Binomial Showdown(P2249)

最新推荐文章于 2018-09-02 08:49:54 发布

原创最新推荐文章于 2018-09-02 08:49:54 发布 · 522 阅读

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#integer #input #each #output #less #bi

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本文介绍了一个计算组合数的算法挑战，通过高效的算法确保在计算过程中避免整数溢出的问题。文章提供了一段C++代码示例，展示了如何通过逐步简化计算过程来减少中间结果的大小，从而使得最终结果能在一个合理的数值范围内得到。

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注意其计算的时候要保证边计算边减少其计算的数字不能超过long long的范围。

#include<iostream>
#include<cstdio>
#include<cstring> 
#include<ctype.h>
#include<vector>
#include<algorithm>
#include<queue>
#include<set>
#include<stack>
using namespace std; 


long long gcd(long long big,long long small)
{
	if (big%small==0)
		return small;
	return gcd(small,big%small);
}

int main()
{
	long long i;
	long long j;
	long long k;
	long long  a;

	double x=23;
	//printf("%.0f\n",x);
	long long b;
	while (cin>>a>>b)
	{
		if (!(a+b))
			break;

		b=min(b,a-b);
		k=1;
		j=1;
		for (i=1;i<=b;i++)
		{
			k*=(a-i+1);
			if (k%i==0)
			{
				k/=i;
			}
			else
			{
				j*=i;
			}
			long long temp=gcd(k,j);
			k/=temp;
			j/=temp;
		}

		cout<<k<<endl;

	}


	return 0;

}

Binomial Showdown

Time Limit: 1000MS		Memory Limit: 65536K
Total Submissions: 15624		Accepted: 4778

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 2 ³¹.
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