51nod 1120 機器人走方格 V3

卡特蘭數介紹

#include <cstdio>
#include <cstring>
#include <algorithm>
#include <iostream>
using namespace std;
typedef long long ll;
const long long int mod=1e4+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;
    scanf("%lld",&n);
    long long ans=2*Lucas(2*n-2,n-1,mod)%mod*mod_pow(n,mod-2,mod)%mod;
    printf("%lld\n",ans);
    return 0;
}