POJ 2249-Binomial Showdown(排列组合计数)

Binomial Showdown

Time Limit: 1000MS		Memory Limit: 65536K
Total Submissions: 18457		Accepted: 5633

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

题意：求C(n,m)；

思路：这个是当中一种办法。就是连乘r个整商：C(n,k)=C(n,k-1)*(n-k+1)/k。时间复杂度O(n);

#include <stdio.h>
#include <math.h>
#include <string.h>
#include <stdlib.h>
#include <iostream>
#include <algorithm>
#include <set>
#include <queue>
#include <stack>
#include <map>
using namespace std;
typedef long long LL;
LL work(LL n,LL m)
{
    if(m>n/2) m=n-m;
    LL a=1,b=1;
    for(int i=1;i<=m;i++){
        a*=n-i+1;
        b*=i;
        if(a%b==0){
            a/=b;
            b=1;
        }
    }
    return a/b;
}
int main()
{
    LL n,m;
    while(~scanf("%lld %lld",&n,&m)){
        if(!n&&!m) break;
        printf("%lld\n",work(n,m));
    }
    return 0;
}