poj2613

题意：给出p,q,r,s，求c(p,q)/c(r,s)

分析：利用组合数公式，写出整体的分子和分母（用数组标记，分子分母各有哪些数），把相同的数字约去。然后把分子乘上，分母除掉。但是这样直接乘除会损失精度。所以我们定义double ans = 1;然后当ans<1时算乘法，ans>=1时算除法，以控制ans始终在1不会和1相差10000倍以上，以保证精度。

#include <iostream>
#include <cstdlib>
#include <cstring>
#include <cstdio>
using namespace std;

#define maxn 10005

int a, b, c, d;
int up[maxn], down[maxn];
int n;

void make(int m, int n, int up[], int down[])
{
    if (n - m < m)
        m = n - m;
    for (int i = n; i > n - m; i--)
        up[i]++;
    for (int i = 1; i <= m; i++)
        down[i]++;
}

void work()
{
    n = max(max(a, b), max(c, d));
    for (int i = 0; i <= n; i++)
    {
        int x = min(up[i], down[i]);
        up[i] -= x;
        down[i] -= x;
    }
    int p = 1, q = 1;
    while (p <= n && !up[p])
        p++;
    while (q <= n && !down[q])
        q++;
    double ans = 1;
    while (p <= n || q <= n)
    {
        if ((ans <= 1 && p <= n) || q > n)
        {
            ans *= p;
            up[p]--;
            while (p <= n && !up[p])
                p++;
        }
        else
        {
            ans /= q;
            down[q]--;
            while (q <= n && !down[q])
                q++;
        }
    }
    printf("%.5f\n", ans);
}

int main()
{
    //freopen("t.txt", "r", stdin);
    while (~scanf("%d%d%d%d", &a, &b, &c, &d))
    {
        memset(up, 0, sizeof(up));
        memset(down, 0, sizeof(down));
        make(b, a, up, down);
        make(d, c, down, up);
        work();
    }
    return 0;
}