How Many Trees?

Time Limit: 2000/1000 MS (Java/Others) Memory Limit: 65536/32768 K (Java/Others)

Problem Description

A binary search tree is a binary tree with root k such that any node v reachable from its left has label (v) <label (k) and any node w reachable from its right has label (w) > label (k). It is a search structure which can find a node
with label x in O(n log n) average time, where n is the size of the tree (number of vertices).

Given a number n, can you tell how many different binary search trees may be constructed with a set of numbers of size n such that each element of the set will be associated to the label of exactly one node in a binary search tree?

Input

The input will contain a number 1 <= i <= 100 per line representing the number of elements of the set.

Output

You have to print a line in the output for each entry with the answer to the previous question.

Sample Input

1
2
3

Sample Output

1
2
5

Source

UVA

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#include<stdio.h>
#include<string.h>
const int maxn=500;
int catalan[101][maxn];
void make(){
	catalan[1][0]=1;
	int i,j,t,res;
	int temp[maxn];
	memset(temp,0,sizeof(temp));
	for(i=2;i<=100;++i){
		t=4*i-2;
		for(j=0;j<maxn;++j){
			catalan[i][j]+=catalan[i-1][j]*t;

		}
		for(j=0;j<maxn;++j){
			if(catalan[i][j]>=10){
				catalan[i][j+1]+=catalan[i][j]/10;
				catalan[i][j]%=10;
			}
		}
		t=i+1;res=0;
		for(j=maxn-1;j>=0;--j){
			res=res*10+catalan[i][j];
			temp[j]=res/t;
			res%=t;
		}
		for(j=maxn-1;j>=0;--j){
			catalan[i][j]=temp[j];
		}
	}

}
int main(){
	make();
	int n;
	while(~scanf("%d",&n)){
	    int i=maxn-1;
	    while(catalan[n][i]==0) --i;
	    for(;i>=0;--i){
	    	printf("%d",catalan[n][i]);
	    }
	    printf("\n");
	}
	return 0;
}

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