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 0 and height of below tree is 3.

Example Tree

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
                                  /    \
                                /         \
                              /             \
                            /                 \
                          /                     \
               maxDepth('1')                  maxDepth('3') = 1
= max(maxDepth('4'), maxDepth('5')) + 1
= 1 + 1   = 2         
                   /    \
                 /        \
               /            \
             /                \
           /                    \
 maxDepth('4') = 1     maxDepth('5') = 1

Implementation:

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("Hight 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 cpontributed by Mayank Jaiswal(mayank_24)

Python


# Python 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)



Time Complexity:
O(n) (Please see our post Tree Traversal for details)

References:
http://cslibrary.stanford.edu/110/BinaryTrees.html

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