Maximum Binary Tree II in C++

Suppose we have a root node of a maximum tree: The maximum tree is a tree where every node has a value greater than any other value in its subtree. Suppose we have a method called construct(). This can construct a root from a list A. The construct() method is like −

  • If list A is empty, return null.

  • Otherwise, let A[i] be the largest element of the list A. Then create a root node with 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[n - 1]]) [n is the length of A]

  • Return root.

Note that we were not given A directly, only a root node root = construct(A). Now suppose B is a copy of A with the value val added to it. It is guaranteed that B has unique values. We have to construct(B). If value is 5 and the input tree is like −

The output tree is like −

To solve this, we will follow these steps −

  • define one recursive method solve(). This is taking root and val

  • If tree is empty, then create a new node with value val, and return that node

  • if value of root < val, then

    • temp := new node whose value is val

    • left of temp := root

    • return temp

  • right of root := solve(right of root, val)

  • return root

Let us see the following implementation to get better understanding −


 Live Demo

#include <bits/stdc++.h>
using namespace std;
class TreeNode{
   int val;
   TreeNode *left, *right;
   TreeNode(int data){
      val = data;
      left = NULL;
      right = NULL;
void insert(TreeNode **root, int val){
   queue<TreeNode*> q;
      TreeNode *temp = q.front();
         if(val != NULL)
            temp->left = new TreeNode(val);
            temp->left = new TreeNode(0);
         if(val != NULL)
            temp->right = new TreeNode(val);
            temp->right = new TreeNode(0);
TreeNode *make_tree(vector<int> v){
   TreeNode *root = new TreeNode(v[0]);
   for(int i = 1; i<v.size(); i++){
      insert(&root, v[i]);
   return root;
void tree_level_trav(TreeNode*root){
   if (root == NULL) return;
   cout << "[";
   queue<TreeNode *> q;
   TreeNode *curr;
   while (q.size() > 1) {
      curr = q.front();
      if (curr == NULL){
      else {
         if(curr == NULL || curr->val == 0){
            cout << "null" << ", ";
            cout << curr->val << ", ";
   cout << "]"<<endl;
class Solution {
   TreeNode* insertIntoMaxTree(TreeNode* root, int val) {
      if(!root)return new TreeNode(val);
      if(root->val < val){
         TreeNode* temp = new TreeNode(val);
         temp->left = root;
         return temp;
      root->right = insertIntoMaxTree(root->right, val);
      return root;
   vector<int> v = {4,1,3,NULL,NULL,2};
   TreeNode *root = make_tree(v);
   Solution ob;
   tree_level_trav(ob.insertIntoMaxTree(root, 5));




[5, 4, 1, 3, null, null, 2, ]