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

Recommended: Please try your approach on {IDE} first, before moving on to the solution.

Following is the implementation of above algorithm.

C++

 /* Program to find height of the tree by Iterative Method */ #include #include 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 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; }

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Java

 // An iterative java program to find height of binary tree     import java.util.LinkedList; import java.util.Queue;     // A binary tree node class Node  {     int data;     Node left, right;         Node(int item)      {         data = item;         left = right;     } }     class BinaryTree  {     Node root;         // Iterative method to find height of Bianry Tree     int treeHeight(Node node)      {         // Base Case         if (node == null)             return 0;             // Create an empty queue for level order tarversal         Queue q = new LinkedList();             // Enqueue Root and initialize height         q.add(node);         int height = 0;             while (1 == 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 newnode = q.peek();                 q.remove();                 if (newnode.left != null)                     q.add(newnode.left);                 if (newnode.right != null)                     q.add(newnode.right);                 nodeCount--;             }         }     }         // Driver program to test above functions     public static void main(String args[])      {         BinaryTree tree = new BinaryTree();                    // Let us create a binary tree shown in above diagram         tree.root = new Node(1);         tree.root.left = new Node(2);         tree.root.right = new Node(3);         tree.root.left.left = new Node(4);         tree.root.left.right = new Node(5);         System.out.println("Height of tree is " + tree.treeHeight(tree.root));     } }     // This code has been contributed by Mayank Jaiswal

Python

 # Program to find height of tree by Iteration Method    # A binary tree node class Node:            # Constructor to create new node     def __init__(self, data):         self.data = data          self.left = None         self.right = None    # Iterative method to find height of Binary Tree def treeHeight(root):            # Base Case     if root is None:         return 0            # Create a empty queue for level order traversal     q = []            # Enqueue Root and Initialize Height      q.append(root)     height = 0         while(True):                    # nodeCount(queue size) indicates number of nodes         # at current level         nodeCount = len(q)         if nodeCount == 0 :             return height                 height += 1             # Dequeue all nodes of current level and Enqueue         # all nodes of next level         while(nodeCount > 0):             node = q             q.pop(0)             if node.left is not None:                 q.append(node.left)             if node.right is not None:                 q.append(node.right)                nodeCount -= 1       # Driver program to test above function # Let us create binary tree shown in above diagram root = Node(1) root.left = Node(2) root.right = Node(3) root.left.left = Node(4) root.left.right = Node(5)    print "Height of tree is", treeHeight(root)    # This code is contributed by Nikhil Kumar Singh(nickzuck_007)

C#

 // An iterative C# program to // find height of binary tree using System; using System.Collections.Generic;     // A binary tree node class Node  {     public int data;     public Node left, right;        public Node(int item)      {         data = item;         left = right;     } }    public class BinaryTree  {     Node root;        // Iterative method to find     // height of Bianry Tree     int treeHeight(Node node)      {         // Base Case         if (node == null)             return 0;            // Create an empty queue          // for level order tarversal         Queue q = new Queue();            // Enqueue Root and initialize height         q.Enqueue(node);         int height = 0;            while (1 == 1)          {             // nodeCount (queue size) indicates             // number of nodes at current lelvel.             int nodeCount = q.Count;             if (nodeCount == 0)                 return height;             height++;                // Dequeue all nodes of current             // level and Enqueue all             // nodes of next level             while (nodeCount > 0)              {                 Node newnode = q.Peek();                 q.Dequeue();                 if (newnode.left != null)                     q.Enqueue(newnode.left);                 if (newnode.right != null)                     q.Enqueue(newnode.right);                 nodeCount--;             }         }     }        // Driver code     public static void Main(String []args)      {         BinaryTree tree = new BinaryTree();                    // Let us create a binary          // tree shown in above diagram         tree.root = new Node(1);         tree.root.left = new Node(2);         tree.root.right = new Node(3);         tree.root.left.left = new Node(4);         tree.root.left.right = new Node(5);         Console.WriteLine("Height of tree is " +                          tree.treeHeight(tree.root));     } }    // This code has been contributed by 29AjayKumar

Output:

Height of tree is 3

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

tags:

Queue Tree Queue Tree