# 0654. Maximum Binary Tree

<https://leetcode.com/problems/maximum-binary-tree>

## Description

You are given an integer array `nums` with no duplicates. A **maximum binary tree** can be built recursively from `nums` using the following algorithm:

1. Create a root node whose value is the maximum value in `nums`.
2. Recursively build the left subtree on the **subarray prefix** to the **left** of the maximum value.
3. Recursively build the right subtree on the **subarray suffix** to the **right** of the maximum value.

Return *the **maximum binary tree** built from* `nums`.

**Example 1:**

![](https://assets.leetcode.com/uploads/2020/12/24/tree1.jpg)

```
**Input:** nums = [3,2,1,6,0,5]
**Output:** [6,3,5,null,2,0,null,null,1]
**Explanation:** The recursive calls are as follow:
- The largest value in [3,2,1,6,0,5] is 6. Left prefix is [3,2,1] and right suffix is [0,5].
    - The largest value in [3,2,1] is 3. Left prefix is [] and right suffix is [2,1].
        - Empty array, so no child.
        - The largest value in [2,1] is 2. Left prefix is [] and right suffix is [1].
            - Empty array, so no child.
            - Only one element, so child is a node with value 1.
    - The largest value in [0,5] is 5. Left prefix is [0] and right suffix is [].
        - Only one element, so child is a node with value 0.
        - Empty array, so no child.
```

**Example 2:**

![](https://assets.leetcode.com/uploads/2020/12/24/tree2.jpg)

```
**Input:** nums = [3,2,1]
**Output:** [3,null,2,null,1]
```

**Constraints:**

* `1 <= nums.length <= 1000`
* `0 <= nums[i] <= 1000`
* All integers in `nums` are **unique**.

## ac

```java
/**
 * Definition for a binary tree node.
 * public class TreeNode {
 *     int val;
 *     TreeNode left;
 *     TreeNode right;
 *     TreeNode(int x) { val = x; }
 * }
 */
class Solution {
    public TreeNode constructMaximumBinaryTree(int[] nums) {
        return build(nums, 0, nums.length-1);
    }

    public TreeNode build(int[] nums, int start, int end) {
        if (start > end) return null;

        // find max
        int maxIdx = -1, max = Integer.MIN_VALUE;
        for (int i = start; i <= end; i++) {
            if (nums[i] > max) {
                max = nums[i];
                maxIdx = i;
            }
        }

        // build
        TreeNode root = new TreeNode(max);
        root.left = build(nums, start, maxIdx-1);
        root.right = build(nums, maxIdx+1, end);

        return root;
    }
}

/*
just recursion build the subtree
*/
```


---

# Agent Instructions: Querying This Documentation

If you need additional information that is not directly available in this page, you can query the documentation dynamically by asking a question.

Perform an HTTP GET request on the current page URL with the `ask` query parameter:

```
GET https://jaywin.gitbook.io/leetcode/solutions/0654-maximum-binary-tree.md?ask=<question>
```

The question should be specific, self-contained, and written in natural language.
The response will contain a direct answer to the question and relevant excerpts and sources from the documentation.

Use this mechanism when the answer is not explicitly present in the current page, you need clarification or additional context, or you want to retrieve related documentation sections.