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, 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 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
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)
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.
C++
/* 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 the height of Binary 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; } |
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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 Binary Tree int treeHeight(Node node) { // Base Case if (node == null) return 0; // Create an empty queue for level order tarversal Queue<Node> 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 |
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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[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) |
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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 tarversal Queue<Node> q = new Queue<Node>(); // 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 |
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Output:
Height of tree is 3
Time Complexity: O(n) where n is number of nodes in given binary tree.
This article is contributed by Rahul Kumar. Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above
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