balance-a-binary-search-tree

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Algorithms

Given the <code>root</code> of a binary search tree, return a balanced binary search tree with the same node values. If there is more than one answer, return any of them.

A binary search tree is balanced if the depth of the two subtrees of every node never differs by more than <code>1</code>.

&nbsp;
Example 1:
<img alt="" src="https://assets.leetcode.com/uploads/2021/08/10/balance1-tree.jpg" style="width: 500px; height: 319px;" />
<pre>
Input: root = [1,null,2,null,3,null,4,null,null]
Output: [2,1,3,null,null,null,4]
Explanation: This is not the only correct answer, [3,1,4,null,2] is also correct.
</pre>

Example 2:
<img alt="" src="https://assets.leetcode.com/uploads/2021/08/10/balanced2-tree.jpg" style="width: 224px; height: 145px;" />
<pre>
Input: root = [2,1,3]
Output: [2,1,3]
</pre>

&nbsp;
Constraints:

<ul>
	<li>The number of nodes in the tree is in the range <code>[1, 104]</code>.</li>
	<li><code>1 &lt;= Node.val &lt;= 105</code></li>
</ul>

balanceBST

Balance a Binary Search Tree

Greedy

Tree

Depth-First Search

Binary Search Tree

Divide and Conquer

Binary Tree

给你一棵二叉搜索树，请你返回一棵&nbsp;平衡后&nbsp;的二叉搜索树，新生成的树应该与原来的树有着相同的节点值。如果有多种构造方法，请你返回任意一种。

如果一棵二叉搜索树中，每个节点的两棵子树高度差不超过 <code>1</code> ，我们就称这棵二叉搜索树是&nbsp;平衡的 。

&nbsp;

示例 1：

<img src="https://assets.leetcode.com/uploads/2021/08/10/balance1-tree.jpg" style="height: 319px; width: 500px;" />

<pre>
输入：root = [1,null,2,null,3,null,4,null,null]
输出：[2,1,3,null,null,null,4]
解释：这不是唯一的正确答案，[3,1,4,null,2,null,null] 也是一个可行的构造方案。
</pre>

示例 2：

<img src="https://assets.leetcode.com/uploads/2021/08/10/balanced2-tree.jpg" style="height: 145px; width: 224px;" />

<pre>
输入: root = [2,1,3]
输出: [2,1,3]
</pre>

&nbsp;

提示：

<ul>
	<li>树节点的数目在&nbsp;<code>[1, 104]</code>&nbsp;范围内。</li>
	<li><code>1 &lt;= Node.val &lt;= 105</code></li>
</ul>