hdu 5673 Robot 卡特兰数+逆元

Posted 2020-08-16 xjhz

Robot

Time Limit: 12000/6000 MS (Java/Others)    Memory Limit: 65536/65536 K (Java/Others)

Problem Description

There is a robot on the origin point of an axis.Every second, the robot can move right one unit length or do nothing.If the robot is 
on the right of origin point,it can also move left one unit length.A route is a series of movement. How many different routes there are
that after n seconds the robot is still located on the origin point?
The answer may be large. Please output the answer modulo 1,000,000,007

 

 

Input

There are multiple test cases. The first line of input contains an integer T(1≤T≤100) indicating the number of test cases. For each test case:

The only line contains one integer n(1≤n≤1,000,000).

 

 

Output

For each test case, output one integer.

 

 

Sample Input

3 1 2 4

 

 

Sample Output

1 2 9

 

 

Source

BestCoder Round #81 (div.2)

思路：把n步当成最多往右走[n/2]步，最多往左走[n/2]步，当成火车出栈和入栈，卡特兰数，枚举到[n/2];

#include<bits/stdc++.h>
using namespace std;
#define ll long long
#define pi (4*atan(1.0))
#define eps 1e-14
const int N=2e5+10,M=4e6+10,inf=1e9+10,mod=1e9+7;
const ll INF=1e18+10;
ll a[M];
ll inv[M];
void init()
{
    inv[1] = 1;
    for(int i=2;i<=1000010;i++)
    {
        if(i >= mod)break;
        inv[i] = (mod - mod / i) * inv[mod % i]% mod;
    }
}
ll c[M];
int main()
{
    a[0]=1;
    init();
    for(ll i=1;i<=1000000;i++)
    {
        a[i]=(((a[i-1]*(4*i-2))%mod)*inv[i+1])%mod;
    }
    int T,cas=1;
    scanf("%d",&T);
    while(T--)
    {
        int n;
        scanf("%d",&n);
        c[0]=1;
        for(int i=1,t=n;i<=n;t--,i++)
        {
            c[i]=(((c[i-1]*t)%mod)*inv[i])%mod;
        }
        ll ans=0;
        for(int i=0;i*2<=n;i++)
        {
            ans=(ans+(a[i]*c[2*i])%mod)%mod;
        }
        printf("%lld\n",ans);
    }
    return 0;
}