# 654. Maximum Binary Tree
## Problem Statement
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:**
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:**
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**.
## Intuition
```
Here, we recursively build the tree, Divide into left
and right sub-tree
Find the maximum and build
```
### Links
### Video Links
### Approach 1:
```
Recursion
```
{% code title="C++" lineNumbers="true" %}
```cpp
class Solution {
public:
TreeNode* find_ans(vector& nums, int i, int j){
if(i>j)
return nullptr;
int index = helper(nums, i, j);
TreeNode *root = new TreeNode(nums[index]);
root->left = find_ans(nums, i, index-1);
root->right = find_ans(nums, index+1, j);
return root;
}
int helper(vector& nums, int i, int j){
int idx = 0;
int maxi = 0;
for(int index=i; index<=j; index++){
if(maxi <= nums[index]){
maxi = nums[index];
idx = index;
}
}
return idx;
}
TreeNode* constructMaximumBinaryTree(vector& nums) {
int i=0;
int j=nums.size()-1;
return find_ans(nums, i, j);
}
};
```
{% endcode %}
### Approach 2:
```
```
{% code title="C++" lineNumbers="true" %}
```cpp
```
{% endcode %}
### Approach 3:
```
```
{% code title="C++" lineNumbers="true" %}
```cpp
```
{% endcode %}
### Approach 4:
{% code title="C++" lineNumbers="true" %}
```cpp
```
{% endcode %}
### Similar Problems
###
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