luogu P3807 卢卡斯定理 模板

Posted 2020-11-06 Misaka_Azusa

题目链接：https://www.luogu.org/problemnew/show/P3807

Lucas定理用来求大组合数对一个质数取模的值，不大于10^5用逆元，大于10^5就用Lucas转化成10^5以内，如果不是质数还要用扩展Lucas

Lucas(n,m,p) = C(n%p,m%p)*Lucas(n/p,m/p,p)

 1 #include <cstdio>
 2 #include <iostream>
 3 #include <algorithm>
 4 using namespace std;
 5 const int maxn = 100010;
 6 int n, m, p, T;
 7 long long a[maxn], b[maxn];
 8 long long Lucas(int n, int m, int p)
 9 {
10     if(n < m) return 0;
11     else if(n < p) return b[n]*a[m]*a[n-m]%p;
12     else return Lucas(n%p,m%p,p)*Lucas(n/p,m/p,p)%p;
13 }
14 int main()
15 {
16     scanf("%d",&T);
17     while(T--)
18     {
19         scanf("%d%d%d",&n,&m,&p);
20         a[0] = 1, a[1] = 1, b[0] = 1, b[1] = 1;
21         for(int i = 2; i <= m+n; i++) b[i] = b[i-1]*i%p;
22         for(int i = 2; i <= m+n; i++) a[i] = (p-p/i)*a[p%i]%p;
23         for(int i = 2; i <= m+n; i++) a[i] = a[i-1]*a[i]%p;
24         printf("%lld\n",Lucas(n+m,m,p));
25     }
26     return 0;
27 }