Choose and divide

The binomial coefficient C(m, n) is defined as C(m, n) = m! (m − n)! n! Given four natural numbers p, q, r, and s, compute the the result of dividing C(p, q) by C(r, s). 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. 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

Sample Outpu

t 0.12587 505606.46055 1.28223 0.48996 2.00000 3.99960

唯一分解定理应用

#include<iostream>

#include<cstdio>

#include<cmath>

#include<cstring>

#include<sstream>

#include<algorithm>

#include<queue>

#include<deque>

#include<iomanip>

#include<vector>

#include<cmath>

#include<map>

#include<stack>

#include<set>

#include<memory>

#include<list>

#include<string>

using namespace std;

typedef long long LL;

typedef unsigned long long ULL;

#define MAXN 10009

#define L 31

#define INF 1000000009

#define eps 0.00000001

/*

唯一分解定理 应用

*/

int prime[MAXN], e[MAXN];

void getprime()

{

    memset(prime, false, sizeof(prime));

    for (int i = ; i <= MAXN; i++)

    {

        if (!prime[i])

            prime[++prime[]] = i;

        for (int j = ; j <= prime[] && prime[j] <= MAXN / i; j++)

        {

            prime[prime[j] * i] = ;

            if (i%prime[j] == ) break;

        }

    }

}

void add_interger(int n, int d)

{

    for (int i = ; i <= prime[]; i++)

    {

        while (n%prime[i] == )

        {

            n /= prime[i];

            e[i] += d;

        }

        if (n == ) break;

    }

}

void add_factorial(int n, int d)

{

    for (int i = ; i <= n; i++)

        add_interger(i, d);

}

int main()

{

    getprime();

    int p, q, r, s;

    while (cin >> p >> q >> r >> s)

    {

        memset(e, , sizeof(e));

        add_factorial(p, );

        add_factorial(q, -);

        add_factorial(p - q, -);

        add_factorial(r, -);

        add_factorial(s, );

        add_factorial(r - s, );

        double ans = ;

        for (int i = ; i <= prime[]; i++)

            ans *= pow(prime[i], e[i]);

        printf("%.5lf\n", ans);

    }

    return ;

}

巴特西

Choose and divide

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