How Many Trees?
Time Limit: 2000/1000 MS (Java/Others) Memory Limit: 65536/32768 K (Java/Others)
Total Submission(s): 4343 Accepted Submission(s): 2412
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
依然是卡特兰数 直接java大整数了
import java.io.*;
import java.math.*;
import java.util.*;
public class Main {
public static void main(String[] args){
Scanner sc = new Scanner(System.in);
BigInteger s[] = new BigInteger[105];
s[1] = BigInteger.ONE;
for(int i = 2;i < 105;i ++){
s[i] = s[i-1].multiply(BigInteger.valueOf(4 * i - 2)).divide(BigInteger.valueOf(i + 1));
}
while(sc.hasNext()){
int n = sc.nextInt();
System.out.println(s[n]);
}
}
}