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 should return 6 for n = 4 and k = 2, and it should 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
