LightOJ 1067 - Combinations【Lucas定理】

題目鏈接：http://www.lightoj.com/volume_showproblem.php?problem=1067

題意： 組合數求模，Lucas定理

代碼：

#include <stdio.h>  
#include <math.h>  
#include <stdlib.h>  
#include <algorithm>  
#include <string.h>    
#include <iostream>

using namespace std;

const long long MOD = 1000003;

long long pow(long long a, long long b, long long c)
{
    long long tmp = 1;
    while (b)
    {
        if (b & 1) tmp = (tmp*a) % c;
        a = (a*a) % c;
        b >>= 1;
    }
    return tmp;
}

long long fac[1000005];

void get_fac(long long p)
{
    fac[0] = 1;
    for (int i = 1;i <= p;i++)
        fac[i] = (fac[i - 1] * i) % p;
}

long long Lucas(long long n, long long m, long long p)
{
    long long tmp = 1;
    while (n && m)
    {
        long long a = n%p, b = m%p;
        if (a < b) return 0;
        tmp = (tmp * fac[a] * pow(fac[b] * fac[a - b] % p, p - 2, p)) % p;

        n /= p;
        m /= p;
    }
    return tmp;
}

int n, m;

int main()
{
    get_fac(MOD);
    int T;
    scanf("%d", &T);
    for (int t = 1;t <= T;t++)
    {
        scanf("%d %d", &n, &m);
        int ans = Lucas(n, m, MOD);
        printf("Case %d: %d\n", t, ans);
    }
    return 0;
}