组合数模板+ 卢卡斯定理

Template one:

#include <stdio.h>
#include <stdlib.h>
long long Combination(int n,int m)
{
    long long nr = 1;
    for (int j = 0; j < m; j++)
    {
        nr *= (n - j);
        nr/=(j+1);
    }
    return nr;
}
int main()
{
    int T,n, m;
    scanf("%d",&T);
    while (T--)
    {
         scanf("%d%d", &n, &m);
          if (m>n/2)
           m=n-m;
         printf("%lld\n",Combination(n, m));
    }
    return 0;
}

Template two:

#include <stdio.h>
#define MAXN 100
long long bc[MAXN][MAXN];
long long binomial_coefficient(int n, int m)
{
    int i, j;
    for (i = 0; i <= n; i++)    
        bc[i][0] = 1;

    for (j = 0; j <= n; j++)    
        bc[j][j] = 1;

    for (i = 1; i <= n; i++)    
        for (j = 1; j < i; j++)
            bc[i][j] = bc[i - 1][j - 1] + bc[i - 1][j];

    return bc[n][m];
}
int main()
{
    int T, n, m;
    scanf("%d", &T);

    while (T--)
    {
        scanf("%d%d", &n, &m);
        if (m > n /2)
        {
            m = n - m;
        }

        printf("%lld\n", binomial_coefficient(n, m));
    }
    return 0;
}

Template three:

#include<bits/stdc++.h>
#define ll long long
using namespace std;
int n,m;
const int p=10007;
int qpow(int a, int b)
{
    int ans;
    for(ans = 1; b; b >>= 1, a = a * a % p)
        if(b & 1)
            ans = ans * a % p;
    return ans;
}
int getc(int n, int m)
{
    if(n < m)
        return 0;
    if(m > n - m)
        m = n - m;
    ll s1 = 1, s2 = 1;
    for(int i = 0; i < m; i++)
    {
        s1 = s1 * (n - i) % p;
        s2 = s2 * (i + 1) % p;
    }
    return s1 * qpow(s2, p - 2) % p;
}
int lucas(int n, int m)
{
    if(m == 0)
        return 1;
    return getc(n % p, m % p) * lucas(n / p, m / p) % p;
}
int main() 
{
    scanf("%d%d", &n, &m);
    printf("%d\n", getc(n, m));
    printf("%d\n", lucas(n, m));
    return 0;
}