Given a binary tree, find height of it. Height of empty tree is 0 and height of below tree is 3.
Example Tree
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 0
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
= 2 + 1
/
/
/
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maxDepth('2') = 1 maxDepth('3') = 1
= max(maxDepth('4'), maxDepth('5')) + 1
= 1 + 1 = 2
/
/
/
/
/
maxDepth('4') = 1 maxDepth('5') = 1
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 rathbhupendra |
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 Mayank Jaiswal(mayank_24) |
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 Nikhil Kumar Singh(nickzuck_007) |
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 29AjayKumar |
Output:
Height of tree is 3
Time Complexity: O(n) (Please see our post Tree Traversal for details)
References:
http://cslibrary.stanford.edu/110/BinaryTrees.html
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