# Iterative Method to find Height of Binary Tree

• Difficulty Level : Easy
• Last Updated : 21 Jun, 2022

There are two conventions to define the height of a Binary Tree

1. Number of nodes on the longest path from the root to the deepest node.
2. Number of edges on the longest path from the root to the deepest node.

In this post, the first convention is followed. For example, the height of the below tree is 3.

The recursive method to find the height of the 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 the count of nodes at the next level is 0.

Following is a detailed algorithm to find level order traversal using a queue.

```Create a queue.
Push root into the queue.
height = 0
nodeCount = 0 // Number of nodes in the current level.

// If the number of nodes in the queue is 0, it implies
// that all the levels of the tree have been parsed. So,
// return the height. Otherwise count the number of nodes
// in the current level and push the children of all the
// nodes in the current level to the queue.

Loop
nodeCount = size of queue

// If the 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)
push its children to queue
pop node from front
decrease nodeCount
// At this point, queue has nodes of next level```

Following is the implementation of the above algorithm.

## C++

 `#include ``#include ` `using` `namespace` `std;` `// This approach counts the number of nodes from root to the``// leaf to calculate the height of the tree.` `// Defining the structure of a Node.` `class` `Node {``public``:``    ``int` `data;``    ``Node* left;``    ``Node* right;``};` `// Helper function to create a newnode.``// Input: Data for the newnode.``// Return: Address of the newly created node.` `Node* createNode(``int` `data)``{` `    ``Node* newnode = ``new` `Node();``    ``newnode->data = data;``    ``newnode->left = NULL;``    ``newnode->right = NULL;` `    ``return` `newnode;``}` `// Function to calculate the height of given Binary Tree.``// Input: Address of the root node of Binary Tree.``// Return: Height of Binary Tree as a integer. This includes``// the number of nodes from root to the leaf.` `int` `calculateHeight(Node* root)``{``    ``queue nodesInLevel;``    ``int` `height = 0;``    ``int` `nodeCount = 0; ``// Calculate  number of nodes in a level.``    ``Node* currentNode; ``// Pointer to store the address of a``                       ``// node in the current level.``    ``if` `(root == NULL) {``        ``return` `0;``    ``}``    ``nodesInLevel.push(root);``    ``while` `(!nodesInLevel.empty()) {``        ``// This while loop runs for every level and``        ``// increases the height by 1 in each iteration. If``        ``// the queue is empty then it implies that the last``        ``// level of tree has been parsed.``        ``height++;``        ``// Create another while loop which will insert all``        ``// the child nodes of the current level in the``        ``// queue.` `        ``nodeCount = nodesInLevel.size();``        ``while` `(nodeCount--) {``            ``currentNode = nodesInLevel.front();` `            ``// Check if the current nodes has left child and``            ``// insert it in the queue.` `            ``if` `(currentNode->left != NULL) {``                ``nodesInLevel.push(currentNode->left);``            ``}` `            ``// Check if the current nodes has right child``            ``// and insert it in the queue.``            ``if` `(currentNode->right != NULL) {``                ``nodesInLevel.push(currentNode->right);``            ``}` `            ``// Once the children of the current node are``            ``// inserted. Delete the current node.` `            ``nodesInLevel.pop();``        ``}``    ``}``    ``return` `height;``}` `// Driver Function.` `int` `main()``{``    ``// Creating a binary tree.` `    ``Node* root = NULL;` `    ``root = createNode(1);``    ``root->left = createNode(2);``    ``root->left->left = createNode(4);``    ``root->left->right = createNode(5);``    ``root->right = createNode(3);` `    ``cout << ``"The height of the binary tree using iterative "``            ``"method is: "` `<< calculateHeight(root) << ``"."``;` `    ``return` `0;``}`

## 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 Binary Tree``    ``int` `treeHeight(Node node)``    ``{``        ``// Base Case``        ``if` `(node == ``null``)``            ``return` `0``;`` ` `        ``// Create an empty queue for level order traversal``        ``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 level.``            ``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`

## Python3

 `# 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[``0``]``            ``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 Binary Tree``    ``int` `treeHeight(Node node)``    ``{``        ``// Base Case``        ``if` `(node == ``null``)``            ``return` `0;` `        ``// Create an empty queue``        ``// for level order traversal``        ``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 level.``            ``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`

## Javascript

 ``

Output

`The height of the binary tree using iterative method is: 3.`

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

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