eHint: See\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://en.wikipedia.org/wiki/Parabolic_antenna#Gain\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003e\u0026lt;https://en.wikipedia.org/wiki/Parabolic_antenna#Gain\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 114.5px 8px; transform-origin: 114.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e\u0026gt; - but don't forget to convert to dBi!\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 319.5px 8px; transform-origin: 319.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eExample: The gain of a typical direct-to-home 60cm TV receiving antenna at 12 GHz is around 36 dBi.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 384px 8px; transform-origin: 384px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eSome future problems in this series will build on work done in previous problems, so if you get a working solution I suggest you hang onto the code!\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function gain = ant_gain(diam,freq,eff)\r\n  gain = diam+freq+eff;\r\nend","test_suite":"%%\r\nd = 10;\r\nf = 299792458/pi;\r\ne = 100;\r\ny_correct = 20;\r\nassert(abs(ant_gain(d,f,e)-y_correct)\u003c1e-8)\r\n\r\n%%\r\nd = 0.6;\r\nf = 12e9;\r\ne = 70;\r\ny_correct = 36.004213724092068;\r\nassert(abs(ant_gain(d,f,e)-y_correct)\u003c1e-8)\r\n\r\n%%\r\nd = 30;\r\nf = 6e9;\r\ne = 65;\r\ny_correct = 63.641167063818799;\r\nassert(abs(ant_gain(d,f,e)-y_correct)\u003c1e-8)\r\n\r\n%%\r\ns=importdata('ant_gain.m');\r\ny_correct=false;\r\nassert(isequal(sum(contains(s,'regexp')),y_correct))\r\n","published":true,"deleted":false,"likes_count":6,"comments_count":3,"created_by":437780,"edited_by":223089,"edited_at":"2022-05-20T19:19:27.000Z","deleted_by":null,"deleted_at":null,"solvers_count":204,"test_suite_updated_at":"2022-05-20T19:19:27.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2020-05-04T11:40:46.000Z","updated_at":"2026-06-11T19:04:02.000Z","published_at":"2020-05-04T12:00:04.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eSatellite and Space Engineering - Problem #2\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eThis is part of a series of problems looking at topics in satellite and space communications and systems engineering.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eDetermine the gain (in dBi) of a circular 'dish' antenna.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eYou are given the diameter of the antenna (in m), the frequency of operation (in Hz) and the antenna efficiency (as a %). Calculate the gain of the antenna (in dBi).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eYou should take the speed of light to be 299,792,458 m/s.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eHint: See\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://en.wikipedia.org/wiki/Parabolic_antenna#Gain\\\"\u003e\u003cw:r\u003e\u003cw:t\u003e\u0026lt;https://en.wikipedia.org/wiki/Parabolic_antenna#Gain\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e\u0026gt; - but don't forget to convert to dBi!\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eExample: The gain of a typical direct-to-home 60cm TV receiving antenna at 12 GHz is around 36 dBi.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eSome future problems in this series will build on work done in previous problems, so if you get a working solution I suggest you hang onto the code!\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":230,"title":"Project Euler: Problem 1, Multiples of 3 and 5","description":"If we list all the natural numbers below 10 that are multiples of 3 or 5, we get 3, 5, 6 and 9. The sum of these multiples is 23.\r\n\r\nFind the sum of all the multiples of 3 or 5 below the input value.\r\n\r\nThank you to \u003chttp://projecteuler.net/problem=1 Project Euler Problem 1\u003e","description_html":"\u003cp\u003eIf we list all the natural numbers below 10 that are multiples of 3 or 5, we get 3, 5, 6 and 9. The sum of these multiples is 23.\u003c/p\u003e\u003cp\u003eFind the sum of all the multiples of 3 or 5 below the input value.\u003c/p\u003e\u003cp\u003eThank you to \u003ca href=\"http://projecteuler.net/problem=1\"\u003eProject Euler Problem 1\u003c/a\u003e\u003c/p\u003e","function_template":"function y = euler001(x)\r\n  y = rand;\r\nend","test_suite":"%%\r\nx = 1000;\r\ny_correct = 233168;\r\nassert(isequal(euler001(x),y_correct))\r\n\r\n%%\r\nx = 4000;\r\ny_correct = 3732668;\r\nassert(isequal(euler001(x),y_correct))\r\n\r\n%%\r\nx = 2340;\r\ny_correct = 1276470;\r\nassert(isequal(euler001(x),y_correct))\r\n\r\n%%\r\nx = 2341;\r\ny_correct = 1278810;\r\nassert(isequal(euler001(x),y_correct))\r\n\r\n","published":true,"deleted":false,"likes_count":49,"comments_count":5,"created_by":240,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":3710,"test_suite_updated_at":"2012-02-02T21:27:24.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2012-02-02T14:46:43.000Z","updated_at":"2026-06-12T11:01:49.000Z","published_at":"2012-02-02T21:43:40.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIf we list all the natural numbers below 10 that are multiples of 3 or 5, we get 3, 5, 6 and 9. The sum of these multiples is 23.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFind the sum of all the multiples of 3 or 5 below the input value.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThank you to\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://projecteuler.net/problem=1\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eProject Euler Problem 1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":42382,"title":"Combined Ages 1 - Symmetric, n = 3","description":"You have probably seen the common riddle wherein combined ages are provided and you must determine the individual ages. For example: If the ages of Alex and Barry sum to 43, the ages of Alex and Chris sum to 55, and the ages of Barry and Chris sum to 66, what are their individual ages?\r\n\r\nFor this problem, we'll assume that the three individuals are represented by A, B, and C, whereas the sums are AB, AC, and BC:\r\n\r\n* A+B = AB (= 43)\r\n* A+C = AC (= 55)\r\n* B+C = BC (= 66)\r\n\r\nAs you might have noticed, this is a simple matrix algebra problem. Write a function to return the individuals' ages [A;B;C] based on the supplied sums [AB AC BC].","description_html":"\u003cp\u003eYou have probably seen the common riddle wherein combined ages are provided and you must determine the individual ages. For example: If the ages of Alex and Barry sum to 43, the ages of Alex and Chris sum to 55, and the ages of Barry and Chris sum to 66, what are their individual ages?\u003c/p\u003e\u003cp\u003eFor this problem, we'll assume that the three individuals are represented by A, B, and C, whereas the sums are AB, AC, and BC:\u003c/p\u003e\u003cul\u003e\u003cli\u003eA+B = AB (= 43)\u003c/li\u003e\u003cli\u003eA+C = AC (= 55)\u003c/li\u003e\u003cli\u003eB+C = BC (= 66)\u003c/li\u003e\u003c/ul\u003e\u003cp\u003eAs you might have noticed, this is a simple matrix algebra problem. Write a function to return the individuals' ages [A;B;C] based on the supplied sums [AB AC BC].\u003c/p\u003e","function_template":"function y = combined_ages(AB,BC,AC)\r\n y = [1;1;1];\r\nend","test_suite":"%%\r\nAB = 43;\r\nBC = 55;\r\nAC = 66;\r\ny = combined_ages(AB,BC,AC);\r\ny_correct = [27 16 39];\r\nfor i = 1:3\r\n assert(isequal(y(i),y_correct(i)))\r\nend\r\n\r\n%%\r\nAB = 30;\r\nBC = 50;\r\nAC = 40;\r\ny = combined_ages(AB,BC,AC);\r\ny_correct = [10 20 30];\r\nfor i = 1:3\r\n assert(isequal(y(i),y_correct(i)))\r\nend\r\n\r\n%%\r\nAB = 20;\r\nBC = 70;\r\nAC = 60;\r\ny = combined_ages(AB,BC,AC);\r\ny_correct = [5 15 55];\r\nfor i = 1:3\r\n assert(isequal(y(i),y_correct(i)))\r\nend\r\n\r\n%%\r\nAB = 34;\r\nBC = 84;\r\nAC = 56;\r\ny = combined_ages(AB,BC,AC);\r\ny_correct = [3 31 53];\r\nfor i = 1:3\r\n assert(isequal(y(i),y_correct(i)))\r\nend\r\n\r\n%%\r\ny_correct = [2 11 21];\r\nAB = y_correct(1) + y_correct(2);\r\nBC = y_correct(2) + y_correct(3);\r\nAC = y_correct(1) + y_correct(3);\r\ny = combined_ages(AB,BC,AC);\r\nfor i = 1:3\r\n assert(isequal(y(i),y_correct(i)))\r\nend\r\n\r\n%%\r\ny_correct = [11 17 21];\r\nAB = y_correct(1) + y_correct(2);\r\nBC = y_correct(2) + y_correct(3);\r\nAC = y_correct(1) + y_correct(3);\r\ny = combined_ages(AB,BC,AC);\r\nfor i = 1:3\r\n assert(isequal(y(i),y_correct(i)))\r\nend\r\n\r\n%%\r\ny_correct = [15 35 55];\r\nAB = y_correct(1) + y_correct(2);\r\nBC = y_correct(2) + y_correct(3);\r\nAC = y_correct(1) + y_correct(3);\r\ny = combined_ages(AB,BC,AC);\r\nfor i = 1:3\r\n assert(isequal(y(i),y_correct(i)))\r\nend","published":true,"deleted":false,"likes_count":2,"comments_count":2,"created_by":26769,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":328,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2015-06-16T17:30:16.000Z","updated_at":"2026-06-07T10:45:58.000Z","published_at":"2015-06-16T17:30:16.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eYou have probably seen the common riddle wherein combined ages are provided and you must determine the individual ages. For example: If the ages of Alex and Barry sum to 43, the ages of Alex and Chris sum to 55, and the ages of Barry and Chris sum to 66, what are their individual ages?\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor this problem, we'll assume that the three individuals are represented by A, B, and C, whereas the sums are AB, AC, and BC:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA+B = AB (= 43)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA+C = AC (= 55)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eB+C = BC (= 66)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eAs you might have noticed, this is a simple matrix algebra problem. Write a function to return the individuals' ages [A;B;C] based on the supplied sums [AB AC BC].\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":1035,"title":"Generate a vector like 1,2,2,3,3,3,4,4,4,4","description":"Generate a vector like 1,2,2,3,3,3,4,4,4,4\r\nSo if n = 3, then return\r\n [1 2 2 3 3 3]\r\nAnd if n = 5, then return\r\n [1 2 2 3 3 3 4 4 4 4 5 5 5 5 5]","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 142.867px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 406.5px 71.4333px; transform-origin: 406.5px 71.4333px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.5px 10.5px; text-align: left; transform-origin: 383.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 131.767px 7.81667px; transform-origin: 131.767px 7.81667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eGenerate a vector like 1,2,2,3,3,3,4,4,4,4\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.5px 10.5px; text-align: left; transform-origin: 383.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 72.5833px 7.81667px; transform-origin: 72.5833px 7.81667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eSo if n = 3, then return\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 20.4333px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 403.5px 10.2167px; transform-origin: 403.5px 10.2167px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1.11667px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1.11667px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1.11667px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1.11667px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; text-wrap-mode: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 54.7167px 8.375px; tab-size: 4; transform-origin: 54.7167px 8.375px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e [1 2 2 3 3 3]\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 10px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 10px; perspective-origin: 383.5px 10.5px; text-align: left; transform-origin: 383.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 76.4917px 7.81667px; transform-origin: 76.4917px 7.81667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eAnd if n = 5, then return\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 20.4333px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 403.5px 10.2167px; transform-origin: 403.5px 10.2167px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1.11667px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1.11667px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1.11667px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1.11667px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; text-wrap-mode: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 125.067px 8.375px; tab-size: 4; transform-origin: 125.067px 8.375px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e [1 2 2 3 3 3 4 4 4 4 5 5 5 5 5]\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function ans = your_fcn_name(n)\r\n n\r\nend","test_suite":"%%\r\nfiletext = fileread('your_fcn_name.m');\r\nassert(isempty(strfind(filetext, 'assignin')))\r\nassert(isempty(strfind(filetext, 'if')))\r\nassert(isempty(strfind(filetext, 'regexp')))\r\n\r\n%%\r\nx = 2;\r\ny_correct = [1 2 2];\r\nassert(isequal(your_fcn_name(x),y_correct))\r\n\r\n%%\r\nx = 5;\r\ny_correct = [1 2 2 3 3 3 4 4 4 4 5 5 5 5 5];\r\nassert(isequal(your_fcn_name(x),y_correct))\r\n\r\n%%\r\nx = 10;\r\ny_correct = [1 2 2 3 3 3 4 4 4 4 5 5 5 5 5 ...\r\n  6 6 6 6 6 6 7 7 7 7 7 7 7 8 8 8 8 8 8 8 8 ...\r\n  9 9 9 9 9 9 9 9 9 10 10 10 10 10 10 10 10 10 10];\r\nassert(isequal(your_fcn_name(x),y_correct))\r\n\r\n%%\r\nx = 12;\r\ny_correct = [1 2 2 3 3 3 4 4 4 4 5 5 5 5 5 ...\r\n  6 6 6 6 6 6 7 7 7 7 7 7 7 8 8 8 8 8 8 8 8 ...\r\n  9 9 9 9 9 9 9 9 9 10 10 10 10 10 10 10 10 10 10 ...\r\n  11 11 11 11 11 11 11 11 11 11 11 ...\r\n  12 12 12 12 12 12 12 12 12 12 12 12];\r\nassert(isequal(your_fcn_name(x),y_correct))\r\n\r\n%%\r\nx = 9;\r\ny_correct = [1 2 2 3 3 3 4 4 4 4 5 5 5 5 5 ...\r\n  6 6 6 6 6 6 7 7 7 7 7 7 7 8 8 8 8 8 8 8 8 ...\r\n  9 9 9 9 9 9 9 9 9];\r\nassert(isequal(your_fcn_name(x),y_correct))\r\n\r\n%%\r\nx = 7;\r\ny_correct = [1 2 2 3 3 3 4 4 4 4 5 5 5 5 5 ...\r\n  6 6 6 6 6 6 7 7 7 7 7 7 7];\r\nassert(isequal(your_fcn_name(x),y_correct))\r\n\r\n%%\r\nx = 15;\r\ny_correct = [1 2 2 3 3 3 4 4 4 4 5 5 5 5 5 ...\r\n  6 6 6 6 6 6 7 7 7 7 7 7 7 8 8 8 8 8 8 8 8 ...\r\n  9 9 9 9 9 9 9 9 9 10 10 10 10 10 10 10 10 10 10 ...\r\n  11 11 11 11 11 11 11 11 11 11 11 ...\r\n  12 12 12 12 12 12 12 12 12 12 12 12 ...\r\n  13 13 13 13 13 13 13 13 13 13 13 13 13 ...\r\n  14 14 14 14 14 14 14 14 14 14 14 14 14 14 ...\r\n  15 15 15 15 15 15 15 15 15 15 15 15 15 15 15];\r\nassert(isequal(your_fcn_name(x),y_correct))\r\n","published":true,"deleted":false,"likes_count":136,"comments_count":29,"created_by":3668,"edited_by":223089,"edited_at":"2024-07-03T14:23:36.000Z","deleted_by":null,"deleted_at":null,"solvers_count":14110,"test_suite_updated_at":"2024-07-03T14:23:36.000Z","rescore_all_solutions":false,"group_id":13,"created_at":"2012-11-15T03:31:29.000Z","updated_at":"2026-06-11T16:46:54.000Z","published_at":"2012-11-15T03:33:41.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGenerate a vector like 1,2,2,3,3,3,4,4,4,4\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eSo if n = 3, then return\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ [1 2 2 3 3 3]]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eAnd if n = 5, then return\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ [1 2 2 3 3 3 4 4 4 4 5 5 5 5 5]]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":12,"title":"Fibonacci sequence","description":"Calculate the nth Fibonacci number.\r\nGiven n, return f where f = fib(n) and f(1) = 1, f(2) = 1, f(3) = 2, ...\r\nExamples:\r\n Input  n = 5\r\n Output f is 5\r\n\r\n Input  n = 7\r\n Output f is 13","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 181px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 468.5px 90.5px; transform-origin: 468.5px 90.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 10.5px; text-align: left; transform-origin: 444.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 111.642px 8px; transform-origin: 111.642px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eCalculate the nth Fibonacci number.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 10.5px; text-align: left; transform-origin: 444.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 199.117px 8px; transform-origin: 199.117px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eGiven n, return f where f = fib(n) and f(1) = 1, f(2) = 1, f(3) = 2, ...\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 444.5px 10.5px; text-align: left; transform-origin: 444.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 32.675px 8px; transform-origin: 32.675px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eExamples:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 90px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 464.5px 45px; transform-origin: 464.5px 45px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 18px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; line-height: 18px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 464.5px 9px; text-wrap-mode: nowrap; transform-origin: 464.5px 9px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(33, 33, 33); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(33, 33, 33); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(33, 33, 33); border-left-style: none; border-left-width: 0px; border-right-color: rgb(33, 33, 33); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 50.05px 8.5px; tab-size: 4; transform-origin: 50.05px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 30.8px 8.5px; transform-origin: 30.8px 8.5px; \"\u003e Input  \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(133, 22, 209); border-block-start-color: rgb(133, 22, 209); border-bottom-color: rgb(133, 22, 209); border-inline-end-color: rgb(133, 22, 209); border-inline-start-color: rgb(133, 22, 209); border-left-color: rgb(133, 22, 209); border-right-color: rgb(133, 22, 209); border-top-color: rgb(133, 22, 209); caret-color: rgb(133, 22, 209); color: rgb(133, 22, 209); column-rule-color: rgb(133, 22, 209); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(133, 22, 209); perspective-origin: 19.25px 8.5px; text-decoration-color: rgb(133, 22, 209); text-emphasis-color: rgb(133, 22, 209); transform-origin: 19.25px 8.5px; \"\u003en = 5\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 18px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; line-height: 18px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 464.5px 9px; text-wrap-mode: nowrap; transform-origin: 464.5px 9px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(33, 33, 33); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(33, 33, 33); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(33, 33, 33); border-left-style: none; border-left-width: 0px; border-right-color: rgb(33, 33, 33); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 53.9px 8.5px; tab-size: 4; transform-origin: 53.9px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 30.8px 8.5px; transform-origin: 30.8px 8.5px; \"\u003e Output \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(133, 22, 209); border-block-start-color: rgb(133, 22, 209); border-bottom-color: rgb(133, 22, 209); border-inline-end-color: rgb(133, 22, 209); border-inline-start-color: rgb(133, 22, 209); border-left-color: rgb(133, 22, 209); border-right-color: rgb(133, 22, 209); border-top-color: rgb(133, 22, 209); caret-color: rgb(133, 22, 209); color: rgb(133, 22, 209); column-rule-color: rgb(133, 22, 209); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(133, 22, 209); perspective-origin: 23.1px 8.5px; text-decoration-color: rgb(133, 22, 209); text-emphasis-color: rgb(133, 22, 209); transform-origin: 23.1px 8.5px; \"\u003ef is 5\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 18px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; line-height: 18px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 464.5px 9px; text-wrap-mode: nowrap; transform-origin: 464.5px 9px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(33, 33, 33); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(33, 33, 33); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(33, 33, 33); border-left-style: none; border-left-width: 0px; border-right-color: rgb(33, 33, 33); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 8.5px; tab-size: 4; transform-origin: 0px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 18px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; line-height: 18px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 464.5px 9px; text-wrap-mode: nowrap; transform-origin: 464.5px 9px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(33, 33, 33); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(33, 33, 33); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(33, 33, 33); border-left-style: none; border-left-width: 0px; border-right-color: rgb(33, 33, 33); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 50.05px 8.5px; tab-size: 4; transform-origin: 50.05px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 30.8px 8.5px; transform-origin: 30.8px 8.5px; \"\u003e Input  \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(133, 22, 209); border-block-start-color: rgb(133, 22, 209); border-bottom-color: rgb(133, 22, 209); border-inline-end-color: rgb(133, 22, 209); border-inline-start-color: rgb(133, 22, 209); border-left-color: rgb(133, 22, 209); border-right-color: rgb(133, 22, 209); border-top-color: rgb(133, 22, 209); caret-color: rgb(133, 22, 209); color: rgb(133, 22, 209); column-rule-color: rgb(133, 22, 209); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(133, 22, 209); perspective-origin: 19.25px 8.5px; text-decoration-color: rgb(133, 22, 209); text-emphasis-color: rgb(133, 22, 209); transform-origin: 19.25px 8.5px; \"\u003en = 7\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 18px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; line-height: 18px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 464.5px 9px; text-wrap-mode: nowrap; transform-origin: 464.5px 9px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(33, 33, 33); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(33, 33, 33); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(33, 33, 33); border-left-style: none; border-left-width: 0px; border-right-color: rgb(33, 33, 33); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 57.75px 8.5px; tab-size: 4; transform-origin: 57.75px 8.5px; unicode-bidi: normal; white-space-collapse: preserve; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 30.8px 8.5px; transform-origin: 30.8px 8.5px; \"\u003e Output \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(133, 22, 209); border-block-start-color: rgb(133, 22, 209); border-bottom-color: rgb(133, 22, 209); border-inline-end-color: rgb(133, 22, 209); border-inline-start-color: rgb(133, 22, 209); border-left-color: rgb(133, 22, 209); border-right-color: rgb(133, 22, 209); border-top-color: rgb(133, 22, 209); caret-color: rgb(133, 22, 209); color: rgb(133, 22, 209); column-rule-color: rgb(133, 22, 209); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(133, 22, 209); perspective-origin: 26.95px 8.5px; text-decoration-color: rgb(133, 22, 209); text-emphasis-color: rgb(133, 22, 209); transform-origin: 26.95px 8.5px; \"\u003ef is 13\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function f = fib(n)\r\n  f = n;\r\nend","test_suite":"%%\r\nfiletext = fileread('fib.m');\r\nillegal = contains(filetext, 'regexp') || contains(filetext, 'assert') || ...\r\n          contains(filetext, 'switch') || contains(filetext, 'elseif') || ...\r\n          contains(filetext, '610')     || contains(filetext, '1597');\r\nassert(~illegal)\r\n\r\n%%\r\nn = 1;\r\nf = 1;\r\nassert(isequal(fib(n),f))\r\n\r\n%%\r\nn = 6;\r\nf = 8;\r\nassert(isequal(fib(n),f))\r\n\r\n%%\r\nn = 7;\r\nf = 13;\r\nassert(isequal(fib(n),f))\r\n\r\n%%\r\nn = 10;\r\nf = 55;\r\nassert(isequal(fib(n),f))\r\n\r\n%%\r\nn = 12;\r\nf = 144;\r\nassert(isequal(fib(n),f))\r\n\r\n%%\r\nn = 15;\r\nf = 610;\r\nassert(isequal(fib(n),f))\r\n\r\n%%\r\nn = 17;\r\nf = 1597;\r\nassert(isequal(fib(n),f))\r\n\r\n%%\r\nn = 20;\r\nf = 6765;\r\nassert(isequal(fib(n),f))","published":true,"deleted":false,"likes_count":109,"comments_count":25,"created_by":1,"edited_by":223089,"edited_at":"2026-02-05T13:22:21.000Z","deleted_by":null,"deleted_at":null,"solvers_count":14263,"test_suite_updated_at":"2026-02-05T13:22:22.000Z","rescore_all_solutions":false,"group_id":2,"created_at":"2012-01-18T01:00:18.000Z","updated_at":"2026-06-12T07:15:24.000Z","published_at":"2012-01-18T01:00:18.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eCalculate the nth Fibonacci number.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven n, return f where f = fib(n) and f(1) = 1, f(2) = 1, f(3) = 2, ...\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eExamples:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ Input  n = 5\\n Output f is 5\\n\\n Input  n = 7\\n Output f is 13]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":56288,"title":"Angle Between Analog Clock Hands","description":"Given a datetime variable t, return the angle (in degrees) between the hour and minute hands of an analog clock at the time represented by t.\r\n\r\nThe angle returned should be the smaller of the two angles between the hands (ie it should always be in the range [0,180]).\r\nAssume the hands are moving continuously (so at 03:30:00, the hour hand will be halfway between 3 and 4; at 03:26:30, the minute hand will be halfway between 26 and 27, etc).\r\nThe time may be am or pm; the angle returned should be assuming a standard 12-hour clock (so 03:26:30 and 15:26:30 will return the same angle).","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.440000534057617px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 441px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003eGiven a datetime variable \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003et\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e, return the angle (in degrees) between the hour and minute hands of an analog clock at the time represented by \u003c/span\u003e\u003c/span\u003e\u003cspan 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\" data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003cul style=\"block-size: 120px; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 40px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; text-align: left; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; \"\u003e\u003cspan style=\"\"\u003eThe angle returned should be the smaller of the two angles between the hands (ie it should always be in the range [0,180]).\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 40px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; text-align: left; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; \"\u003e\u003cspan style=\"\"\u003eAssume the hands are moving continuously (so at 03:30:00, the hour hand will be halfway between 3 and 4; at 03:26:30, the minute hand will be halfway between 26 and 27, etc).\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 40px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; text-align: left; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; \"\u003e\u003cspan style=\"\"\u003eThe time may be am or pm; the angle returned should be assuming a standard 12-hour clock (so 03:26:30 and 15:26:30 will return the same angle).\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function angle = clockHands(time)\r\nangle = time;\r\nend","test_suite":"%% Some obvious times/angles\r\nassert(isequal(clockHands(datetime(\"12:00:00\")),0))\r\nassert(isequal(clockHands(datetime(\"3:00:00\")),90))\r\nassert(isequal(clockHands(datetime(\"6:00:00\")),180))\r\nassert(isequal(clockHands(datetime(\"9:00:00\")),90))\r\n%% A bunch of random times\r\nt = datetime(2022,10,12,13,55,22);\r\nassert( abs(clockHands(t) - 85.4833) \u003c 0.01 )\r\nt = datetime(2022,10,12,16,27,59);\r\nassert( abs(clockHands(t) - 33.9083) \u003c 0.01 )\r\nt = datetime(2022,10,12,23,48,14);\r\nassert( abs(clockHands(t) - 64.7167) \u003c 0.01 )\r\nt = datetime(2022,10,12,03,38,27);\r\nassert( abs(clockHands(t) - 121.475) \u003c 0.01 )\r\nt = datetime(2022,10,12,07,46,10);\r\nassert( abs(clockHands(t) - 43.9167) \u003c 0.01 )\r\nt = datetime(2022,10,12,02,50,24);\r\nassert( abs(clockHands(t) - 142.8) \u003c 0.01 )\r\nt = datetime(2022,10,12,02,15,06);\r\nassert( abs(clockHands(t) - 23.05) \u003c 0.01 )\r\nt = datetime(2022,10,12,13,53,32);\r\nassert( abs(clockHands(t) - 95.5667) \u003c 0.01 )\r\nt = datetime(2022,10,12,11,18,47);\r\nassert( abs(clockHands(t) - 133.3083) \u003c 0.01 )\r\nt = datetime(2022,10,12,21,27,08);\r\nassert( abs(clockHands(t) - 120.7667) \u003c 0.01 )\r\nt = datetime(2022,10,12,03,44,52);\r\nassert( abs(clockHands(t) - 156.7667) \u003c 0.01 )\r\nt = datetime(2022,10,12,01,51,15);\r\nassert( abs(clockHands(t) - 108.125) \u003c 0.01 )\r\nt = datetime(2022,10,12,07,55,05);\r\nassert( abs(clockHands(t) - 92.9583) \u003c 0.01 )\r\nt = datetime(2022,10,12,04,59,58);\r\nassert( abs(clockHands(t) - 150.1833) \u003c 0.01 )\r\nt = datetime(2022,10,12,05,04,53);\r\nassert( abs(clockHands(t) - 123.1417) \u003c 0.01 )\r\nt = datetime(2022,10,12,00,57,39);\r\nassert( abs(clockHands(t) - 42.925) \u003c 0.01 )\r\nt = datetime(2022,10,12,23,35,20);\r\nassert( abs(clockHands(t) - 135.6667) \u003c 0.01 )\r\nt = datetime(2022,10,12,05,09,41);\r\nassert( abs(clockHands(t) - 96.7417) \u003c 0.01 )\r\nt = datetime(2022,10,12,09,34,44);\r\nassert( abs(clockHands(t) - 78.9667) \u003c 0.01 )\r\nt = datetime(2022,10,12,01,28,44);\r\nassert( abs(clockHands(t) - 128.0333) \u003c 0.01 )\r\nt = datetime(2022,10,12,10,43,28);\r\nassert( abs(clockHands(t) - 60.9333) \u003c 0.01 )\r\nt = datetime(2022,10,12,17,45,44);\r\nassert( abs(clockHands(t) - 101.5333) \u003c 0.01 )\r\nt = datetime(2022,10,12,03,28,40);\r\nassert( abs(clockHands(t) - 67.6667) \u003c 0.01 )\r\nt = datetime(2022,10,12,12,16,53);\r\nassert( abs(clockHands(t) - 92.8583) \u003c 0.01 )\r\nt = datetime(2022,10,12,19,26,47);\r\nassert( abs(clockHands(t) - 62.6917) \u003c 0.01 )","published":true,"deleted":false,"likes_count":4,"comments_count":3,"created_by":287,"edited_by":26769,"edited_at":"2022-10-29T01:32:29.000Z","deleted_by":null,"deleted_at":null,"solvers_count":115,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2022-10-12T20:40:09.000Z","updated_at":"2026-05-24T21:08:55.000Z","published_at":"2022-10-24T13:18:57.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven a datetime variable \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003et\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, return the angle (in degrees) between the hour and minute hands of an analog clock at the time represented by \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003et\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"254\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"553\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe angle returned should be the smaller of the two angles between the hands (ie it should always be in the range [0,180]).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eAssume the hands are moving continuously (so at 03:30:00, the hour hand will be halfway between 3 and 4; at 03:26:30, the minute hand will be halfway between 26 and 27, etc).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe time may be am or pm; the angle returned should be assuming a standard 12-hour clock (so 03:26:30 and 15:26:30 will return the same 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\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":769,"title":"Calculate the area of a triangle between three points","description":"Calculate the area of a triangle between three points:\r\nP1(X1,Y1)\r\nP2(X2,Y2)\r\nP3(X3,Y3)\r\nthese three points are the vertices of the triangle.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 141px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 70.5px; transform-origin: 407px 70.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 167.5px 8px; transform-origin: 167.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eCalculate the area of a triangle between three points:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 32px 8px; transform-origin: 32px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eP1(X1,Y1)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 32px 8px; transform-origin: 32px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eP2(X2,Y2)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 32px 8px; transform-origin: 32px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eP3(X3,Y3)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 155.5px 8px; transform-origin: 155.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ethese three points are the vertices of the triangle.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"% X=[x1 x2 x3]\r\n% Y=[y1 y2 y3]\r\nfunction y = your_fcn_name(X,Y)\r\n  y = X.*Y;\r\nend","test_suite":"%%\r\nX=[1 0 0];\r\nY=[0 0 1];\r\ny_correct = 0.5;\r\nassert(abs(your_fcn_name(X,Y)-y_correct)\u003c1e-3)\r\n\r\n%%\r\nX=[1 1.5 2];\r\nY=[0 1 0];\r\ny_correct = 0.5;\r\nassert(abs(your_fcn_name(X,Y)-y_correct)\u003c1e-3)\r\n\r\n%%\r\nX=[2 3 1];\r\nY=[0 3 4];\r\ny_correct = 3.500;\r\nassert(abs(your_fcn_name(X,Y)-y_correct)\u003c1e-3)\r\n\r\n%%\r\nX=[10 12 -10];\r\nY=[-7 -3 -47];\r\ny_correct = 0;\r\nassert(abs(your_fcn_name(X,Y)-y_correct)\u003c1e-3)\r\n\r\n%%\r\nX=[0 5 0];\r\nY=[6 0 0];\r\ny_correct = 15;\r\nassert(abs(your_fcn_name(X,Y)-y_correct)\u003c1e-3)","published":true,"deleted":false,"likes_count":32,"comments_count":6,"created_by":4320,"edited_by":223089,"edited_at":"2023-02-02T09:07:51.000Z","deleted_by":null,"deleted_at":null,"solvers_count":3520,"test_suite_updated_at":"2023-02-02T09:07:51.000Z","rescore_all_solutions":false,"group_id":17,"created_at":"2012-06-15T14:26:12.000Z","updated_at":"2026-06-11T09:35:59.000Z","published_at":"2012-06-15T14:26:12.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eCalculate the area of a triangle between three points:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eP1(X1,Y1)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eP2(X2,Y2)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eP3(X3,Y3)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ethese three points are the vertices of the triangle.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":558,"title":"Is the Point in a Triangle?","description":"Check whether a point or multiple points is/are in a triangle with three corners\r\n Points = [x, y]; \r\n Triangle = [x1, y1; x2, y2; x3, y3]\r\nReturn true or false for each point tested.\r\n For example,\r\n input: Points = [0, 0.5]; Triangle = [0, 0; 1, 0; 1, 1]\r\n output: y = 0;","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 174.167px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 406.5px 87.0833px; transform-origin: 406.5px 87.0833px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.5px 10.5px; text-align: left; transform-origin: 383.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 249.017px 7.81667px; transform-origin: 249.017px 7.81667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eCheck whether a point or multiple points is/are in a triangle with three corners\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 40.8667px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 403.5px 20.4333px; transform-origin: 403.5px 20.4333px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1.11667px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1.11667px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1.11667px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1.11667px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 403.5px 10.2167px; text-wrap-mode: nowrap; transform-origin: 403.5px 10.2167px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 70.35px 8.375px; tab-size: 4; transform-origin: 70.35px 8.375px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e Points = [x, y]; \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1.11667px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1.11667px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1.11667px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1.11667px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 403.5px 10.2167px; text-wrap-mode: nowrap; transform-origin: 403.5px 10.2167px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 140.7px 8.375px; tab-size: 4; transform-origin: 140.7px 8.375px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e Triangle = [x1, y1; x2, y2; x3, y3]\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 10px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 10px; perspective-origin: 383.5px 10.5px; text-align: left; transform-origin: 383.5px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 131.767px 7.81667px; transform-origin: 131.767px 7.81667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eReturn true or false for each point tested.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 61.3px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 403.5px 30.65px; transform-origin: 403.5px 30.65px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1.11667px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1.11667px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1.11667px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1.11667px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 403.5px 10.2167px; text-wrap-mode: nowrap; transform-origin: 403.5px 10.2167px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 50.8083px 8.375px; tab-size: 4; transform-origin: 50.8083px 8.375px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 19.5417px 8.375px; transform-origin: 19.5417px 8.375px; \"\u003e For \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(170, 4, 249); border-block-start-color: rgb(170, 4, 249); border-bottom-color: rgb(170, 4, 249); border-inline-end-color: rgb(170, 4, 249); border-inline-start-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(170, 4, 249); perspective-origin: 27.3583px 8.375px; text-decoration-color: rgb(170, 4, 249); text-emphasis-color: rgb(170, 4, 249); transform-origin: 27.3583px 8.375px; \"\u003eexample\u003c/span\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 3.90833px 8.375px; transform-origin: 3.90833px 8.375px; \"\u003e,\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1.11667px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1.11667px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1.11667px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1.11667px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 403.5px 10.2167px; text-wrap-mode: nowrap; transform-origin: 403.5px 10.2167px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 218.867px 8.375px; tab-size: 4; transform-origin: 218.867px 8.375px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e input: Points = [0, 0.5]; Triangle = [0, 0; 1, 0; 1, 1]\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1.11667px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1.11667px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1.11667px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1.11667px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 403.5px 10.2167px; text-wrap-mode: nowrap; transform-origin: 403.5px 10.2167px; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 58.625px 8.375px; tab-size: 4; transform-origin: 58.625px 8.375px; unicode-bidi: normal; white-space-collapse: preserve; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e output: y = 0;\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = your_fcn_name(Points, Triangle)\r\n  y = 0;\r\nend","test_suite":"%%\r\nTriangle = [0, 0; 1, 0; 1, 1]; Points = [0, 0.5]\r\ny_correct = 0;\r\nassert(isequal(your_fcn_name(Points,Triangle),y_correct))\r\n\r\n%%\r\nTriangle = [0, 0; 1, 0; 1, 1]; Points = [0.8, 0.5]\r\ny_correct = 1;\r\nassert(isequal(your_fcn_name(Points,Triangle),y_correct))\r\n\r\n%%\r\nTriangle = [0.8147, 0.9134; 0.9058, 0.6324; 0.1270, 0.0975]; \r\nPoints = [0.8, 0.7; 0.9, 0.4]\r\ny_correct = [1 0];\r\nassert(isequal(your_fcn_name(Points,Triangle),y_correct))\r\n\r\n%%\r\nr = randi(10);\r\nTriangle = [0 0; 0 r; r 0]; \r\nPoints = 2*r*[1 1];\r\ny_correct = [0];\r\nassert(isequal(your_fcn_name(Points,Triangle),y_correct))\r\n\r\n%%\r\nfiletext = fileread('your_fcn_name.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'regexp') || ...\r\n    contains(filetext, 'flip(');\r\nassert(~illegal)\r\n","published":true,"deleted":false,"likes_count":36,"comments_count":12,"created_by":2906,"edited_by":223089,"edited_at":"2024-06-30T15:42:06.000Z","deleted_by":null,"deleted_at":null,"solvers_count":1765,"test_suite_updated_at":"2024-06-30T15:42:06.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2012-04-04T08:27:00.000Z","updated_at":"2026-06-12T03:10:47.000Z","published_at":"2012-04-04T08:31:13.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eCheck whether a point or multiple points is/are in a triangle with three corners\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ Points = [x, y]; \\n Triangle = [x1, y1; x2, y2; x3, y3]]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eReturn true or false for each point tested.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ For example,\\n input: Points = [0, 0.5]; Triangle = [0, 0; 1, 0; 1, 1]\\n output: y = 0;]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":113,"title":"N-Queens Checker","description":"Picture a chessboard populated with a number of queens (i.e. pieces that can move like a queen in chess). The board is a matrix, a, filled mostly with zeros, while the queens are given as ones. Your job is to verify that the board is a legitimate answer to the \u003chttp://en.wikipedia.org/wiki/Eight_queens_puzzle N-Queens problem\u003e. The board is good only when no queen can \"see\" (and thus capture) another queen.\r\n\r\nExample\r\n\r\nThe matrix below shows two queens on a 3-by-3 chessboard. The queens can't see each other, so the function should return TRUE.\r\n\r\n 1 0 0\r\n 0 0 1\r\n 0 0 0\r\n\r\nHere is a bigger board with more queens. Since the queens on rows 3 and 4 are adjacent along a diagonal, they can see each other and the function should return FALSE.\r\n\r\n 0 0 0 1\r\n 1 0 0 0\r\n 0 0 1 0 \r\n 0 1 0 0\r\n\r\nThe board doesn't have to be square, but it always has 2 or more rows and 2 or more columns. This matrix returns FALSE.\r\n\r\n 1 0 0 0 0 \r\n 0 0 0 1 1\r\n","description_html":"\u003cp\u003ePicture a chessboard populated with a number of queens (i.e. pieces that can move like a queen in chess). The board is a matrix, a, filled mostly with zeros, while the queens are given as ones. Your job is to verify that the board is a legitimate answer to the \u003ca href=\"http://en.wikipedia.org/wiki/Eight_queens_puzzle\"\u003eN-Queens problem\u003c/a\u003e. The board is good only when no queen can \"see\" (and thus capture) another queen.\u003c/p\u003e\u003cp\u003eExample\u003c/p\u003e\u003cp\u003eThe matrix below shows two queens on a 3-by-3 chessboard. The queens can't see each other, so the function should return TRUE.\u003c/p\u003e\u003cpre\u003e 1 0 0\r\n 0 0 1\r\n 0 0 0\u003c/pre\u003e\u003cp\u003eHere is a bigger board with more queens. Since the queens on rows 3 and 4 are adjacent along a diagonal, they can see each other and the function should return FALSE.\u003c/p\u003e\u003cpre\u003e 0 0 0 1\r\n 1 0 0 0\r\n 0 0 1 0 \r\n 0 1 0 0\u003c/pre\u003e\u003cp\u003eThe board doesn't have to be square, but it always has 2 or more rows and 2 or more columns. This matrix returns FALSE.\u003c/p\u003e\u003cpre\u003e 1 0 0 0 0 \r\n 0 0 0 1 1\u003c/pre\u003e","function_template":"function tf = queens(a)\r\n  tf = true;\r\nend","test_suite":"%%\r\n\r\na = [1 0 0; 0 0 1; 0 0 0];\r\ntf_correct = true;\r\nassert(isequal(queens(a),tf_correct))\r\n\r\n%%\r\n\r\na = [0 0 0 1; 1 0 0 0; 0 0 1 0; 0 1 0 0];\r\ntf_correct = false;\r\nassert(isequal(queens(a),tf_correct))\r\n\r\n%%\r\n\r\na = [1 0 0 0 0; 0 0 0 1 1];\r\ntf_correct = false;\r\nassert(isequal(queens(a),tf_correct))\r\n\r\n\r\n%%\r\n\r\na = [ ...\r\n  0 0 1 0 0 0 0 0; 0 0 0 0 0 0 1 0; 0 1 0 0 0 0 0 0; 0 0 0 0 0 0 0 1;\r\n  0 0 0 0 0 1 0 0; 0 0 0 1 0 0 0 0; 1 0 0 0 0 0 0 0; 0 0 0 0 1 0 0 0];\r\ntf_correct = true;\r\nassert(isequal(queens(a),tf_correct))\r\n\r\n%%\r\n\r\na = ones(15,7);\r\ntf_correct = false;\r\nassert(isequal(queens(a),tf_correct))\r\n\r\n%%\r\n\r\na = zeros(20,23);\r\na(1,22) = 1;\r\na(2,23) = 1;\r\ntf_correct = false;\r\nassert(isequal(queens(a),tf_correct))\r\n\r\n%%\r\n\r\na = [1 0; 0 1];\r\ntf_correct = false;\r\nassert(isequal(queens(a),tf_correct))\r\n\r\n%%\r\n\r\na = [1 0 1; 0 0 0; 0 1 0];\r\ntf_correct = false;\r\nassert(isequal(queens(a),tf_correct))\r\n","published":true,"deleted":false,"likes_count":4,"comments_count":0,"created_by":7,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":313,"test_suite_updated_at":"2017-03-15T16:59:10.000Z","rescore_all_solutions":true,"group_id":1,"created_at":"2012-01-26T20:33:45.000Z","updated_at":"2026-04-26T00:45:54.000Z","published_at":"2012-01-30T15:34:35.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ePicture a chessboard populated with a number of queens (i.e. pieces that can move like a queen in chess). The board is a matrix, a, filled mostly with zeros, while the queens are given as ones. Your job is to verify that the board is a legitimate answer to the\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://en.wikipedia.org/wiki/Eight_queens_puzzle\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eN-Queens problem\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e. The board is good only when no queen can \\\"see\\\" (and thus capture) another queen.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eExample\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe matrix below shows two queens on a 3-by-3 chessboard. The queens can't see each other, so the function should return TRUE.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ 1 0 0\\n 0 0 1\\n 0 0 0]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eHere is a bigger board with more queens. Since the queens on rows 3 and 4 are adjacent along a diagonal, they can see each other and the function should return FALSE.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ 0 0 0 1\\n 1 0 0 0\\n 0 0 1 0 \\n 0 1 0 0]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe board doesn't have to be square, but it always has 2 or more rows and 2 or more columns. This matrix returns FALSE.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ 1 0 0 0 0 \\n 0 0 0 1 1]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":44951,"title":"Verify Law of Large Numbers","description":"If a large number of fair N-sided dice are rolled, the average of the simulated rolls is likely to be close to the mean of 1,2,...N i.e. the expected value of one die. For example, the expected value of a 6-sided die is 3.5.\r\nGiven N, simulate 1e8 N-sided dice rolls by creating a vector of 1e8 uniformly distributed random integers. Return the difference between the mean of this vector and the mean of integers from 1 to N.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 94.5px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 47.25px; transform-origin: 407px 47.25px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 42.5px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21.25px; text-align: left; transform-origin: 384px 21.25px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 366px 8px; transform-origin: 366px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eIf a large number of fair N-sided dice are rolled, the average of the simulated rolls is likely to be close to the mean of 1,2,...N i.e. the expected value of one die. For example, the expected value of a 6-sided die is\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 12px 8px; transform-origin: 12px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; perspective-origin: 12px 8.5px; transform-origin: 12px 8.5px; \"\u003e3.5\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 43px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21.5px; text-align: left; transform-origin: 384px 21.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 18.5px 8px; transform-origin: 18.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eGiven\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 4px 8px; transform-origin: 4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; perspective-origin: 4px 8.5px; transform-origin: 4px 8.5px; \"\u003eN\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 30px 8px; transform-origin: 30px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, simulate\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 12px 8px; transform-origin: 12px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; perspective-origin: 12px 8.5px; transform-origin: 12px 8.5px; \"\u003e1e8\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 128.5px 8px; transform-origin: 128.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e N-sided dice rolls by creating a vector of\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 12px 8px; transform-origin: 12px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; perspective-origin: 12px 8.5px; transform-origin: 12px 8.5px; \"\u003e1e8\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 158.5px 8px; transform-origin: 158.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e uniformly distributed random integers. Return the difference between the mean of this vector and the mean of integers from\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 4px 8px; transform-origin: 4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; perspective-origin: 4px 8.5px; transform-origin: 4px 8.5px; \"\u003e1\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 8px 8px; transform-origin: 8px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e to\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 4px 8px; transform-origin: 4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; perspective-origin: 4px 8.5px; transform-origin: 4px 8.5px; \"\u003eN\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function dice_diff = loln(N)\r\n  \r\ndice_diff = N;\r\nend","test_suite":"%%\r\nfiletext = fileread('loln.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'regexp'); \r\nassert(~illegal)\r\n%%\r\nN = 6;\r\nrng(7);\r\nassert((round(abs(loln(N)),7) == 7.2900e-05))\r\n%%\r\nN = 10;\r\nrng(1000);\r\nassert((round(abs(loln(N)),7)  == 8.7600e-05))\r\n%%\r\nN = 11;\r\nrng(5);\r\nassert(abs(loln(N))\u003c2e-4)\r\n%%\r\nN = 12;\r\nrng(2);\r\nassert(abs(loln(N))\u003c9e-4)\r\n%%\r\nN = 19;\r\nrng(4);\r\nassert(abs(loln(N))\u003c9e-4)\r\n%%\r\nN = 10;\r\nrng(4);\r\nassert(abs(loln(N))\u003c9e-4)\r\n%%\r\nN = 11;\r\nrng(8);\r\nassert(abs(loln(N))\u003e2e-4)","published":true,"deleted":false,"likes_count":171,"comments_count":29,"created_by":162851,"edited_by":223089,"edited_at":"2023-02-03T09:40:38.000Z","deleted_by":null,"deleted_at":null,"solvers_count":12883,"test_suite_updated_at":"2023-02-03T09:40:38.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2019-08-19T16:48:50.000Z","updated_at":"2026-06-12T09:34:24.000Z","published_at":"2019-09-09T19:54:15.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIf a large number of fair N-sided dice are rolled, the average of the simulated rolls is likely to be close to the mean of 1,2,...N i.e. the expected value of one die. For example, the expected value of a 6-sided die is\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e3.5\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eN\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, simulate\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e1e8\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e N-sided dice rolls by creating a vector of\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e1e8\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e uniformly distributed random integers. Return the difference between the mean of this vector and the mean of integers from\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e1\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e to\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eN\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":18,"title":"Bullseye Matrix","description":"Given n (always odd), return output a that has concentric rings of the numbers 1 through (n+1)/2 around the center point. Examples:\r\n Input  n = 3\r\n Output a is [ 2 2 2 \r\n               2 1 2\r\n               2 2 2 ]\r\n\r\n Input  n = 5\r\n Output a is [ 3 3 3 3 3\r\n               3 2 2 2 3 \r\n               3 2 1 2 3\r\n               3 2 2 2 3 \r\n               3 3 3 3 3 ]","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 276.767px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 138.383px; transform-origin: 407px 138.383px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 384px 8px; transform-origin: 384px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eGiven n (always odd), return output a that has concentric rings of the numbers 1 through (n+1)/2 around the center point. Examples:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 224.767px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 404px 112.383px; transform-origin: 404px 112.383px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 52px 8.5px; tab-size: 4; transform-origin: 52px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 32px 8.5px; transform-origin: 32px 8.5px; \"\u003e Input  \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(170, 4, 249); border-block-start-color: rgb(170, 4, 249); border-bottom-color: rgb(170, 4, 249); border-inline-end-color: rgb(170, 4, 249); border-inline-start-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(170, 4, 249); perspective-origin: 20px 8.5px; text-decoration-color: rgb(170, 4, 249); text-emphasis-color: rgb(170, 4, 249); transform-origin: 20px 8.5px; \"\u003en = 3\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 84px 8.5px; tab-size: 4; transform-origin: 84px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 32px 8.5px; transform-origin: 32px 8.5px; \"\u003e Output \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(170, 4, 249); border-block-start-color: rgb(170, 4, 249); border-bottom-color: rgb(170, 4, 249); border-inline-end-color: rgb(170, 4, 249); border-inline-start-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(170, 4, 249); perspective-origin: 52px 8.5px; text-decoration-color: rgb(170, 4, 249); text-emphasis-color: rgb(170, 4, 249); transform-origin: 52px 8.5px; \"\u003ea is [ 2 2 2 \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 80px 8.5px; tab-size: 4; transform-origin: 80px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e               2 1 2\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 88px 8.5px; tab-size: 4; transform-origin: 88px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e               2 2 2 ]\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 8.5px; tab-size: 4; transform-origin: 0px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 52px 8.5px; tab-size: 4; transform-origin: 52px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 32px 8.5px; transform-origin: 32px 8.5px; \"\u003e Input  \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(170, 4, 249); border-block-start-color: rgb(170, 4, 249); border-bottom-color: rgb(170, 4, 249); border-inline-end-color: rgb(170, 4, 249); border-inline-start-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(170, 4, 249); perspective-origin: 20px 8.5px; text-decoration-color: rgb(170, 4, 249); text-emphasis-color: rgb(170, 4, 249); transform-origin: 20px 8.5px; \"\u003en = 5\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 96px 8.5px; tab-size: 4; transform-origin: 96px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 32px 8.5px; transform-origin: 32px 8.5px; \"\u003e Output \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(170, 4, 249); border-block-start-color: rgb(170, 4, 249); border-bottom-color: rgb(170, 4, 249); border-inline-end-color: rgb(170, 4, 249); border-inline-start-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(170, 4, 249); perspective-origin: 64px 8.5px; text-decoration-color: rgb(170, 4, 249); text-emphasis-color: rgb(170, 4, 249); transform-origin: 64px 8.5px; \"\u003ea is [ 3 3 3 3 3\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 100px 8.5px; tab-size: 4; transform-origin: 100px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e               3 2 2 2 3 \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 96px 8.5px; tab-size: 4; transform-origin: 96px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e               3 2 1 2 3\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 100px 8.5px; tab-size: 4; transform-origin: 100px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e               3 2 2 2 3 \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 104px 8.5px; tab-size: 4; transform-origin: 104px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e               3 3 3 3 3 ]\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function a = bullseye(n)\r\n  a = 1;\r\nend","test_suite":"%%\r\nfiletext = fileread('bullseye.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'regexp'); \r\nassert(~illegal)\r\n\r\n%%\r\nn = 3;\r\na = [2 2 2; \r\n     2 1 2; \r\n     2 2 2]; \r\nassert(isequal(bullseye(n),a));\r\n\r\n%%\r\nn = 5;\r\na = [3 3 3 3 3; \r\n     3 2 2 2 3; \r\n     3 2 1 2 3; \r\n     3 2 2 2 3; \r\n     3 3 3 3 3]; \r\nassert(isequal(bullseye(n),a));\r\n\r\n%%\r\nn = 7;\r\na = [4 4 4 4 4 4 4;\r\n     4 3 3 3 3 3 4;\r\n     4 3 2 2 2 3 4;\r\n     4 3 2 1 2 3 4;\r\n     4 3 2 2 2 3 4;\r\n     4 3 3 3 3 3 4; \r\n     4 4 4 4 4 4 4];\r\nassert(isequal(bullseye(n),a))\r\n\r\n%%\r\nn = 9;\r\na = [ 5     5     5     5     5     5     5     5     5\r\n     5     4     4     4     4     4     4     4     5\r\n     5     4     3     3     3     3     3     4     5\r\n     5     4     3     2     2     2     3     4     5\r\n     5     4     3     2     1     2     3     4     5\r\n     5     4     3     2     2     2     3     4     5\r\n     5     4     3     3     3     3     3     4     5\r\n     5     4     4     4     4     4     4     4     5\r\n     5     5     5     5     5     5     5     5     5];\r\nassert(isequal(bullseye(n),a))","published":true,"deleted":false,"likes_count":99,"comments_count":35,"created_by":1,"edited_by":223089,"edited_at":"2023-07-07T08:26:28.000Z","deleted_by":null,"deleted_at":null,"solvers_count":6098,"test_suite_updated_at":"2023-07-07T08:26:28.000Z","rescore_all_solutions":false,"group_id":2,"created_at":"2012-01-18T01:00:19.000Z","updated_at":"2026-05-27T13:26:09.000Z","published_at":"2012-01-18T01:00:19.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven n (always odd), return output a that has concentric rings of the numbers 1 through (n+1)/2 around the center point. Examples:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ Input  n = 3\\n Output a is [ 2 2 2 \\n               2 1 2\\n               2 2 2 ]\\n\\n Input  n = 5\\n Output a is [ 3 3 3 3 3\\n               3 2 2 2 3 \\n               3 2 1 2 3\\n               3 2 2 2 3 \\n               3 3 3 3 3 ]]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":63,"title":"Encode Roman Numerals","description":"Create a function taking a non-negative integer as its parameter and returning a string containing the Roman Numeral representation of that integer.\r\nBy convention, \"modern\" Roman numerals are written by expressing each digit separately starting with the leftmost digit and skipping any digit with a value of zero.\r\nExamples\r\nIf n is 1990 then romStr = 'MCMXC' since 1000=M, 900=CM, 90=XC.\r\nIf n is 2008 then romStr = 'MMVIII' since 2000=MM, 8=VIII.\r\nIf n is 1666 then romStr = 'MDCLXVI'.\r\nIf n is 0 then romStr is empty ([] and '' are both acceptable)\r\nn will always be an integer between 0 and 3999 (inclusive).\r\nThis problem is adapted from Rosetta Code.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 285.733px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 142.867px; transform-origin: 407px 142.867px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 373px 8px; transform-origin: 373px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eCreate a function taking a non-negative integer as its parameter and returning a string containing the Roman Numeral representation of that integer.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 376px 8px; transform-origin: 376px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eBy convention, \"modern\" Roman numerals are written by expressing each digit separately starting with the leftmost digit and skipping any digit with a value of zero.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 30px 8px; transform-origin: 30px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eExamples\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 81.7333px; counter-reset: list-item 0; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; perspective-origin: 391px 40.8667px; transform-origin: 391px 40.8667px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2167px; text-align: left; transform-origin: 363px 10.2167px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 213px 8px; transform-origin: 213px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eIf n is 1990 then romStr = 'MCMXC' since 1000=M, 900=CM, 90=XC.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2167px; text-align: left; transform-origin: 363px 10.2167px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 179px 8px; transform-origin: 179px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eIf n is 2008 then romStr = 'MMVIII' since 2000=MM, 8=VIII.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2167px; text-align: left; transform-origin: 363px 10.2167px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 116px 8px; transform-origin: 116px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eIf n is 1666 then romStr = 'MDCLXVI'.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2167px; text-align: left; transform-origin: 363px 10.2167px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 184.5px 8px; transform-origin: 184.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eIf n is 0 then romStr is empty ([] and '' are both acceptable)\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 184.5px 8px; transform-origin: 184.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003en will always be an integer between 0 and 3999 (inclusive).\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 92px 8px; transform-origin: 92px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eThis problem is adapted from\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"/#null\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"font-style: italic; \"\u003eRosetta Code\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function romStr = dec2rom(n)\r\n  romStr = 'I';\r\nend","test_suite":"%%\r\nx = 1990;\r\ny_correct = 'MCMXC';\r\nassert(isequal(dec2rom(x),y_correct))\r\n\r\n%%\r\nx = 2008;\r\ny_correct = 'MMVIII';\r\nassert(isequal(dec2rom(x),y_correct))\r\n\r\n%%\r\nx = 1666;\r\ny_correct = 'MDCLXVI';\r\nassert(isequal(dec2rom(x),y_correct))\r\n\r\n%%\r\nx = 444;\r\ny_correct = 'CDXLIV';\r\nassert(isequal(dec2rom(x),y_correct))\r\n\r\n%%\r\nx = 199;\r\ny_correct = 'CXCIX';\r\nassert(isequal(dec2rom(x),y_correct))\r\n\r\n%%\r\nx = 49;\r\ny_correct = 'XLIX';\r\nassert(isequal(dec2rom(x),y_correct))\r\n\r\n%%\r\nx = 14;\r\ny_correct = 'XIV';\r\nassert(isequal(dec2rom(x),y_correct))\r\n\r\n%%\r\nx = 0;\r\ny_correct = '';\r\nassert(isempty(dec2rom(x)))\r\n","published":true,"deleted":false,"likes_count":16,"comments_count":1,"created_by":1,"edited_by":223089,"edited_at":"2022-07-07T05:50:19.000Z","deleted_by":null,"deleted_at":null,"solvers_count":2012,"test_suite_updated_at":"2022-07-07T05:50:19.000Z","rescore_all_solutions":false,"group_id":2,"created_at":"2012-01-18T01:00:26.000Z","updated_at":"2026-05-05T20:58:36.000Z","published_at":"2012-01-18T01:00:26.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eCreate a function taking a non-negative integer as its parameter and returning a string containing the Roman Numeral representation of that integer.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eBy convention, \\\"modern\\\" Roman numerals are written by expressing each digit separately starting with the leftmost digit and skipping any digit with a value of zero.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eExamples\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIf n is 1990 then romStr = 'MCMXC' since 1000=M, 900=CM, 90=XC.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIf n is 2008 then romStr = 'MMVIII' since 2000=MM, 8=VIII.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIf n is 1666 then romStr = 'MDCLXVI'.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIf n is 0 then romStr is empty ([] and '' are both acceptable)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003en will always be an integer between 0 and 3999 (inclusive).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eThis problem is adapted from\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eRosetta Code\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":4,"title":"Make a checkerboard matrix","description":"Given an integer n, make an n-by-n matrix made up of alternating ones and zeros as shown below. The a(1,1) should be 1.\r\nExample:\r\n Input  n = 5\r\n Output a is [1 0 1 0 1\r\n              0 1 0 1 0\r\n              1 0 1 0 1\r\n              0 1 0 1 0 \r\n              1 0 1 0 1]","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 204.6px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 102.3px; transform-origin: 407px 102.3px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 379.5px 8px; transform-origin: 379.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eGiven an integer n, make an n-by-n matrix made up of alternating ones and zeros as shown below. The a(1,1) should be 1.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 28.5px 8px; transform-origin: 28.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eExample:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 122.6px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 404px 61.3px; transform-origin: 404px 61.3px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 52px 8.5px; tab-size: 4; transform-origin: 52px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 32px 8.5px; transform-origin: 32px 8.5px; \"\u003e Input  \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(170, 4, 249); border-block-start-color: rgb(170, 4, 249); border-bottom-color: rgb(170, 4, 249); border-inline-end-color: rgb(170, 4, 249); border-inline-start-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(170, 4, 249); perspective-origin: 20px 8.5px; text-decoration-color: rgb(170, 4, 249); text-emphasis-color: rgb(170, 4, 249); transform-origin: 20px 8.5px; \"\u003en = 5\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 92px 8.5px; tab-size: 4; transform-origin: 92px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 32px 8.5px; transform-origin: 32px 8.5px; \"\u003e Output \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(170, 4, 249); border-block-start-color: rgb(170, 4, 249); border-bottom-color: rgb(170, 4, 249); border-inline-end-color: rgb(170, 4, 249); border-inline-start-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(170, 4, 249); perspective-origin: 60px 8.5px; text-decoration-color: rgb(170, 4, 249); text-emphasis-color: rgb(170, 4, 249); transform-origin: 60px 8.5px; \"\u003ea is [1 0 1 0 1\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 92px 8.5px; tab-size: 4; transform-origin: 92px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e              0 1 0 1 0\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 92px 8.5px; tab-size: 4; transform-origin: 92px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e              1 0 1 0 1\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 96px 8.5px; tab-size: 4; transform-origin: 96px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e              0 1 0 1 0 \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 96px 8.5px; tab-size: 4; transform-origin: 96px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e              1 0 1 0 1]\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function a = checkerboard(n)\r\n  a = ones(n);\r\nend","test_suite":"%%\r\nfiletext = fileread('checkerboard.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'regexp'); \r\nassert(~illegal)\r\n\r\n%%\r\nn = 1;\r\na = [1];\r\nassert(isequal(a,checkerboard(n)))\r\n\r\n%%\r\nn = 2;\r\na = eye(n);\r\nassert(isequal(a,checkerboard(n)))\r\n\r\n%%\r\nn = 3;\r\na = eye(n);\r\na = a | flip(a);\r\nassert(isequal(a,checkerboard(n)))\r\n\r\n%%\r\nn = 5;\r\na = [1 0 1 0 1;\r\n     0 1 0 1 0;\r\n     1 0 1 0 1;\r\n     0 1 0 1 0;\r\n     1 0 1 0 1];\r\nassert(isequal(a,checkerboard(n)))\r\n\r\n%%\r\nn = 16;\r\na = [1 0 1 0;\r\n     0 1 0 1;\r\n     1 0 1 0;\r\n     0 1 0 1];\r\na = repmat(a,4,4);\r\nassert(isequal(a,checkerboard(n)))\r\n\r\n%%\r\nn = 7;\r\na = [1     0     1     0     1     0     1\r\n     0     1     0     1     0     1     0\r\n     1     0     1     0     1     0     1\r\n     0     1     0     1     0     1     0\r\n     1     0     1     0     1     0     1\r\n     0     1     0     1     0     1     0\r\n     1     0     1     0     1     0     1];\r\nassert(isequal(a,checkerboard(n)))\r\n\r\n%%\r\nn = 22;\r\na = repmat(checkerboard(2),11,11);\r\na(2:end-1,2:end-1)=checkerboard(20);\r\nassert(isequal(a,checkerboard(n)))\r\n","published":true,"deleted":false,"likes_count":221,"comments_count":39,"created_by":1,"edited_by":223089,"edited_at":"2023-04-12T10:52:05.000Z","deleted_by":null,"deleted_at":null,"solvers_count":16206,"test_suite_updated_at":"2023-04-12T10:52:05.000Z","rescore_all_solutions":false,"group_id":2,"created_at":"2012-01-18T01:00:17.000Z","updated_at":"2026-06-08T09:22:11.000Z","published_at":"2012-01-18T01:00:17.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven an integer n, make an n-by-n matrix made up of alternating ones and zeros as shown below. The a(1,1) should be 1.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eExample:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ Input  n = 5\\n Output a is [1 0 1 0 1\\n              0 1 0 1 0\\n              1 0 1 0 1\\n              0 1 0 1 0 \\n              1 0 1 0 1]]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":21,"title":"Return the 3n+1 sequence for n","description":"A Collatz sequence is the sequence where, for a given number n, the next number in the sequence is either n/2 if the number is even or 3n+1 if the number is odd. The sequence always terminates with 1.\r\nSo if\r\n n = 13\r\nthen\r\n c = [13    40    20    10     5    16     8     4     2     1]","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 163.867px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 81.9333px; transform-origin: 407px 81.9333px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 369px 8px; transform-origin: 369px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eA Collatz sequence is the sequence where, for a given number n, the next number in the sequence is either n/2 if the number is even or 3n+1 if the number is odd. The sequence always terminates with 1.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 14px 8px; transform-origin: 14px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eSo if\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 20.4333px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 28px 8.5px; tab-size: 4; transform-origin: 28px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e n = 13\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 10px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 10px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 14px 8px; transform-origin: 14px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ethen\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 20.4333px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 252px 8.5px; tab-size: 4; transform-origin: 252px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e c = [13    40    20    10     5    16     8     4     2     1]\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function c = collatz(n)\r\n  c = n;\r\nend","test_suite":"%%\r\nfiletext = fileread('collatz.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'regexp'); \r\nassert(~illegal)\r\n\r\n%%\r\nn = 1;\r\nc_correct = 1;\r\nassert(isequal(collatz(n),c_correct))\r\n\r\n%%\r\nn = 2;\r\nc_correct = [2 1];\r\nassert(isequal(collatz(n),c_correct))\r\n\r\n%%\r\nn = 5;\r\nc_correct = [5 16 8 4 2 1];\r\nassert(isequal(collatz(n),c_correct))\r\n\r\n%%\r\nn = 22;\r\nc_correct = [22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1];\r\nassert(isequal(collatz(n),c_correct))\r\n\r\n%%\r\nn = 69;\r\nc_correct = [69 208 104 52 26 13 40 20 10 5 16 8 4 2 1];\r\nassert(isequal(collatz(n),c_correct))\r\n\r\n%%\r\nn = 2^randi(20);\r\ntemp = log2(n);\r\nc_correct = 2.^(temp:-1:0);\r\nassert(isequal(collatz(n),c_correct))\r\n\r\n%%\r\nn = 420;\r\nc_correct = [420, 210, 105, 316, 158, 79, 238, 119, 358, 179, 538, 269, 808, 404, 202, 101, 304, 152, 76, 38, 19, 58, 29, 88, 44, 22, 11, 34, 17, 52, 26, 13, 40, 20, 10, 5, 16, 8, 4, 2, 1];\r\nassert(isequal(collatz(n),c_correct))","published":true,"deleted":false,"likes_count":82,"comments_count":6,"created_by":1,"edited_by":223089,"edited_at":"2023-06-23T09:31:11.000Z","deleted_by":null,"deleted_at":null,"solvers_count":8511,"test_suite_updated_at":"2023-06-23T09:31:11.000Z","rescore_all_solutions":false,"group_id":2,"created_at":"2012-01-18T01:00:19.000Z","updated_at":"2026-06-08T04:44:20.000Z","published_at":"2012-01-18T01:00:19.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA Collatz sequence is the sequence where, for a given number n, the next number in the sequence is either n/2 if the number is even or 3n+1 if the number is odd. The sequence always terminates with 1.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eSo if\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ n = 13]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ethen\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ c = [13    40    20    10     5    16     8     4     2     1]]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":52,"title":"What is the next step in Conway's Life?","description":"Given a matrix A that represents the state of Conway's game of Life at one instant (time t=n), return the matrix B that represents the state of the game at the next instant (time t=n+1).\r\nAssume a toroidal game board, so the edges of the matrix wrap left to right and top to bottom.\r\nExamples:\r\n Input  A = [ 1   1   0   0\r\n              0   1   0   0\r\n              1   1   0   0\r\n              0   0   0   0 ]\r\n\r\n Output B = [ 1   1   0   0\r\n              0   0   1   0\r\n              1   1   0   0\r\n              0   0   0   0 ]\r\n\r\n Input  A = [ 0   1   1   0\r\n              1   1   1   0\r\n              0   0   1   0\r\n              0   0   0   0 ]\r\n\r\n Output B = [ 1   0   1   1\r\n              1   0   0   0\r\n              0   0   1   1\r\n              0   1   1   0 ]","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 500.233px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 250.117px; transform-origin: 407px 250.117px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 139px 8px; transform-origin: 139px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eGiven a matrix A that represents the state of\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://conwaylife.com/wiki/Conway%27s_Game_of_Life\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eConway's game of Life\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 155px 8px; transform-origin: 155px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e at one instant (time t=n), return the matrix B that represents the state of the game at the next instant (time t=n+1).\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 294px 8px; transform-origin: 294px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eAssume a toroidal game board, so the edges of the matrix wrap left to right and top to bottom.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 32px 8px; transform-origin: 32px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eExamples:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 388.233px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 404px 194.117px; transform-origin: 404px 194.117px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 108px 8.5px; tab-size: 4; transform-origin: 108px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 32px 8.5px; transform-origin: 32px 8.5px; \"\u003e Input  \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(170, 4, 249); border-block-start-color: rgb(170, 4, 249); border-bottom-color: rgb(170, 4, 249); border-inline-end-color: rgb(170, 4, 249); border-inline-start-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(170, 4, 249); perspective-origin: 76px 8.5px; text-decoration-color: rgb(170, 4, 249); text-emphasis-color: rgb(170, 4, 249); transform-origin: 76px 8.5px; \"\u003eA = [ 1   1   0   0\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 108px 8.5px; tab-size: 4; transform-origin: 108px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e              0   1   0   0\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 108px 8.5px; tab-size: 4; transform-origin: 108px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e              1   1   0   0\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 116px 8.5px; tab-size: 4; transform-origin: 116px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e              0   0   0   0 ]\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 8.5px; tab-size: 4; transform-origin: 0px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 108px 8.5px; tab-size: 4; transform-origin: 108px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 32px 8.5px; transform-origin: 32px 8.5px; \"\u003e Output \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(170, 4, 249); border-block-start-color: rgb(170, 4, 249); border-bottom-color: rgb(170, 4, 249); border-inline-end-color: rgb(170, 4, 249); border-inline-start-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(170, 4, 249); perspective-origin: 76px 8.5px; text-decoration-color: rgb(170, 4, 249); text-emphasis-color: rgb(170, 4, 249); transform-origin: 76px 8.5px; \"\u003eB = [ 1   1   0   0\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 108px 8.5px; tab-size: 4; transform-origin: 108px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e              0   0   1   0\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 108px 8.5px; tab-size: 4; transform-origin: 108px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e              1   1   0   0\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 116px 8.5px; tab-size: 4; transform-origin: 116px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e              0   0   0   0 ]\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 8.5px; tab-size: 4; transform-origin: 0px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 108px 8.5px; tab-size: 4; transform-origin: 108px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 32px 8.5px; transform-origin: 32px 8.5px; \"\u003e Input  \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(170, 4, 249); border-block-start-color: rgb(170, 4, 249); border-bottom-color: rgb(170, 4, 249); border-inline-end-color: rgb(170, 4, 249); border-inline-start-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(170, 4, 249); perspective-origin: 76px 8.5px; text-decoration-color: rgb(170, 4, 249); text-emphasis-color: rgb(170, 4, 249); transform-origin: 76px 8.5px; \"\u003eA = [ 0   1   1   0\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 108px 8.5px; tab-size: 4; transform-origin: 108px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e              1   1   1   0\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 108px 8.5px; tab-size: 4; transform-origin: 108px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e              0   0   1   0\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 116px 8.5px; tab-size: 4; transform-origin: 116px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e              0   0   0   0 ]\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 8.5px; tab-size: 4; transform-origin: 0px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 108px 8.5px; tab-size: 4; transform-origin: 108px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; perspective-origin: 32px 8.5px; transform-origin: 32px 8.5px; \"\u003e Output \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(170, 4, 249); border-block-start-color: rgb(170, 4, 249); border-bottom-color: rgb(170, 4, 249); border-inline-end-color: rgb(170, 4, 249); border-inline-start-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(170, 4, 249); perspective-origin: 76px 8.5px; text-decoration-color: rgb(170, 4, 249); text-emphasis-color: rgb(170, 4, 249); transform-origin: 76px 8.5px; \"\u003eB = [ 1   0   1   1\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 108px 8.5px; tab-size: 4; transform-origin: 108px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e              1   0   0   0\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 108px 8.5px; tab-size: 4; transform-origin: 108px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e              0   0   1   1\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 116px 8.5px; tab-size: 4; transform-origin: 116px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e              0   1   1   0 ]\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function B = gameOfLife(A)\r\n  B = A;\r\nend","test_suite":"%%\r\nA = [ ...\r\n 1     1     0     0\r\n 0     1     0     0\r\n 1     1     0     0\r\n 0     0     0     0];\r\n\r\nB = [ ...\r\n 1     1     0     0\r\n 0     0     1     0\r\n 1     1     0     0\r\n 0     0     0     0];\r\n\r\nassert(isequal(gameOfLife(A),B))\r\n\r\n%%\r\nA = [ ...\r\n 0     1     1     0\r\n 1     1     1     0\r\n 0     0     1     0\r\n 0     0     0     0];\r\n\r\nB = [ ...\r\n 1     0     1     1\r\n 1     0     0     0\r\n 0     0     1     1\r\n 0     1     1     0];\r\n\r\nassert(isequal(gameOfLife(A),B))\r\n\r\n%%\r\nA = zeros(4);\r\nassert(isequal(gameOfLife(A),A))\r\n\r\n%%\r\nA = ones(4);\r\nassert(isequal(gameOfLife(A),1-A))\r\n","published":true,"deleted":false,"likes_count":29,"comments_count":13,"created_by":1,"edited_by":223089,"edited_at":"2023-08-22T14:45:24.000Z","deleted_by":null,"deleted_at":null,"solvers_count":680,"test_suite_updated_at":"2022-10-16T10:41:00.000Z","rescore_all_solutions":false,"group_id":2,"created_at":"2012-01-18T01:00:24.000Z","updated_at":"2026-04-28T17:34:48.000Z","published_at":"2012-01-18T01:00:24.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven a matrix A that represents the state of\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://conwaylife.com/wiki/Conway%27s_Game_of_Life\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eConway's game of Life\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e at one instant (time t=n), return the matrix B that represents the state of the game at the next instant (time t=n+1).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eAssume a toroidal game board, so the edges of the matrix wrap left to right and top to bottom.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eExamples:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ Input  A = [ 1   1   0   0\\n              0   1   0   0\\n              1   1   0   0\\n              0   0   0   0 ]\\n\\n Output B = [ 1   1   0   0\\n              0   0   1   0\\n              1   1   0   0\\n              0   0   0   0 ]\\n\\n Input  A = [ 0   1   1   0\\n              1   1   1   0\\n              0   0   1   0\\n              0   0   0   0 ]\\n\\n Output B = [ 1   0   1   1\\n              1   0   0   0\\n              0   0   1   1\\n              0   1   1   0 ]]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":15,"title":"Find the longest sequence of 1's in a binary sequence.","description":"Given a string such as\n\n s = '011110010000000100010111'\n\nfind the length of the longest string of consecutive 1's. In this example, the answer would be 4.\n\nExample:\n\n Input  x = '110100111'\n Output y is 3","description_html":"\u003cp\u003eGiven a string such as\u003c/p\u003e\u003cpre\u003e s = '011110010000000100010111'\u003c/pre\u003e\u003cp\u003efind the length of the longest string of consecutive 1's. In this example, the answer would be 4.\u003c/p\u003e\u003cp\u003eExample:\u003c/p\u003e\u003cpre\u003e Input  x = '110100111'\n Output y is 3\u003c/pre\u003e","function_template":"function y = lengthOnes(x)\n  y = x\nend","test_suite":"%%\nx = '0';\ny_correct = 0;\nassert(isequal(lengthOnes(x),y_correct))\n\n%%\nx = '1';\ny_correct = 1;\nassert(isequal(lengthOnes(x),y_correct))\n\n%%\nx = '01';\ny_correct = 1;\nassert(isequal(lengthOnes(x),y_correct))\n\n%%\nx = '10';\ny_correct = 1;\nassert(isequal(lengthOnes(x),y_correct))\n\n%%\nx = '00';\ny_correct = 0;\nassert(isequal(lengthOnes(x),y_correct))\n\n%%\nx = '11';\n y_correct = 2;\nassert(isequal(lengthOnes(x),y_correct))\n%%\nx = '1111111111';\ny_correct = 10;\nassert(isequal(lengthOnes(x),y_correct))\n\n%%\nx = '100101011111010011111';\ny_correct = 5;\nassert(isequal(lengthOnes(x),y_correct))\n\n%%\nx = '01010101010101010101010101';\ny_correct = 1;\nassert(isequal(lengthOnes(x),y_correct))\n\n%%\nx = '0101010111000101110001011100010100001110110100000000110001001000001110001000111010101001101100001111';\ny_correct = 4;\nassert(isequal(lengthOnes(x),y_correct))","published":true,"deleted":false,"likes_count":81,"comments_count":10,"created_by":1,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":6805,"test_suite_updated_at":"2012-01-18T01:00:19.000Z","rescore_all_solutions":false,"group_id":2,"created_at":"2012-01-18T01:00:19.000Z","updated_at":"2026-06-12T05:46:18.000Z","published_at":"2012-01-18T01:00:19.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven a string such as\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ s = '011110010000000100010111']]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003efind the length of the longest string of consecutive 1's. In this example, the answer would be 4.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eExample:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ Input  x = '110100111'\\n Output y is 3]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":258,"title":"linear least squares fitting","description":"Inputs:\r\n\r\n* |f|: cell-array of function handles\r\n* |x|: column vector of |x| values\r\n* |y|: column vector of |y| values, same length as |x|\r\n\r\nOutput:\r\n\r\n* |a|: column vector of coefficients, same length as |f|\r\n\r\nIn a correct answer the coefficients |a| take values such that the function\r\n\r\n   fit = @(x) a(1)*f{1}(x) + a(2)*f{2}(x) + a(3)*f{3}(x) +...+ a(end)*f{end}(x)\r\n\r\nminimizes the sum of the squared deviations between |fit(x)| and |y|, i.e.\r\n    sum((fit(x)-y).^2)\r\nis minimal. \r\n\r\nRemarks:\r\n\r\n* The functions will all be vectorized, so e.g. |f{1}(x)| will return results for the whole vector x\r\n* The absolute errors of |a| must be smaller than 1e-6 to pass the tests","description_html":"\u003cp\u003eInputs:\u003c/p\u003e\u003cul\u003e\u003cli\u003e\u003ctt\u003ef\u003c/tt\u003e: cell-array of function handles\u003c/li\u003e\u003cli\u003e\u003ctt\u003ex\u003c/tt\u003e: column vector of \u003ctt\u003ex\u003c/tt\u003e values\u003c/li\u003e\u003cli\u003e\u003ctt\u003ey\u003c/tt\u003e: column vector of \u003ctt\u003ey\u003c/tt\u003e values, same length as \u003ctt\u003ex\u003c/tt\u003e\u003c/li\u003e\u003c/ul\u003e\u003cp\u003eOutput:\u003c/p\u003e\u003cul\u003e\u003cli\u003e\u003ctt\u003ea\u003c/tt\u003e: column vector of coefficients, same length as \u003ctt\u003ef\u003c/tt\u003e\u003c/li\u003e\u003c/ul\u003e\u003cp\u003eIn a correct answer the coefficients \u003ctt\u003ea\u003c/tt\u003e take values such that the function\u003c/p\u003e\u003cpre\u003e   fit = @(x) a(1)*f{1}(x) + a(2)*f{2}(x) + a(3)*f{3}(x) +...+ a(end)*f{end}(x)\u003c/pre\u003e\u003cp\u003eminimizes the sum of the squared deviations between \u003ctt\u003efit(x)\u003c/tt\u003e and \u003ctt\u003ey\u003c/tt\u003e, i.e.\r\n    sum((fit(x)-y).^2)\r\nis minimal.\u003c/p\u003e\u003cp\u003eRemarks:\u003c/p\u003e\u003cul\u003e\u003cli\u003eThe functions will all be vectorized, so e.g. \u003ctt\u003ef{1}(x)\u003c/tt\u003e will return results for the whole vector x\u003c/li\u003e\u003cli\u003eThe absolute errors of \u003ctt\u003ea\u003c/tt\u003e must be smaller than 1e-6 to pass the tests\u003c/li\u003e\u003c/ul\u003e","function_template":"function a = fit_coefficients(f,x,y)\r\n  a = zeros(length(f),1);\r\nend","test_suite":"%%% first test: fit to a constant\r\nx = [1,2,3,4]';\r\ny = rand(4,1);\r\nf{1} = @(x) ones(size(x));\r\naref=mean(y);\r\nassert(norm(fit_coefficients(f,x,y)-aref)\u003c1e-6)\r\n\r\n%%% second test: fit to a straight line (linear regression)\r\nx = [1,2,3,4,5]' + randn(5,1);\r\ny = [1,2,3,4,5]' + randn(5,1);\r\nf{1} = @(x) ones(size(x));\r\nf{2} = @(x) x;\r\naref(2) = sum((x-mean(x)).*(y-mean(y)))/sum((x-mean(x)).^2);\r\naref(1) = mean(y)-aref(2)*mean(x);\r\nassert(norm(fit_coefficients(f,x,y)-aref')\u003c1e-6)\r\n\r\n%%% third test: polynomial fit\r\nx = [1:15]' + randn(15,1);\r\ny = -10+0.2*x-0.5*x.^2+0.4*x.^3+0.001*log(abs(x)) + 0.2*randn(15,1);\r\nf{1} = @(x) ones(size(x));\r\nf{2} = @(x) x;\r\nf{3} = @(x) x.^2;\r\nf{4} = @(x) x.^3;\r\naref = fliplr(polyfit(x,y,3));\r\nassert(norm(fit_coefficients(f,x,y)-aref')\u003c1e-6)\r\n\r\n%%% fourth test: non-polynomial fit (yes, we are that crazy)\r\nx = [0:0.1:2*pi]';\r\ny = 0.123 + 0.456*sin(x).*exp(0.1*x);\r\nf{1} = @(x) ones(size(x));\r\nf{2} = @(x) sin(x).*exp(0.1*x);\r\naref=[0.123 0.456]';\r\nassert(norm(fit_coefficients(f,x,y)-aref)\u003c1e-6)","published":true,"deleted":false,"likes_count":5,"comments_count":6,"created_by":203,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":166,"test_suite_updated_at":"2013-01-10T10:23:17.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2012-02-04T19:59:00.000Z","updated_at":"2026-06-06T11:36:47.000Z","published_at":"2013-01-09T22:29:23.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eInputs:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ef\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e: cell-array of function handles\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ex\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e: column vector of\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ex\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e values\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ey\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e: column vector of\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ey\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e values, same length as\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ex\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eOutput:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ea\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e: column vector of coefficients, same length as\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ef\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIn a correct answer the coefficients\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ea\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e take values such that the function\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[   fit = @(x) a(1)*f{1}(x) + a(2)*f{2}(x) + a(3)*f{3}(x) +...+ a(end)*f{end}(x)]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eminimizes the sum of the squared deviations between\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003efit(x)\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e and\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ey\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, i.e. sum((fit(x)-y).^2) is minimal.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eRemarks:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe functions will all be vectorized, so e.g.\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ef{1}(x)\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e will return results for the whole vector x\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe absolute errors of\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ea\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e must be smaller than 1e-6 to pass the tests\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":78,"title":"Implement a ROT13 cipher","description":"Replace each character in string s1 with the character that is shifted 13 positions from it (wrap back to the beginning if necessary). So A ? N, B ? O, and so on until Y ? L and Z ? M. Case of the output should match the case of the input, so a ? n. Non-alphabetic characters are left in place and untouched.\n\nIf\n\n s1 = 'I love MATLAB'\n\nthen\n\n s2 = 'V ybir ZNGYNO'\n\nSee the \u003chttp://en.wikipedia.org/wiki/ROT13 Wikipedia article\u003e for more info.","description_html":"\u003cp\u003eReplace each character in string s1 with the character that is shifted 13 positions from it (wrap back to the beginning if necessary). So A ? N, B ? O, and so on until Y ? L and Z ? M. Case of the output should match the case of the input, so a ? n. Non-alphabetic characters are left in place and untouched.\u003c/p\u003e\u003cp\u003eIf\u003c/p\u003e\u003cpre\u003e s1 = 'I love MATLAB'\u003c/pre\u003e\u003cp\u003ethen\u003c/p\u003e\u003cpre\u003e s2 = 'V ybir ZNGYNO'\u003c/pre\u003e\u003cp\u003eSee the \u003ca href=\"http://en.wikipedia.org/wiki/ROT13\"\u003eWikipedia article\u003c/a\u003e for more info.\u003c/p\u003e","function_template":"function s2 = rot13(s1)\n  s2 = s1;\nend","test_suite":"%% Test #1\n\ns1 = 'I love MATLAB';\ns2_correct = 'V ybir ZNGYNO';\nassert(isequal(rot13(s1),s2_correct))\n\n%% Test #2\n\ns1 = 'I \u003c3 MATLAB!!';\ns2_correct = 'V \u003c3 ZNGYNO!!';\nassert(isequal(rot13(s1),s2_correct))\n\n%% Test #3\n\ns1 = 'The quick fox stumbled over the confusing instructions.';\ns2_correct = 'Gur dhvpx sbk fghzoyrq bire gur pbashfvat vafgehpgvbaf.';\nassert(isequal(rot13(s1),s2_correct))\n\n%% Test #4\n\ns1 = 'Snape kills Dumbledore on page 606. Also, there is no Santa.';\ns2_correct = 'Fancr xvyyf Qhzoyrqber ba cntr 606. Nyfb, gurer vf ab Fnagn.';\nassert(isequal(rot13(s1),s2_correct))\n\n","published":true,"deleted":false,"likes_count":13,"comments_count":3,"created_by":1,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":1717,"test_suite_updated_at":"2012-01-18T01:00:28.000Z","rescore_all_solutions":false,"group_id":2,"created_at":"2012-01-18T01:00:28.000Z","updated_at":"2026-05-06T03:27:30.000Z","published_at":"2012-01-18T01:00:28.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eReplace each character in string s1 with the character that is shifted 13 positions from it (wrap back to the beginning if necessary). So A ? N, B ? O, and so on until Y ? L and Z ? M. Case of the output should match the case of the input, so a ? n. Non-alphabetic characters are left in place and untouched.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIf\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ s1 = 'I love MATLAB']]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ethen\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ s2 = 'V ybir ZNGYNO']]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eSee the\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://en.wikipedia.org/wiki/ROT13\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eWikipedia article\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e for more info.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":81,"title":"Mandelbrot Numbers","description":"The \u003chttp://en.wikipedia.org/wiki/Mandelbrot_set Mandelbrot Set\u003e is built around a simple iterative equation.\r\n\r\n z(1)   = c\r\n z(n+1) = z(n)^2 + c\r\n\r\nFor any complex c, we can continue this iteration until either\r\nabs(z(n+1)) \u003e 2 or n == lim, then return the iteration count n.\r\n\r\n* If c = 0   and lim = 3, then z = [0 0 0] and n = 3.\r\n* If c = 1   and lim = 5, then z = [1 2], and n = length(z) or 2.\r\n* If c = 0.5 and lim = 5, then z = [0.5000 0.7500 1.0625 1.6289] and n = 4.\r\n\r\nFor a matrix of complex numbers C, return a corresponding matrix N such\r\nthat each element of N is the iteration count n for each complex number c\r\nin the matrix C, subject to the iteration count limit of lim.\r\n\r\nIf C = [0 0.5; 1 4] and lim = 5, then N = [5 4; 2 1]\r\n\r\nCleve Moler has a whole chapter on the Mandelbrot set in his book Experiments\r\nwith MATLAB: \u003chttp://www.mathworks.com/moler/exm/chapters/mandelbrot.pdf \r\nChapter 10, Mandelbrot Set (PDF)\u003e","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 296.167px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 148.083px; transform-origin: 407px 148.083px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; 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padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 44px 8.5px; transform-origin: 44px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e z(1)   = c\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 80px 8.5px; transform-origin: 80px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e z(n+1) = z(n)^2 + c\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 10px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 10px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 379.5px 8px; transform-origin: 379.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFor any complex c, we can continue this iteration until either abs(z(n+1)) \u0026gt; 2 or n == lim, then return the iteration count n.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 61.3px; counter-reset: list-item 0; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; perspective-origin: 391px 30.65px; transform-origin: 391px 30.65px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2167px; text-align: left; transform-origin: 363px 10.2167px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 142.5px 8px; transform-origin: 142.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eIf c = 0 and lim = 3, then z = [0 0 0] and n = 3.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2167px; text-align: left; transform-origin: 363px 10.2167px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 176.5px 8px; transform-origin: 176.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eIf c = 1 and lim = 5, then z = [1 2], and n = length(z) or 2.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2167px; text-align: left; transform-origin: 363px 10.2167px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 226.5px 8px; transform-origin: 226.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eIf c = 0.5 and lim = 5, then z = [0.5000 0.7500 1.0625 1.6289] and n = 4.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 377px 8px; transform-origin: 377px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFor a matrix of complex numbers C, return a corresponding matrix N such that each element of N is the iteration count n for each complex number c in the matrix C, subject to the iteration count limit of lim.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 149.5px 8px; transform-origin: 149.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eIf C = [0 0.5; 1 4] and lim = 5, then N = [5 4; 2 1]\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 127px 8px; transform-origin: 127px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eCleve Moler has a whole chapter on the \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/content/dam/mathworks/mathworks-dot-com/moler/exm/chapters/mandelbrot.pdf\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eMandelbrot set\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 38px 8px; transform-origin: 38px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e in his book \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/moler/exm/chapters.html\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eExperiments with MATLAB\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function N = mandelbrot(C,lim)\r\n  N = ones(size(C));\r\nend","test_suite":"%%\r\nC = 0;\r\nlim = 5;\r\nN_correct = 5;\r\nassert(isequal(mandelbrot(C,lim),N_correct))\r\n\r\n%%\r\nC = [0 0.5; 1 4];\r\nlim = 5;\r\nN_correct = [5 4; 2 1];\r\nassert(isequal(mandelbrot(C,lim),N_correct))\r\n\r\n%%\r\ni = sqrt(-1);\r\nC = [i 1 -2*i -2];\r\nlim = 10;\r\nN_correct = [10 2 1 10];\r\nassert(isequal(mandelbrot(C,lim),N_correct))","published":true,"deleted":false,"likes_count":17,"comments_count":9,"created_by":1,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":1781,"test_suite_updated_at":"2012-01-26T03:21:20.000Z","rescore_all_solutions":false,"group_id":2,"created_at":"2012-01-18T01:00:28.000Z","updated_at":"2026-05-05T05:05:17.000Z","published_at":"2012-01-18T01:00:28.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://en.wikipedia.org/wiki/Mandelbrot_set\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eMandelbrot Set\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e is built around a simple iterative equation.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ z(1)   = c\\n z(n+1) = z(n)^2 + c]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor any complex c, we can continue this iteration until either abs(z(n+1)) \u0026gt; 2 or n == lim, then return the iteration count n.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIf c = 0 and lim = 3, then z = [0 0 0] and n = 3.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIf c = 1 and lim = 5, then z = [1 2], and n = length(z) or 2.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIf c = 0.5 and lim = 5, then z = [0.5000 0.7500 1.0625 1.6289] and n = 4.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor a matrix of complex numbers C, return a corresponding matrix N such that each element of N is the iteration count n for each complex number c in the matrix C, subject to the iteration count limit of lim.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIf C = [0 0.5; 1 4] and lim = 5, then N = [5 4; 2 1]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eCleve Moler has a whole chapter on the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/content/dam/mathworks/mathworks-dot-com/moler/exm/chapters/mandelbrot.pdf\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eMandelbrot set\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e in his book \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/moler/exm/chapters.html\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eExperiments with MATLAB\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"}],"no_progress_badge":{"id":53,"name":"Unknown","symbol":"unknown","description":"Partially completed groups","description_html":null,"image_location":"/images/responsive/supporting/matlabcentral/cody/badges/problem_groups_unknown_2.png","bonus":null,"players_count":0,"active":false,"created_by":null,"updated_by":null,"deleted_by":null,"deleted_at":null,"restored_by":null,"restored_at":null,"created_at":"2018-01-10T23:20:29.000Z","updated_at":"2018-01-10T23:20:29.000Z","community_badge_id":null,"award_multiples":false}}