leetcode--Unique Binary Search Trees

Given n, how many structurally unique BST's (binary search trees) that store values 1...n?

For example,
Given n = 3, there are a total of 5 unique BST's.

   1         3     3      2      1
           /     /      /       
     3     2     1      1   3      2
    /     /                        
   2     1         2                 3

This is a simple problem. Each number between 1 and n can be the root node.
1-d dynamical programming can be used to solve this problem.

public class Solution {
    public int numTrees(int n) {
        int num = 0;
		if(n > 0){
			int[] trees = new int[n + 1];
			trees[0] = 1;
			trees[1] = 1;
			if( n > 1){
				for(int i = 2;  i < n + 1; ++i){
					trees[i] = 0;
					for(int j = 0; j < i; ++j){
						 trees[i] += trees[j] * trees[i - 1 - j];
					}
				}			
			}
			num = trees[n];
		}
		return num;
    }
}

  

原文地址:https://www.cnblogs.com/averillzheng/p/3537450.html