Lucas定理模板

Lucas定理是用來求解C(m,n)mod p的值的。其中m和n的值可以很大，p一定是素數。

對階乘打表的模板

LL quick_mod(LL a, LL b, LL c)//費馬小定理+快速冪求逆元  
{  
    LL ans = 1;  
    while (b)  
    {  
        if (b%2==1)  
            ans = (ans*a) % c;  
        b /=2;  
        a = (a*a) % c;  
    }  
    return ans;  
}  
  
  
LL fac[MAXN];  
void Get_Fac(LL m)//階乘打表  
{  
    fac[0] = 1;  
    for (int i = 1; i <= m; i++)  
        fac[i] = (fac[i - 1] * i) % m;  
}  
LL Lucas(LL n, LL m, LL p)//盧卡斯定理  
{  
    LL ans = 1;  
    while (n && m)  
    {  
        LL a = n % p;  
        LL b = m % p;  
        if (a < b)  
            return 0;  
        ans = ((ans*fac[a] % p) * (quick_mod(fac[b] * fac[a - b] % p, p - 2, p))) % p;  
        n /= p;  
        m /= p;  
    }  
    return ans;  
}  

不用對階乘打表的模板

LL quick_mod(LL a, LL b, LL c)  
{
	LL ans = 1;
	while (b)
	{
		if (b % 2 == 1)
			ans = (ans*a) % c;
		b /= 2;
		a = (a*a) % c;
	}
	return ans;
}


LL C(LL n, LL k,LL p) {
	if (n < k)
		return 0;
	if (k > n - k)
		k = n - k;
	LL a = 1, b = 1;
	for (int i = 0; i < k; i++) 
	{
		a = a * (n - i) % p;
		b = b * (i + 1) % p;
	}
	return a * quick_mod(b, p - 2,p) % p;
}

LL lucas(LL a, LL b,LL p)
{
	if (b == 0)
		return 1;
	return C(a % p, b % p,p) * lucas(a / p, b / p,p) % p;
}