Compute binomial coefficient or combinations with Dynamic Programming

The Problem
Write a function that takes two parameters N and K and returns the value of binomial coefficient C (n, k ).For example, your function shocould return 6 for n = 4 and K = 2, and it shoshould return 10 for n = 5 and K = 2.

 1   Def  Computebinomialcoefficients (n, k ):  2       #  Computebinomialcoefficients (5, 2) shoud return 10  3 Table = [0] * (k + 1)  4 Table [0] = 1 5       For I In Range (1, n + 1 ):  6           For J In Range (min (I, K), 0,-1 ): #  Why begin with Min (I, K): 1) We do not need any results more than K. 2) Yang Hui (Pascal) triangle: J must be less than I  7 Table [J] = table [J] + Table [J-1]#  This comes from Yang Hui triangle (or Pascal trianle) of Binomial Coefficients  8       9       Return Table [k]

 

Referece:

Http://www.geeksforgeeks.org/dynamic-programming-set-9-binomial-coefficient/

Http://en.wikipedia.org/wiki/Pascal%27s_triangle

Compute binomial coefficient or combinations with Dynamic Programming