大組合數取膜模板C_n^m%p

【模板代碼】

【模板一】

#include<iostream>
#include<stdio.h>
using namespace std;
int pow_mod(int a,int n,int p)
{
    int ans=1,t=a;
    while(n)
    {
        if(n&1)
            ans=(long long)ans*t%p;
        t=(long long)t*t%p;
        n>>=1;
    }
    return ans;
}
int cal(int n,int m,long p)
{
    if(m>n-m) m=n-m;
    int ans=1;
    for(int i=1;i<=m;i++)
    {
        ans=(long long)ans*(n-i+1)%p;
        int a=pow_mod(i,p-2,p);
        ans=(long long)ans*a%p;
    }
    return ans;
}

int com_mod(int n,int m,long p)
{
    if(n<m)return 0;
    return cal(n,m,p);
}

int lucas(int n,int m,long p)
{
    int r=1;
    while(n&&m&&r)
    {
        r=(long long)r*com_mod(n%p,m%p,p)%p;
        n/=p;
        m/=p;
    }
    return r;
}

int main()
{
    int t;
    scanf("%d",&t);
    while(t--)
    {
        int n,m,p;
        scanf("%d%d%d",&n,&m,&p);
        printf("%d\n",lucas(n,m,p));<span style="white-space:pre">	</span>//求組合數C n m ，然後對 p 取膜
    }
}

【模板二】

#include<stdio.h>

long long  min(long long  a,long long  b)
{
    if(a>b)return b;
    else return a;
}

long long  ext_gcd(long long  a,long long  b,long long  &x,long long  &y)
{
    if(b==0){x=1,y=0;return a;}
    long long  res=ext_gcd(b,a%b,y,x);
    y-=a/b*x;
    return res;
}

long long  retx(long long  a,long long  b,long long  n)
{
    long long  res,x,y,t;
    res=ext_gcd(a,b,x,y);
    if(n%res==0)
    {
        x=x*n/res;
        t=b/res;
        if(t<0)t=-t;
        x=(x%t+t)%t;
        return x;
    }
    return -1;
}

long long Cfun(long long n,long long m,long long p)
{
    long long  up=n,all=1,i;
    long long  down=m;
    for(i=1;i<=m;i++)
    {
        all=all*up;
        all=all%p;

        if(all%down==0)
            all=all/down;
        else
            all=retx(down,p,all);
        down--;
        up--;
    }
    return all;
}

int main()
{
    long long  n,m,p,t,i;
    scanf("%lld",&t);
    while(t--)
    {
        scanf("%lld%lld%lld",&n,&m,&p);
        m=min(m,n-m);
        printf("%lld\n",Cfun(n,m,p));
    }
}