# Maximum Binary Tree II Problem

## Description

LeetCode Problem 998.

A maximum tree is a tree where every node has a value greater than any other value in its subtree. You are given the root of a maximum binary tree and an integer val.

Just as in the previous problem, the given tree was constructed from a list a (root = Construct(a)) recursively with the following Construct(a) routine:

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

Note that we were not given a directly, only a root node root = Construct(a).

Suppose b is a copy of a with the value val appended to it. It is guaranteed that b has unique values. Return Construct(b).

Example 1:

``````1
2
3
Input: root = [4,1,3,null,null,2], val = 5
Output: [5,4,null,1,3,null,null,2]
Explanation: a = [1,4,2,3], b = [1,4,2,3,5]
``````

Example 2:

``````1
2
3
Input: root = [5,2,4,null,1], val = 3
Output: [5,2,4,null,1,null,3]
Explanation: a = [2,1,5,4], b = [2,1,5,4,3]
``````

Example 3:

``````1
2
3
Input: root = [5,2,3,null,1], val = 4
Output: [5,2,4,null,1,3]
Explanation: a = [2,1,5,3], b = [2,1,5,3,4]
``````

Constraints:

• The number of nodes in the tree is in the range [1, 100].
• 1 <= Node.val <= 100
• All the values of the tree are unique.
• 1 <= val <= 100

## Sample C++ Code

``````1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
/**
* 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* insertIntoMaxTree(TreeNode* root, int val) {
if (root == nullptr)
return new TreeNode(val);

if (val > root->val)
return new TreeNode(val, root, nullptr);

root->right = insertIntoMaxTree(root->right, val);

return root;
}
};
``````