poj2249 Binomial Showdown 求组合数

Binomial Showdown

Time Limit: 1000MS		Memory Limit: 65536K
Total Submissions: 18925		Accepted: 5788

Description

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. 

Sample Input

4 2
10 5
49 6
0 0

Sample Output

6
252
13983816

Pascal公式

和一些恒等式

用C(n,m) = (n - m + 1) * C(n, m - 1) / m，由于除以m相对没那么容易越界

#include <cstdio>
#include <cstring>
#include <iostream>

using namespace std;

typedef long long ll;
ll a[100000000];

int main()
{
	ll n, m;
	while (~scanf("%I64d%I64d", &n, &m) && (n || m)) {
		if (n - m < m)
			m = n - m;
		a[0] = 1;
		for (int i = 1; i <= m; i++) {
			a[i] = (n - i + 1) * a[i - 1] / i;
		}
		printf("%d\n", a[m]);
	}
	return 0;
}