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LeetCode: Unique Binary Search Trees II 解题报告

2024-11-20 08:00:39   202人阅读

Unique Binary Search Trees II

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.

 

Hide Tags Tree Dynamic Programming

SOLUTION 1:

使用递归来做。

1. 先定义递归的参数为左边界、右边界，即1到n.

2. 考虑从left, 到right 这n个数字中选取一个作为根，余下的使用递归来构造左右子树。 

3. 当无解时，应该返回一个null树，这样构造树的时候，我们会比较方便，不会出现左边解为空，或是右边解为空的情况。

4. 如果说左子树有n种组合，右子树有m种组合，那最终的组合数就是n*m. 把这所有的组合组装起来即可

技术分享
 1 /** 2  * Definition for binary tree 3  * public class TreeNode { 4  *     int val; 5  *     TreeNode left; 6  *     TreeNode right; 7  *     TreeNode(int x) { val = x; left = null; right = null; } 8  * } 9  */10 public class Solution {11     public List<TreeNode> generateTrees(int n) {12         // 0.0713         return dfs(1, n);14     }15     16     public List<TreeNode> dfs(int left, int right) {17         List<TreeNode> ret = new ArrayList<TreeNode>();18         19         // The base case;20         if (left > right) {21             ret.add(null);22             return ret;23         }24         25         for (int i = left; i <= right; i++) {26             List<TreeNode> lTree = dfs(left, i - 1);27             List<TreeNode> rTree = dfs(i + 1, right);28             for (TreeNode nodeL: lTree) {29                 for (TreeNode nodeR: rTree) {30                     TreeNode root = new TreeNode(i);31                     root.left = nodeL;32                     root.right = nodeR;33                     ret.add(root);34                 }35             }36         }37         38         return ret;39     }40 }
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CODE:

https://github.com/yuzhangcmu/LeetCode_algorithm/blob/72f914daab2fd9e2eb8a63e4643297d78d4fadaa/tree/GenerateTree2.java

LeetCode: Unique Binary Search Trees II 解题报告


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