[Codevs] 3112 Binary Tree count

Time Limit: 1 s space limit: 128000 kb title level: gold Gold Title Description Description

The total number of Binary Trees with N nodes

Input description Input description

Reads a positive integer n.

Output description Output description

Output a positive integer to indicate the answer

Sample Input Sample Input

6

Sample output Sample output

132

Data range and prompt Data size & hint

1 <= n <= 20

Analysis

Catalan count

F [2] = f [3] = 1;

F [n + 1] = (4n-6)/n * f [N];

 1 # include<cstdio> 2 # include<cstring> 3 # include<iostream> 4 # include<algorithm> 5 using namespace std; 6 typedef unsigned long long LL; 7 const int maxn=25; 8 LL f[maxn]; 9 int main(){10     f[2]=f[3]=1;11     for(int i=3;i<=maxn;i++)12     f[i+1]=(4*i-6)*f[i]/i;13     int n;cin>>n;14     cout<<f[n+2];15     return 0;16 }

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[Codevs] 3112 Binary Tree count