Problem 1855. Usage of java.math : N Choose K with unlimited precision
Calculate the binomial coefficient nchoosek with full accuracy. This challenge may use the wonderful word of java.math that allows unlimited precision calculations. The primary reference sites are Java Math, Java BigDecimal, and Java BigInteger.
The usage of BigDecimal functions add, multiply, and divide may be required.
Java Math:
vd-decimal value, vstr-string, vi-integer value xBD=java.math.BigDecimal(vd); % valid vd,vstr,vi creates xBD a BigDecimal variable import java.math.*; % simplifies statements xBD=BigDecimal(vstr); xplusyBD=xBD.add(BigDecimal(y)); % add input requires BD type xmultiplyzBD=xBD.multiply(BigDecimal(z)); % multiply input requires BD type xdividezBD=xBD.divide(BigDecimal(z)); % divide input requires BD type xmultydivz=xBD.multiply(yBD).divide(zBD); out=x*y/z
To convert java to string of unlimited length can be achieved via java toString or Matlab char
xstr=toString(xBD) or xstr=char(xBD)
Input: [N,K] [ Inputs to nchoosek(N,K) 0<=K<=N<200 ]
Output: C (char variable of C=nchoosek(n,k) or BigDecimal variable type )
Theory:
C(n,k) link shows multiple evaluation methods.
C(n,k)= n!/(k!(n-k)!)
The factorial method gives a direct solution while the multiplicative may require fewer operations.
Hint: C(5,3)=(5/3)*(4/2)*(3/1)= (5/1)*(4/2)*(3/3); numerator has k terms
Future Challenges:
2. nchoosek_large (full precision) 3. Next Prime 4. factor_large
5. Factorial
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