soj 3290 Distribute The Apples I 组合数对素数取余

由于素数P比较小，所以可以先打表，求出小于P的数的阶乘对与该素数的余数，这样节省了中间求阶乘的时间。

/*
 * soj3290.c
 *
 *  Created on: 2011-10-10
 *      Author: bjfuwangzhu
 */

#include<stdio.h>
#define LL long long
#define nmod 10009
int num[nmod];
void init() {
    int i;
    for (i = 1, num[0] = 1; i < nmod; i++) {
        num[i] = num[i - 1] * i % nmod;
    }
}
int modular_exp(int a, int b) {
    int res, temp;
    res = 1 % nmod,temp = a % nmod;
    while (b) {
        if (b & 1) {
            res = res * temp % nmod;
        }
        temp = temp * temp % nmod;
        b >>= 1;
    }
    return res;
}
int C(int a, int b) {
    int res;
    if (b > a) {
        return 0;
    }
    b = num[b] * num[a - b] % nmod;
    a = num[a];
    res = modular_exp(b, nmod - 2);
    res = res * a % nmod;
    return res;
}
void solve(int n, int m) {
    int a, b, res;
    res = 1;
    while (n || m) {
        a = n % nmod,b = m % nmod;
        res = res * C(a, b) % nmod;
        n /= nmod,m /= nmod;
    }
    printf("%d\n", res);
}
int main() {
#ifndef ONLINE_JUDGE
    freopen("data.in", "r", stdin);
#endif
    int n, k;
    LL temp;
    init();
    while (~scanf("%d %d", &n, &k)) {
        temp = (LL) k;
        temp = temp * (temp + 1) / 2;
        if (temp > n) {
            puts("0");
            continue;
        }
        n = n - (int) temp;
        solve(n + k - 1, n);
    }
    return 0;
}

若不是先打表求N！，则求组合数的函数又可以这么写：

int C(int a, int b) {
    int i, resa, resb, res;
    if (b > a) {
        return 0;
    }
    for (i = 0, resa = 1, resb = 1; i < b; i++) {
        resa = resa * (a - i) % nmod;
        resb = resb * (b - i) % nmod;
    }
    res = modular_exp(resb, nmod - 2);
    res = res * resa % nmod;
    return res;
}