# 654. Maximum Binary Tree

**<font color=red>难度: Medium</font>**

## 刷题内容

> 原题连接

* https://leetcode.com/problems/maximum-binary-tree/

> 内容描述

```
Given an integer array with no duplicates. A maximum tree building on this array is defined as follow:

The root is the maximum number in the array.
The left subtree is the maximum tree constructed from left part subarray divided by the maximum number.
The right subtree is the maximum tree constructed from right part subarray divided by the maximum number.
Construct the maximum tree by the given array and output the root node of this tree.

Example 1:
Input: [3,2,1,6,0,5]
Output: return the tree root node representing the following tree:

      6
    /   \
   3     5
    \    / 
     2  0   
       \
        1
Note:
The size of the given array will be in the range [1,1000].
```

## 解题方案

> 思路 1
******- 时间复杂度: O(N^2)******- 空间复杂度: O(N)******

递归


```python
class Solution:
    def constructMaximumBinaryTree(self, nums: List[int]) -> TreeNode:
        if not nums:
            return None
        maxx, idx = -sys.maxsize, -1
        for i, num in enumerate(nums):
            if num > maxx:
                maxx = num
                idx = i
        root = TreeNode(maxx)
        root.left = self.constructMaximumBinaryTree(nums[:idx])
        root.right = self.constructMaximumBinaryTree(nums[idx+1:])
        return root
```




























