2053 - Binomial Showdown
In how many ways can you choose k elements out of n elements, not taking order into account? Write a program to compute this number.
Input
The input will contain one or more test cases. Each test case consists of one line containing two integers n (n>=1) and k (0<=k<=n). Input is terminated by two zeroes for n and k.
Output
For each test case, print one line containing the required number. This number will always fit into an integer, i.e. it will be less than 231. Warning: Don't underestimate the problem. The result will fit into an integer - but if all intermediate results arising during the computation will also fit into an integer depends on your algorithm. The test cases will go to the limit.
Examples
Input
4 2 10 5 49 6 0 0
Output
6 252 13983816
Solution C++
#include <bits/stdc++.h> using namespace std; int main() { int n, k; while (scanf("%d%d", &n, &k) == 2) { if (n == 0 && k == 0) break; if (k < n - k) k = n - k; long long res = 1; for (int i = 1; i <= n - k; i ++) { res = res * (k + i) / i; } printf("%d\n", res); } return 0; }