<p>A <strong>maximum tree</strong> is a tree where every node has a value greater than any other value in its subtree.</p>

<p>You are given the <code>root</code> of a maximum binary tree and an integer <code>val</code>.</p>

<p>Just as in the <a href="https://leetcode.com/problems/maximum-binary-tree/" target="_blank">previous problem</a>, the given tree was constructed from a list <code>a</code> (<code>root = Construct(a)</code>) recursively with the following <code>Construct(a)</code> routine:</p>

<ul>
	<li>If <code>a</code> is empty, return <code>null</code>.</li>
	<li>Otherwise, let <code>a[i]</code> be the largest element of <code>a</code>. Create a <code>root</code> node with the value <code>a[i]</code>.</li>
	<li>The left child of <code>root</code> will be <code>Construct([a[0], a[1], ..., a[i - 1]])</code>.</li>
	<li>The right child of <code>root</code> will be <code>Construct([a[i + 1], a[i + 2], ..., a[a.length - 1]])</code>.</li>
	<li>Return <code>root</code>.</li>
</ul>

<p>Note that we were not given <code>a</code> directly, only a root node <code>root = Construct(a)</code>.</p>

<p>Suppose <code>b</code> is a copy of <code>a</code> with the value <code>val</code> appended to it. It is guaranteed that <code>b</code> has unique values.</p>

<p>Return <code>Construct(b)</code>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2021/08/09/maxtree1.JPG" style="width: 376px; height: 235px;" />
<pre>
<strong>Input:</strong> root = [4,1,3,null,null,2], val = 5
<strong>Output:</strong> [5,4,null,1,3,null,null,2]
<strong>Explanation:</strong> a = [1,4,2,3], b = [1,4,2,3,5]
</pre>

<p><strong class="example">Example 2:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2021/08/09/maxtree21.JPG" style="width: 358px; height: 156px;" />
<pre>
<strong>Input:</strong> root = [5,2,4,null,1], val = 3
<strong>Output:</strong> [5,2,4,null,1,null,3]
<strong>Explanation:</strong> a = [2,1,5,4], b = [2,1,5,4,3]
</pre>

<p><strong class="example">Example 3:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2021/08/09/maxtree3.JPG" style="width: 404px; height: 180px;" />
<pre>
<strong>Input:</strong> root = [5,2,3,null,1], val = 4
<strong>Output:</strong> [5,2,4,null,1,3]
<strong>Explanation:</strong> a = [2,1,5,3], b = [2,1,5,3,4]
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li>The number of nodes in the tree is in the range <code>[1, 100]</code>.</li>
	<li><code>1 &lt;= Node.val &lt;= 100</code></li>
	<li>All the values of the tree are <strong>unique</strong>.</li>
	<li><code>1 &lt;= val &lt;= 100</code></li>
</ul>

/**
 * Definition for a binary tree node.
 * struct TreeNode {
 *     int val;
 *     TreeNode *left;
 *     TreeNode *right;
 *     TreeNode() : val(0), left(nullptr), right(nullptr) {}
 *     TreeNode(int x) : val(x), left(nullptr), right(nullptr) {}
 *     TreeNode(int x, TreeNode *left, TreeNode *right) : val(x), left(left), right(right) {}
 * };
 */
class Solution {
public:
      TreeNode* construct(int s,int e,vector<int>&nums){
        if(s>e){
            return NULL;
        }
        int maxval=INT_MIN;
        int maxidx=-1;
        for(int i=s;i<=e;i++){
            if(nums[i]>maxval){
                maxval=nums[i];
                maxidx=i;
            }
        }
        TreeNode* root=new TreeNode(maxval);
        root->left=construct(s,maxidx-1,nums);
        root->right=construct(maxidx+1,e,nums);
        return root;
    }

     void inorder(TreeNode* root,vector<int>&ans){
        if(root==NULL){
            return;
        }      
        inorder(root->left,ans);
        ans.push_back(root->val);
        inorder(root->right,ans);
    }

    TreeNode* insertIntoMaxTree(TreeNode* root, int val) {
        vector<int>arr;
        inorder(root,arr);
        arr.push_back(val);
        return construct(0,arr.size()-1,arr);
    }
};
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