95. Unique Binary Search Trees II

题目：

Given n, generate all structurally unique BST's (binary search trees) that store values 1...n.

For example,
Given n = 3, your program should return all 5 unique BST's shown below.

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

confused what "{1,#,2,3}" means? > read more on how binary tree is serialized on OJ.

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

6/5/2017

抄的

4ms, 52%

思路：以1-n里每一个值为root，找到所有的情况

注意的问题

1. 递归退出时需要add null，这个也作为叶子节点

2. 左子树和右子树也是通过两个范围内所有的值作为left, right来建的

3. 不理解时间复杂度和空间复杂度：exponential complexity

/**
 * Definition for a binary tree node.
 * public class TreeNode {
 *     int val;
 *     TreeNode left;
 *     TreeNode right;
 *     TreeNode(int x) { val = x; }
 * }
 */
public class Solution {
    public List<TreeNode> generateTrees(int n) {
        if (n <= 0) {
            return new ArrayList<>();
        }
        return generateTrees(1, n);
    }
    
    private List<TreeNode> generateTrees(int lo, int hi) {
        List<TreeNode> ret = new ArrayList<>();
        if (lo > hi) {
            ret.add(null);
            return ret;
        }
        for (int i = lo; i <= hi; i++) {
            List<TreeNode> left = generateTrees(lo, i - 1);
            List<TreeNode> right = generateTrees(i + 1, hi);
            
            for (TreeNode l: left) {
                for (TreeNode r: right) {
                    TreeNode root = new TreeNode(i);
                    root.left = l;
                    root.right = r;
                    ret.add(root);
                }
            }
        }
        return ret;
    }
}

别人的DP做法

https://discuss.leetcode.com/topic/2940/java-solution-with-dp

更多讨论

https://discuss.leetcode.com/category/103/unique-binary-search-trees-ii