Problem 2190. Order of things - 2

Created by J-G van der Toorn

Solve Later

{"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":"<?xml version=\"1.0\" encoding=\"UTF-8\"?>\n<w:document xmlns:w=\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\"><w:body><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>This problem is closely related to</w:t></w:r><w:r><w:t> </w:t></w:r><w:hyperlink w:docLocation=\"http://www.mathworks.nl/matlabcentral/cody/problems/2189-order-of-things-1\"><w:r><w:t>Problem 2189, Order of things - 1</w:t></w:r></w:hyperlink><w:r><w:t>. For the details, see the description for that problem. Basically, we have to find the order in which to execute tasks of which the results and prerequisites depend on each other.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"ListParagraph\"/><w:numPr><w:numId w:val=\"1\"/></w:numPr></w:pPr><w:r><w:t>However, this time it may be impossible to find a solution, since dependencies may be cyclic. In that case, return an empty vector.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"ListParagraph\"/><w:numPr><w:numId w:val=\"1\"/></w:numPr></w:pPr><w:r><w:t>Furthermore, if there are multiple orders possible, return them as multiple rows of the output vector.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>Again, the dependencies of the tasks on each other is expressed in a matrix, where each row and column corresponds to a specific task. Each row expresses on which result that task depends. A</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rPr><w:rFonts w:cs=\"monospace\"/></w:rPr><w:t>1</w:t></w:r><w:r><w:t> indicates that the calculation on that row depends on the one mentioned at the top of that column.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>Return the new row/column order as a numeric row-vector, referring to the rows/columns of the input matrix. Of an empty array when no solution is possible. Or a matrix of rows containing the orders, where each row is a different solution, in case multiple solutions exist.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"code\"/></w:pPr><w:r><w:t><![CDATA[ A B C D E\nA 0 1 0 0 0\nB 0 0 0 0 0\nC 1 0 0 1 0\nD 1 0 1 0 0\nE 1 1 1 1 0]]></w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>The above problem can not be solved, since</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rPr><w:rFonts w:cs=\"monospace\"/></w:rPr><w:t>C</w:t></w:r><w:r><w:t> depends on</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rPr><w:rFonts w:cs=\"monospace\"/></w:rPr><w:t>D</w:t></w:r><w:r><w:t>, which in its place depends on</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rPr><w:rFonts w:cs=\"monospace\"/></w:rPr><w:t>C</w:t></w:r><w:r><w:t>. The returned value would be</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rPr><w:rFonts w:cs=\"monospace\"/></w:rPr><w:t>[]</w:t></w:r><w:r><w:t> .</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"code\"/></w:pPr><w:r><w:t><![CDATA[ A B C D E\nA 0 1 0 0 0\nB 0 0 0 0 0\nC 1 0 0 0 0\nD 1 0 0 0 0\nE 1 1 1 1 0]]></w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>The returned matrix should be</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"code\"/></w:pPr><w:r><w:t><![CDATA[ [\n 2 1 3 4 5 \n 2 1 4 3 5\n ]]]></w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>Good luck!</w:t></w:r></w:p></w:body></w:document>"},{"partUri":"/matlab/output.xml","contentType":"text/xml","content":"<?xml version=\"1.0\" encoding=\"UTF-8\" standalone=\"no\" ?><embeddedOutputs><metaData><evaluationState>manual</evaluationState><layoutState>code</layoutState><outputStatus>ready</outputStatus></metaData><outputArray type=\"array\"/><regionArray type=\"array\"/></embeddedOutputs>"}]}

This problem is closely related to <a href = "http://www.mathworks.nl/matlabcentral/cody/problems/2189-order-of-things-1">Problem 2189, Order of things - 1</a>. For the details, see the description for that problem. Basically, we have to find the order in which to execute tasks of which the results and prerequisites depend on each other.<ul><li>However, this time it may be impossible to find a solution, since dependencies may be cyclic. In that case, return an empty vector.</li><li>Furthermore, if there are multiple orders possible, return them as multiple rows of the output vector.</li></ul>Again, the dependencies of the tasks on each other is expressed in a matrix, where each row and column corresponds to a specific task. Each row expresses on which result that task depends. A <tt>1</tt> indicates that the calculation on that row depends on the one mentioned at the top of that column.Return the new row/column order as a numeric row-vector, referring to the rows/columns of the input matrix. Of an empty array when no solution is possible. Or a matrix of rows containing the orders, where each row is a different solution, in case multiple solutions exist.<pre> A B C D E
A 0 1 0 0 0
B 0 0 0 0 0
C 1 0 0 1 0
D 1 0 1 0 0
E 1 1 1 1 0</pre>The above problem can not be solved, since <tt>C</tt> depends on <tt>D</tt>, which in its place depends on <tt>C</tt>. The returned value would be <tt>[]</tt> .<pre> A B C D E
A 0 1 0 0 0
B 0 0 0 0 0
C 1 0 0 0 0
D 1 0 0 0 0
E 1 1 1 1 0</pre>The returned matrix should be<pre> [
 2 1 3 4 5 
 2 1 4 3 5
 ]</pre>Good luck!

Solve

Solution Stats

9 Solutions
7 Solvers

Last Solution submitted on Oct 20, 2018

Last 200 Solutions

Solution Comments

Solution 406514

1 Comment

1 Comment

J-G van der Toorn on 20 Feb 2014

Since Cody, I dislike for-loops, but your solution is way simpler than my own algorithm. Mission accomplished...
Nevertheless, I would hope for a non-looped piece of code. Let's see in phase 3.

Problem Recent Solvers7

Problem Tags

Problem 2190. Order of things - 2

Solution Stats

Last 200 Solutions

Solution Comments

Problem Recent Solvers7

Suggested Problems

More from this Author31

Problem Tags

Problem 2190. Order of things - 2

Solution Stats

Last 200 Solutions

Solution Comments

Problem Recent Solvers7

Suggested Problems

More from this Author31

Problem Tags

Players