96. Unique Binary Search Trees

题目:

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

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 (M) Unique Binary Search Trees II

 

链接： http://leetcode.com/problems/unique-binary-search-trees/

6/5/2017

抄的答案，DP做法

注意

1. 第11行当中的两个部分dp[j], dp[i-j-1]都是之前算好了的，是总数为i的条件下成树的个数

2. i从1-n都是在为n来做准备的

public class Solution {
    public int numTrees(int n) {
        if (n <= 0) {
            return 0;
        }
        int[] dp = new int[n + 1];
        dp[0] = 1;
        
        for (int i = 1; i <= n; i++) {
            for (int j = 0; j < i; j++) {
                dp[i] += dp[j] * dp[i - j - 1]; // j: elements less than i, i - j - 1: elements larger than i
            }
        }
        return dp[n];
    }
}

参考

http://www.cnblogs.com/yrbbest/p/4437169.html

别人的答案以及解释

https://discuss.leetcode.com/topic/8398/dp-solution-in-6-lines-with-explanation-f-i-n-g-i-1-g-n-i

更多讨论

https://discuss.leetcode.com/category/104/unique-binary-search-trees