(組合)51nod 1119 機器人走方格 V2
阿新 • • 發佈:2018-12-18
#include <cstdio> #include <cstring> #include <algorithm> #include <iostream> using namespace std; typedef long long ll; const long long int mod=1e9+7; ll mod_pow(ll x, ll n, ll p){ //快速冪 ll res = 1; while(n){ if(n & 1) res =res * x % p; x = x * x % p; n >>= 1; } return res; } ll comb(ll n, ll m, ll p){ //comb用來求解組合數 if(m > n) return 0; ll ret = 1; m = min(n - m, m); for(int i = 1; i <= m; i ++){ ll a = (n + i - m) % p; ll b = i % p; ret = ret * (a * mod_pow(b, p - 2, p) % p) % p; } return ret; } ll Lucas(ll n, ll m, ll p){ //盧卡斯定理---處理大的組合數對素數取模的情況,因為這時如果遞推的話將會特別耗時 if(m == 0) return 1; return comb(n % p, m % p, p) * Lucas(n / p, m / p, p) % p; } int main(){ ll n, m; scanf("%lld%lld",&m,&n); long long ans=Lucas(n+m-2,min(n-1,m-1),mod); printf("%lld\n",ans); return 0; }