ACM_算法_Lucas定理

Lucas定理是用于求解C(n,m)%p的问题

这里小编用一张图：

这张图就很完整的说明了Lucas定理的内容，比较简单，也比较好理解，小编也就不多说了。

#include <cstdio>#include <cstring>#include <iostream>#include <algorithm>using namespace std;typedef long long LL;LL Power_mod(LL a, LL b, LL p){LL res = 1;while(b!=0){if(b&1) res = (res*a)%p;a = (a*a)%p;b >>= 1;}return res;}LL Comb(LL a,LL b, LL p){if(a < b) return 0;if(a == b) return 1;if(b > a-b) b = a-b;LL ans = 1, ca = 1, cb = 1;for(LL i=0; i<b; ++i){ca = (ca*(a-i))%p;cb = (cb*(b-i))%p;}ans = (ca*Power_mod(cb, p-2, p))%p;return ans;}LL Lucas(int n, int m, int p){LL ans = 1;while(n && m && ans){ans = (ans * Comb(n%p, m%p, p))%p;n /= p;m /= p;}return ans;}int main(){int n,m,p;while(scanf("%d%d%d",&n,&m,&p) !=EOF){printf("%lld\n",Lucas(n,m,p));}return 0;}