Iterative Method to find Height of Binary Tree

There are two conventions to define height of Binary Tree
1) Number of nodes on longest path from root to the deepest node.
2) Number of edges on longest path from root to the deepest node.
In this post, the first convention is followed. For example, height of the below tree is 3.

Example Tree

Recursive method to find height of Binary Tree is discussed here. How to find height without recursion? We can use level order traversal to find height without recursion. The idea is to traverse level by level. Whenever move down to a level, increment height by 1 (height is initialized as 0). Count number of nodes at each level, stop traversing when count of nodes at next level is 0.
Following is detailed algorithm to find level order traversal using queue.

Create a queue.
Push root into the queue.
height = 0
Loop
 nodeCount = size of queue
        
        // If number of nodes at this level is 0, return height
 if nodeCount is 0
  return Height;
 else
  increase Height

        // Remove nodes of this level and add nodes of 
        // next level
 while (nodeCount > 0)
  pop node from front
  push its children to queue
  decrease nodeCount
       // At this point, queue has nodes of next level

Following is the implementation of above algorithm.

/* Program to find height of the tree by Iterative Method */ #include <iostream> #include <queue> using namespace std;   // A Binary Tree Node struct node {     struct node *left;     int data;     struct node *right; };   // Iterative method to find height of Bianry Tree int treeHeight(node *root) {     // Base Case     if (root == NULL)         return 0;       // Create an empty queue for level order tarversal     queue<node *> q;       // Enqueue Root and initialize height     q.push(root);     int height = 0;       while (1)     {         // nodeCount (queue size) indicates number of nodes         // at current lelvel.         int nodeCount = q.size();         if (nodeCount == 0)             return height;           height++;           // Dequeue all nodes of current level and Enqueue all         // nodes of next level         while (nodeCount > 0)         {             node *node = q.front();             q.pop();             if (node->left != NULL)                 q.push(node->left);             if (node->right != NULL)                 q.push(node->right);             nodeCount--;         }     } }   // Utility function to create a new tree node node* newNode(int data) {     node *temp = new node;     temp->data = data;     temp->left = NULL;     temp->right = NULL;     return temp; }   // Driver program to test above functions int main() {     // Let us create binary tree shown in above diagram     node *root = newNode(1);     root->left = newNode(2);     root->right = newNode(3);     root->left->left = newNode(4);     root->left->right = newNode(5);       cout << "Height of tree is " << treeHeight(root);     return 0; }

Output:

Height of tree is 3

Time Complexity: O(n) where n is number of nodes in given binary tree.