Count the Trees

最新推荐文章于 2022-08-20 05:30:00 发布

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本文介绍了一种计算使用特定数量的不同元素可以构建的不同标记二叉树数量的方法。通过递推公式预计算出所需数值，并利用这些数值快速解决输入问题。示例展示了不同元素数量下可构建的二叉树数量。

Count the Trees

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

Total Submission(s): 925 Accepted Submission(s): 608

Problem Description

Another common social inability is known as ACM (Abnormally Compulsive Meditation). This psychological disorder is somewhat common among programmers. It can be described as the temporary (although frequent) loss of the faculty of speech when the whole power of the brain is applied to something extremely interesting or challenging.
Juan is a very gifted programmer, and has a severe case of ACM (he even participated in an ACM world championship a few months ago). Lately, his loved ones are worried about him, because he has found a new exciting problem to exercise his intellectual powers, and he has been speechless for several weeks now. The problem is the determination of the number of different labeled binary trees that can be built using exactly n different elements.

For example, given one element A, just one binary tree can be formed (using A as the root of the tree). With two elements, A and B, four different binary trees can be created, as shown in the figure.

If you are able to provide a solution for this problem, Juan will be able to talk again, and his friends and family will be forever grateful.

Input

The input will consist of several input cases, one per line. Each input case will be specified by the number n ( 1 ≤ n ≤ 100 ) of different elements that must be used to form the trees. A number 0 will mark the end of input and is not to be processed.

Output

For each input case print the number of binary trees that can be built using the n elements, followed by a newline character.

Sample Input

Sample Output

1
4
60949324800
75414671852339208296275849248768000000

import java.math.BigInteger;
import java.util.Scanner;

public class Main {
    public static void main(String[] args) {
        BigInteger[] f = new BigInteger[301];
        BigInteger[] g = new BigInteger[301];
        f[1] = BigInteger.valueOf(1);
        g[1] = BigInteger.valueOf(1);
        for(int i = 2; i <= 300; i++) {
            f[i] = f[i-1].multiply(BigInteger.valueOf(4*i-2)).divide(BigInteger.valueOf(i+1));
            g[i] = g[i-1].multiply(BigInteger.valueOf(i));
        }
        
        Scanner cin = new Scanner(System.in);
        while(cin.hasNext()) {
            int n = cin.nextInt();
            if(n == 0)
                break;
            System.out.println(f[n].multiply(g[n]));
        }
    }
}