Binomial Showdown（组合计数模板）

Link：http://poj.org/problem?id=2249

Binomial Showdown

Time Limit: 1000MS Memory Limit: 65536KTotal Submissions: 18459 Accepted: 5635

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

4 210 549 60 0

Sample Output

625213983816

Source

Ulm Local 1997

题意&解题思路：计算组合数c(n,m)

AC  code：

#include<iostream>#include<algorithm>#include<cstring>#include<cstdio>#include<cmath>#include<queue>#include<vector>#define LL long long#define MAXN 1000100using namespace std;LL n,m;LL Cnm(LL n,LL m)//计算组合数C(n,m) {if(m>n/2)//根据组合公式，可以减少枚举量 m=n-m;LL a=1,b=1;for(int i=1;i<=m;i++)//顺序进行m次运算 {a*=n+1-i;//计算前i项运算结果的分子a和分母 b b*=i;if(a%b==0){a/=b;b=1;}}return a/b;}int main(){while(cin>>n>>m){if(n==0&&m==0)break;cout<<Cnm(n,m)<<endl;}return 0; }