51nod_1119:机器人走方格 V2

Posted 2020-08-31

题目链接： https://www.51nod.com/onlineJudge/questionCode.html#!problemId=1119

转化成杨辉三角就好辣@[email protected]

#include<bits/stdc++.h>
using namespace std;
typedef long long LL;

const LL mod=1e9+7;
const LL M=2e6;
LL fac[M+5];                //阶乘    
LL inv_of_fac[M+5];        //阶乘的逆元 
LL qpow(LL x,LL n)
{
    LL ret=1;
    for(; n; n>>=1)
    {
        if(n&1) ret=ret*x%mod;
        x=x*x%mod;
    }
    return ret;
}
void init()
{
    fac[0]=1;
    for(int i=1; i<=M; i++)
        fac[i]=fac[i-1]*i%mod;
    inv_of_fac[M]=qpow(fac[M],mod-2);
    for(int i=M-1; i>=0; i--)
        inv_of_fac[i]=inv_of_fac[i+1]*(i+1)%mod;
}
LL C(LL a,LL b)
{
    if(b<0||a<b) return 0;
    return fac[a]*inv_of_fac[b]%mod*inv_of_fac[a-b]%mod;
}

int main()
{
    init();
    int n,m;
    while(cin>>n>>m)
    {
        if(n<m) swap(n,m);
        cout<<C(n+m-2,m-1)<<endl;
    }
}