Write a Program to Find the Maximum Depth or Height of a Tree
Given a binary tree, find height of it. Height of empty tree is -1, height of tree with one node is 0 and height of below tree is 2.
Recursively calculate height of left and right subtrees of a node and assign height to the node as max of the heights of two children plus 1. See below pseudo code and program for details.
Algorithm:
maxDepth() 1. If tree is empty then return -1 2. Else (a) Get the max depth of left subtree recursively i.e., call maxDepth( tree->left-subtree) (a) Get the max depth of right subtree recursively i.e., call maxDepth( tree->right-subtree) (c) Get the max of max depths of left and right subtrees and add 1 to it for the current node. max_depth = max(max dept of left subtree, max depth of right subtree) + 1 (d) Return max_depth
See the below diagram for more clarity about execution of the recursive function maxDepth() for above example tree.
maxDepth('1') = max(maxDepth('2'), maxDepth('3')) + 1 = 1 + 1 / \ / \ / \ / \ / \ maxDepth('2') = 1 maxDepth('3') = 0 = max(maxDepth('4'), maxDepth('5')) + 1 = 1 + 0 = 1 / \ / \ / \ / \ / \ maxDepth('4') = 0 maxDepth('5') = 0
Implementation:
C++
// C++ program to find height of tree #include <bits/stdc++.h> using namespace std; /* A binary tree node has data, pointer to left child and a pointer to right child */ class node { public : int data; node* left; node* right; }; /* Compute the "maxDepth" of a tree -- the number of nodes along the longest path from the root node down to the farthest leaf node.*/ int maxDepth(node* node) { if (node == NULL) return 0; else { /* compute the depth of each subtree */ int lDepth = maxDepth(node->left); int rDepth = maxDepth(node->right); /* use the larger one */ if (lDepth > rDepth) return (lDepth + 1); else return (rDepth + 1); } } /* Helper function that allocates a new node with the given data and NULL left and right pointers. */ node* newNode( int data) { node* Node = new node(); Node->data = data; Node->left = NULL; Node->right = NULL; return (Node); } // Driver code int main() { 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 " << maxDepth(root); return 0; } // This code is contributed by Amit Srivastav |
C
#include <stdio.h> #include <stdlib.h> /* A binary tree node has data, pointer to left child and a pointer to right child */ struct node { int data; struct node* left; struct node* right; }; /* Compute the "maxDepth" of a tree -- the number of nodes along the longest path from the root node down to the farthest leaf node.*/ int maxDepth( struct node* node) { if (node == NULL) return 0; else { /* compute the depth of each subtree */ int lDepth = maxDepth(node->left); int rDepth = maxDepth(node->right); /* use the larger one */ if (lDepth > rDepth) return (lDepth + 1); else return (rDepth + 1); } } /* Helper function that allocates a new node with the given data and NULL left and right pointers. */ struct node* newNode( int data) { struct node* node = ( struct node*) malloc ( sizeof ( struct node)); node->data = data; node->left = NULL; node->right = NULL; return (node); } int main() { struct node* root = newNode(1); root->left = newNode(2); root->right = newNode(3); root->left->left = newNode(4); root->left->right = newNode(5); printf ( "Height of tree is %d" , maxDepth(root)); getchar (); return 0; } |
Java
// Java program to find height of tree // A binary tree node class Node { int data; Node left, right; Node( int item) { data = item; left = right = null ; } } class BinaryTree { Node root; /* Compute the "maxDepth" of a tree -- the number of nodes along the longest path from the root node down to the farthest leaf node.*/ int maxDepth(Node node) { if (node == null ) return 0 ; else { /* compute the depth of each subtree */ int lDepth = maxDepth(node.left); int rDepth = maxDepth(node.right); /* use the larger one */ if (lDepth > rDepth) return (lDepth + 1 ); else return (rDepth + 1 ); } } /* Driver program to test above functions */ public static void main(String[] args) { BinaryTree tree = new BinaryTree(); 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.maxDepth(tree.root)); } } // This code has been contributed by Amit Srivastav |
Python3
# Python3 program to find the maximum depth of tree # A binary tree node class Node: # Constructor to create a new node def __init__( self , data): self .data = data self .left = None self .right = None # Compute the "maxDepth" of a tree -- the number of nodes # along the longest path from the root node down to the # farthest leaf node def maxDepth(node): if node is None : return 0 ; else : # Compute the depth of each subtree lDepth = maxDepth(node.left) rDepth = maxDepth(node.right) # Use the larger one if (lDepth > rDepth): return lDepth + 1 else : return rDepth + 1 # Driver program to test above function 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 %d" % (maxDepth(root))) # This code is contributed by Amit Srivastav |
C#
// C# program to find height of tree using System; // A binary tree node public class Node { public int data; public Node left, right; public Node( int item) { data = item; left = right = null ; } } public class BinaryTree { Node root; /* Compute the "maxDepth" of a tree -- the number of nodes along the longest path from the root node down to the farthest leaf node.*/ int maxDepth(Node node) { if (node == null ) return 0; else { /* compute the depth of each subtree */ int lDepth = maxDepth(node.left); int rDepth = maxDepth(node.right); /* use the larger one */ if (lDepth > rDepth) return (lDepth + 1); else return (rDepth + 1); } } /* Driver code */ public static void Main(String[] args) { BinaryTree tree = new BinaryTree(); 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.maxDepth(tree.root)); } } // This code has been contributed by // Correction done by Amit Srivastav |
Javascript
<script> // JavaScript program to find height of tree // A binary tree node class Node { constructor(item) { this .data=item; this .left= this .right= null ; } } let root; /* Compute the "maxDepth" of a tree -- the number of nodes along the longest path from the root node down to the farthest leaf node.*/ function maxDepth(node) { if (node == null ) return 0; else { /* compute the depth of each subtree */ let lDepth = maxDepth(node.left); let rDepth = maxDepth(node.right); /* use the larger one */ if (lDepth > rDepth) return (lDepth + 1); else return (rDepth + 1); } } /* Driver program to test above functions */ root = new Node(1); root.left = new Node(2); root.right = new Node(3); root.left.left = new Node(4); root.left.right = new Node(5); document.write( "Height of tree is : " + maxDepth(root)); // This code is contributed by rag2127 //Correction done by Amit Srivastav </script> |
Height of tree is 3
Time Complexity: O(n) (Please see our post Tree Traversal for details)
Auxiliary Space: O(n) due to recursive calls.
Method 2: Another method to solve this problem is to do Level Order Traversal. While doing the level order traversal, while adding Nodes at each level to Queue, we have to add NULL Node so that whenever it is encountered, we can increment the value of variable and that level get counted.
Implementation:
C++
#include <iostream> #include <bits/stdc++.h> using namespace std; // A Tree node struct Node { int key; struct Node* left, *right; }; // Utility function to create a new node Node* newNode( int key) { Node* temp = new Node; temp->key = key; temp->left = temp->right = NULL; return (temp); } /*Function to find the height(depth) of the tree*/ int height( struct Node* root){ //Initialising a variable to count the //height of tree int depth = 0; queue<Node*>q; //Pushing first level element along with NULL q.push(root); q.push(NULL); while (!q.empty()){ Node* temp = q.front(); q.pop(); //When NULL encountered, increment the value if (temp == NULL){ depth++; } //If NULL not encountered, keep moving if (temp != NULL){ if (temp->left){ q.push(temp->left); } if (temp->right){ q.push(temp->right); } } //If queue still have elements left, //push NULL again to the queue. else if (!q.empty()){ q.push(NULL); } } return depth; } // Driver program int main() { // Let us create Binary Tree shown in above example Node *root = newNode(1); root->left = newNode(12); root->right = newNode(13); root->right->left = newNode(14); root->right->right = newNode(15); root->right->left->left = newNode(21); root->right->left->right = newNode(22); root->right->right->left = newNode(23); root->right->right->right = newNode(24); cout<< "Height(Depth) of tree is: " <<height(root); } |
Java
// Java program for above approach import java.util.LinkedList; import java.util.Queue; class GFG { // A tree node structure static class Node { int key; Node left; Node right; } // Utility function to create // a new node static Node newNode( int key) { Node temp = new Node(); temp.key = key; temp.left = temp.right = null ; return temp; } /*Function to find the height(depth) of the tree*/ public static int height( Node root){ //Initialising a variable to count the //height of tree int depth = 0 ; Queue<Node> q= new LinkedList<>(); //Pushing first level element along with null q.add(root); q.add( null ); while (!q.isEmpty()){ Node temp = q.peek(); q.remove(); //When null encountered, increment the value if (temp == null ){ depth++; } //If null not encountered, keep moving if (temp != null ){ if (temp.left!= null ){ q.add(temp.left); } if (temp.right!= null ){ q.add(temp.right); } } //If queue still have elements left, //push null again to the queue. else if (!q.isEmpty()){ q.add( null ); } } return depth; } // Driver Code public static void main(String args[]) { Node root = newNode( 1 ); root.left = newNode( 12 ); root.right = newNode( 13 ); root.right.left = newNode( 14 ); root.right.right = newNode( 15 ); root.right.left.left = newNode( 21 ); root.right.left.right = newNode( 22 ); root.right.right.left = newNode( 23 ); root.right.right.right = newNode( 24 ); System.out.println( "Height(Depth) of tree is: " +height(root)); } } // This code is contributed by jana_sayantan. |
Python3
# Python code to implement the approach # A Tree node class Node: def __init__( self ): self .key = 0 self .left, self .right = None , None # Utility function to create a new node def newNode(key): temp = Node() temp.key = key temp.left,temp.right = None , None return temp # Function to find the height(depth) of the tree def height(root): #Initialising a variable to count the #height of tree depth = 0 q = [] #appending first level element along with None q.append(root) q.append( None ) while ( len (q)> 0 ): temp = q[ 0 ] q = q[ 1 :] #When None encountered, increment the value if (temp = = None ): depth + = 1 #If None not encountered, keep moving if (temp ! = None ): if (temp.left): q.append(temp.left) if (temp.right): q.append(temp.right) #If queue still have elements left, #append None again to the queue. elif ( len (q)> 0 ): q.append( None ) return depth # Driver program # Let us create Binary Tree shown in above example root = newNode( 1 ) root.left = newNode( 12 ) root.right = newNode( 13 ) root.right.left = newNode( 14 ) root.right.right = newNode( 15 ) root.right.left.left = newNode( 21 ) root.right.left.right = newNode( 22 ) root.right.right.left = newNode( 23 ) root.right.right.right = newNode( 24 ) print (f "Height(Depth) of tree is: {height(root)}" ) # This code is contributed by shinjanpatra |
Javascript
<script> // JavaScript code to implement the approach // A Tree node class Node{ constructor(){ this .key = 0 this .left = null this .right = null } } // Utility function to create a new node function newNode(key){ let temp = new Node() temp.key = key temp.left = null temp.right = null return temp } // Function to find the height(depth) of the tree function height(root){ // Initialising a variable to count the // height of tree let depth = 0 let q = [] // pushing first level element along with null q.push(root) q.push( null ) while (q.length>0){ let temp = q.shift() // When null encountered, increment the value if (temp == null ) depth += 1 // If null not encountered, keep moving if (temp != null ){ if (temp.left) q.push(temp.left) if (temp.right) q.push(temp.right) } // If queue still have elements left, // push null again to the queue. else if (q.length>0) q.push( null ) } return depth } // Driver program // Let us create Binary Tree shown in above example let root = newNode(1) root.left = newNode(12) root.right = newNode(13) root.right.left = newNode(14) root.right.right = newNode(15) root.right.left.left = newNode(21) root.right.left.right = newNode(22) root.right.right.left = newNode(23) root.right.right.right = newNode(24) document.write(`Height(Depth) of tree is: ${height(root)}`, "</br>" ) // This code is contributed by shinjanpatra </script> |
Height(Depth) of tree is: 4
Time Complexity: O(n)
Auxiliary Space: O(n)