数论的一些模板《阶乘、快速幂、费马小定理、卢卡斯定理、欧拉函数》

#include<cstdio>
#include<cstring>
#include<algorithm>
#include<iostream>
#include<cmath>
using namespace std;
#define ll long long
const int Max = 1e6;
#define MOD 1000003
ll fac[Max];

void init(ll Max)//循环求阶乘 
{
    fac[0] = 1;
    for(int i = 1; i <= Max; i++)
        fac[i] = fac[i-1] * i % MOD;
    return;
}


ll _pow(ll x, ll y, ll p)//快速幂 
{
    ll res = 1,tmp = x % p;
    while(y)
    {
        if(y & 1)
            res = res * tmp % p;
        tmp = tmp * tmp % p;
        y >>= 1;
    }
    return res;
}


ll C(ll n, ll m, ll p)//费马小定理求逆元 
{
    if(m > n)
        return 0;
    return fac[n] * _pow(fac[m] * fac[n-m], p-2, p) % p;
}

ll lucas(ll n, ll m, ll p)//lucas递归 
{
    if(m == 0)
        return 1;
    return (C(n%p, m%p, p)*lucas(n/p, m/p, p))%p;
}

int main()
{
    int t;
    cin >> t;
    int k = 0;
    init(Max);
    while(t--)
    {
        k++;
        int n,m;
        cin >> n >> m;
        cout << "Case " << k << ": " << lucas(n, m, MOD) << endl;
    }
    return 0;
}

欧拉函数:

#include<iostream>
using namespace std;

int euler(int n) 
{
	int res=n,i;
	for(i=2; i*i<=n; i++)
		if(n%i==0) 
		{
			res=res/i*(i-1);
			while(n%i==0)
				n/=i;
		}
	if(n>1)
		res=res/n*(n-1);
	return res;
}
int main() 
{
	int n;
	while(cin>>n&&n)
		cout<<euler(n)<<endl;
	return 0;
}

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转载自blog.csdn.net/Xylon_/article/details/81532642