UVA10375 Choose and divide 质因数分解

质因数分解：

Choose and divide

Time Limit: 3000MS

Memory Limit: Unknown

64bit IO Format: %lld & %llu

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Description

Problem D: Choose and divide

The binomial coefficient C(m,n) is defined as

         m!
C(m,n) = --------
         n!(m-n)!

Given four natural numbers p, q, r, and s, compute the the result of dividing C(p,q) by C(r,s).

The Input

Input consists of a sequence of lines. Each line contains four non-negative integer numbers giving values for p, q, r, and s, respectively, separated by a single space. All the numbers will be smaller than 10,000 with p>=q and r>=s.

The Output

For each line of input, print a single line containing a real number with 5 digits of precision in the fraction, giving the number as described above. You may assume the result is not greater than 100,000,000.

Sample Input

10 5 14 9
93 45 84 59
145 95 143 92
995 487 996 488
2000 1000 1999 999
9998 4999 9996 4998

Output for Sample Input

0.12587
505606.46055
1.28223
0.48996
2.00000
3.99960

Source

Root :: AOAPC II: Beginning Algorithm Contests (Second Edition) (Rujia Liu) :: Chapter 10. Maths :: Examples
Root :: AOAPC I: Beginning Algorithm Contests (Rujia Liu) :: Volume 6. Mathematical Concepts and Methods
Root :: Competitive Programming 2: This increases the lower bound of Programming Contests. Again (Steven & Felix Halim) :: Mathematics :: Combinatorics :: Binomial Coefficients
Root :: Competitive Programming 3: The New Lower Bound of Programming Contests (Steven & Felix Halim) :: Mathematics :: Combinatorics :: Binomial Coefficients

Root :: Competitive Programming: Increasing the Lower Bound of Programming Contests (Steven & Felix Halim) :: Chapter 5. Mathematics :: Combinatorics
Root :: Prominent Problemsetters :: Gordon V. Cormack

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

using namespace std;

const int maxn=10010;

int p,q,r,s;

int prime[maxn],pn;
long long int fnum[maxn],pnum[maxn];
bool vis[maxn];

void pre_init()
{
    memset(vis,true,sizeof(vis));
    for(int i=2; i<maxn; i++)
    {
        if(i%2==0&&i!=2) continue;
        if(vis[i]==true)
        {
            prime[pn++]=i;
            for(int j=2*i; j<maxn; j+=i)
            {
                vis[j]=false;
            }
        }
    }
}

void fenjie_x(int x,long long int* arr)
{
    for(int i=0; i<pn&&x!=1; i++)
    {
        while(x%prime[i]==0)
        {
            arr[i]++;
            x/=prime[i];
        }
    }
}

void fenjie(int x,long long int* arr)
{
    for(int i=2; i<=x; i++)
        fenjie_x(i,arr);
}

void jianshao()
{
    for(int i=0; i<pn; i++)
    {
        long long int Min=min(fnum[i],pnum[i]);
        fnum[i]-=Min;
        pnum[i]-=Min;
    }
}

int main()
{
    pre_init();
    while(scanf("%d%d%d%d",&p,&q,&r,&s)!=EOF)
    {
        memset(pnum,0,sizeof(pnum));
        memset(fnum,0,sizeof(fnum));
        fenjie(p,pnum);fenjie(s,pnum);fenjie(r-s,pnum);
        fenjie(q,fnum);fenjie(r,fnum);fenjie(p-q,fnum);
        jianshao();
        double ans=1.;
        for(int i=0; i<pn; i++)
        {
            while(pnum[i]--)
            {
                ans*=1.*prime[i];
            }
            while(fnum[i]--)
            {
                ans/=1.*prime[i];
            }
        }
        printf("%.5lf\n",ans);
    }
    return 0;
}

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