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Find Minimum Depth of a Binary Tree

Find the Deepest Node in a Binary Tree

Last Updated : 15 Feb, 2023

Given a binary tree, find the deepest node in it.

Examples:

Input : Root of below tree             1           /   \          2      3         / \    / \         4   5  6   7                    \                     8 Output : 8  Input : Root of below tree             1           /   \          2      3                /                6   Output : 6

Method 1: The idea is to do Inorder traversal of a given binary tree. While doing Inorder traversal, we pass level of current node also. We keep track of the maximum level seen so far and the value of the deepest node seen so far.

Implementation:

C++

   // A C++ program to find value of the deepest node
// in a given binary tree
#include <bits/stdc++.h>
using namespace std;
 
// A tree node
struct Node
{
    int data;
    struct Node *left, *right;
};
 
// Utility function to create a new node
Node *newNode(int data)
{
    Node *temp = new Node;
    temp->data = data;
    temp->left = temp->right = NULL;
    return temp;
}
 
// maxLevel : keeps track of maximum level seen so far.
// res :  Value of deepest node so far.
// level : Level of root
void find(Node *root, int level, int &maxLevel, int &res)
{
    if (root != NULL)
    {
        find(root->left, ++level, maxLevel, res);
 
        // Update level and rescue
        if (level > maxLevel)
        {
            res = root->data;
            maxLevel = level;
        }
 
        find(root->right, level, maxLevel, res);
    }
}
 
// Returns value of deepest node
int deepestNode(Node *root)
{
    // Initialize result and max level
    int res = -1;
    int maxLevel = -1;
 
    // Updates value "res" and "maxLevel"
    // Note that res and maxLen are passed
    // by reference.
    find(root, 0, maxLevel, res);
    return res;
}
 
// Driver program
int main()
{
    Node* root = newNode(1);
    root->left = newNode(2);
    root->right = newNode(3);
    root->left->left = newNode(4);
    root->right->left = newNode(5);
    root->right->right = newNode(6);
    root->right->left->right = newNode(7);
    root->right->right->right = newNode(8);
    root->right->left->right->left = newNode(9);
    cout << deepestNode(root);
    return 0;
}
 
  

Java

   // Java program to find value of the deepest node 
// in a given binary tree 
class GFG 
{
 
    // A tree node 
    static class Node
    {
 
        int data;
        Node left, right;
 
        Node(int key) 
        {
            data = key;
            left = null;
            right = null;
        }
    }
    static int maxLevel = -1;
    static int res = -1;
 
    // maxLevel : keeps track of maximum level seen so far. 
    // res : Value of deepest node so far. 
    // level : Level of root 
    static void find(Node root, int level) 
    {
        if (root != null) 
        {
            find(root.left, ++level);
 
            // Update level and rescue 
            if (level > maxLevel) 
            {
                res = root.data;
                maxLevel = level;
            }
 
            find(root.right, level);
        }
    }
 
    // Returns value of deepest node 
    static int deepestNode(Node root) 
    {
        // Initialize result and max level 
        /* int res = -1; 
        int maxLevel = -1; */
 
        // Updates value "res" and "maxLevel" 
        // Note that res and maxLen are passed 
        // by reference. 
        find(root, 0);
        return res;
    }
 
    // Driver code 
    public static void main(String[] args)
    {
 
        Node root = new Node(1);
        root.left = new Node(2);
        root.right = new Node(3);
        root.left.left = new Node(4);
        root.right.left = new Node(5);
        root.right.right = new Node(6);
        root.right.left.right = new Node(7);
        root.right.right.right = new Node(8);
        root.right.left.right.left = new Node(9);
        System.out.println(deepestNode(root));
    }
}
 
// This code is contributed by Princi Singh
 
  

Python3

   """Python3 program to find value of the 
deepest node in a given binary tree"""
 
# A Binary Tree Node 
# Utility function to create a
# new tree node 
class newNode: 
 
    # Constructor to create a newNode 
    def __init__(self, data): 
        self.data= data 
        self.left = None
        self.right = None
        self.visited = False
 
# maxLevel : keeps track of maximum 
# level seen so far. 
# res : Value of deepest node so far. 
# level : Level of root 
def find(root, level, maxLevel, res):
 
    if (root != None):
        level += 1
        find(root.left, level, maxLevel, res) 
 
        # Update level and rescue 
        if (level > maxLevel[0]):
         
            res[0] = root.data 
            maxLevel[0] = level 
         
        find(root.right, level, maxLevel, res) 
         
# Returns value of deepest node 
def deepestNode(root) :
 
    # Initialize result and max level 
    res = [-1] 
    maxLevel = [-1] 
 
    # Updates value "res" and "maxLevel" 
    # Note that res and maxLen are passed 
    # by reference. 
    find(root, 0, maxLevel, res) 
    return res[0]
                         
# Driver Code
if __name__ == '__main__':
    root = newNode(1) 
    root.left = newNode(2) 
    root.right = newNode(3) 
    root.left.left = newNode(4) 
    root.right.left = newNode(5) 
    root.right.right = newNode(6) 
    root.right.left.right = newNode(7) 
    root.right.right.right = newNode(8) 
    root.right.left.right.left = newNode(9) 
    print(deepestNode(root))
 
# This code is contributed by
# SHUBHAMSINGH10
 
  

C#

   // C# program to find value of the deepest node 
// in a given binary tree 
using System;
     
class GFG 
{
 
    // A tree node 
    public class Node
    {
 
        public int data;
        public Node left, right;
 
        public Node(int key) 
        {
            data = key;
            left = null;
            right = null;
        }
    }
    static int maxLevel = -1;
    static int res = -1;
 
    // maxLevel : keeps track of maximum level seen so far. 
    // res : Value of deepest node so far. 
    // level : Level of root 
    static void find(Node root, int level) 
    {
        if (root != null) 
        {
            find(root.left, ++level);
 
            // Update level and rescue 
            if (level > maxLevel) 
            {
                res = root.data;
                maxLevel = level;
            }
 
            find(root.right, level);
        }
    }
 
    // Returns value of deepest node 
    static int deepestNode(Node root) 
    {
        // Initialize result and max level 
        /* int res = -1; 
        int maxLevel = -1; */
 
        // Updates value "res" and "maxLevel" 
        // Note that res and maxLen are passed 
        // by reference. 
        find(root, 0);
        return res;
    }
 
    // Driver code 
    public static void Main(String[] args)
    {
 
        Node root = new Node(1);
        root.left = new Node(2);
        root.right = new Node(3);
        root.left.left = new Node(4);
        root.right.left = new Node(5);
        root.right.right = new Node(6);
        root.right.left.right = new Node(7);
        root.right.right.right = new Node(8);
        root.right.left.right.left = new Node(9);
        Console.WriteLine(deepestNode(root));
    }
}
 
// This code is contributed by 29AjayKumar
 
  

Javascript

   <script>
 
// JavaScript program to find value of the deepest node
// in a given binary tree
 
class Node
{
    constructor(key)
    {
        this.data = key;
            this.left = null;
            this.right = null;
    }
}
 
let maxLevel = -1;
let res = -1;
 
// maxLevel : keeps track of maximum level seen so far.
    // res : Value of deepest node so far.
    // level : Level of root
function find(root,level)
{
    if (root != null)
        {
            find(root.left, ++level);
  
            // Update level and rescue
            if (level > maxLevel)
            {
                res = root.data;
                maxLevel = level;
            }
  
            find(root.right, level);
        }
}
 
// Returns value of deepest node
function deepestNode(root)
{
    // Initialize result and max level
        /* int res = -1;
        int maxLevel = -1; */
  
        // Updates value "res" and "maxLevel"
        // Note that res and maxLen are passed
        // by reference.
        find(root, 0);
        return res;
}
 
// Driver code
let root = new Node(1);
root.left = new Node(2);
root.right = new Node(3);
root.left.left = new Node(4);
root.right.left = new Node(5);
root.right.right = new Node(6);
root.right.left.right = new Node(7);
root.right.right.right = new Node(8);
root.right.left.right.left = new Node(9);
document.write(deepestNode(root));
 
 
// This code is contributed by rag2127
 
</script>
 
  

Output

Time Complexity: O(n)

Auxiliary Space: O(n) for call stack

Method 2: The idea here is to find the height of the given tree and then print the node at the bottom-most level.

Implementation:

C++

   // A C++ program to find value of the 
// deepest node in a given binary tree
#include <bits/stdc++.h>
using namespace std;
 
// A tree node with constructor
class Node
{
public:
    int data;
    Node *left, *right;
     
    // constructor    
    Node(int key)
    {
        data = key;
        left = NULL;
        right = NULL;
    }
};
 
// Utility function to find height 
// of a tree, rooted at 'root'.
int height(Node* root)
{
  if(!root) return 0;
   
  int leftHt = height(root->left);
  int rightHt = height(root->right);
   
  return max(leftHt, rightHt) + 1;
}
 
// levels : current Level
// Utility function to print all 
// nodes at a given level.
void deepestNode(Node* root, int levels)
{
    if(!root) return;
     
    if(levels == 1)
    cout << root->data;
     
    else if(levels > 1)
    {
        deepestNode(root->left, levels - 1);
        deepestNode(root->right, levels - 1);
    }
}
 
// Driver program
int main()
{
    Node* root = new Node(1);
    root->left = new Node(2);
    root->right = new Node(3);
    root->left->left = new Node(4);
    root->right->left = new Node(5);
    root->right->right = new Node(6);
    root->right->left->right = new Node(7);
    root->right->right->right = new Node(8);
    root->right->left->right->left = new Node(9);
     
    // Calculating height of tree
    int levels = height(root);
     
    // Printing the deepest node
    deepestNode(root, levels);
     
    return 0;
}
 
// This code is contributed by decode2207.
 
  

Java

   // A Java program to find value of the 
// deepest node in a given binary tree
class GFG
{
     
// A tree node with constructor
static class Node
{
    int data;
    Node left, right;
     
    // constructor 
    Node(int key)
    {
        data = key;
        left = null;
        right = null;
    }
};
 
// Utility function to find height 
// of a tree, rooted at 'root'.
static int height(Node root)
{
    if(root == null) return 0;
         
    int leftHt = height(root.left);
    int rightHt = height(root.right);
         
    return Math.max(leftHt, rightHt) + 1;
}
 
// levels : current Level
// Utility function to print all 
// nodes at a given level.
static void deepestNode(Node root, 
                        int levels)
{
    if(root == null) return;
     
    if(levels == 1)
    System.out.print(root.data + " ");
     
    else if(levels > 1)
    {
        deepestNode(root.left, levels - 1);
        deepestNode(root.right, levels - 1);
    }
}
 
// Driver Codede
public static void main(String args[])
{
    Node root = new Node(1);
    root.left = new Node(2);
    root.right = new Node(3);
    root.left.left = new Node(4);
    root.right.left = new Node(5);
    root.right.right = new Node(6);
    root.right.left.right = new Node(7);
    root.right.right.right = new Node(8);
    root.right.left.right.left = new Node(9);
     
    // Calculating height of tree
    int levels = height(root);
     
    // Printing the deepest node
    deepestNode(root, levels);
}
}
 
// This code is contributed by Arnab Kundu
 
  

Python3

   # A Python3 program to find value of the 
# deepest node in a given binary tree 
class new_Node:
    def __init__(self, key):
        self.data = key
        self.left = self.right = None
         
# Utility function to find height 
# of a tree, rooted at 'root'. 
def height(root):
    if(not root):
        return 0
     
    leftHt = height(root.left) 
    rightHt = height(root.right) 
     
    return max(leftHt, rightHt) + 1
 
# levels : current Level 
# Utility function to print all 
# nodes at a given level. 
def deepestNode(root, levels):
    if(not root):
        return
     
    if(levels == 1):
        print(root.data) 
    elif(levels > 1):
        deepestNode(root.left, levels - 1) 
        deepestNode(root.right, levels - 1)
 
# Driver Code
if __name__ == '__main__':
 
    root = new_Node(1) 
    root.left = new_Node(2) 
    root.right = new_Node(3) 
    root.left.left = new_Node(4) 
    root.right.left = new_Node(5) 
    root.right.right = new_Node(6) 
    root.right.left.right = new_Node(7) 
    root.right.right.right = new_Node(8) 
    root.right.left.right.left = new_Node(9) 
     
    # Calculating height of tree 
    levels = height(root) 
     
    # Printing the deepest node 
    deepestNode(root, levels)
 
# This code is contributed by PranchalK
 
  

C#

   // C# program to find value of the 
// deepest node in a given binary tree
using System;
     
class GFG
{
     
// A tree node with constructor
public class Node
{
    public int data;
    public Node left, right;
     
    // constructor 
    public Node(int key)
    {
        data = key;
        left = null;
        right = null;
    }
};
 
// Utility function to find height 
// of a tree, rooted at 'root'.
static int height(Node root)
{
    if(root == null) return 0;
         
    int leftHt = height(root.left);
    int rightHt = height(root.right);
         
    return Math.Max(leftHt, rightHt) + 1;
}
 
// levels : current Level
// Utility function to print all 
// nodes at a given level.
static void deepestNode(Node root, 
                        int levels)
{
    if(root == null) return;
     
    if(levels == 1)
    Console.Write(root.data + " ");
     
    else if(levels > 1)
    {
        deepestNode(root.left, levels - 1);
        deepestNode(root.right, levels - 1);
    }
}
 
// Driver Code
public static void Main(String []args)
{
    Node root = new Node(1);
    root.left = new Node(2);
    root.right = new Node(3);
    root.left.left = new Node(4);
    root.right.left = new Node(5);
    root.right.right = new Node(6);
    root.right.left.right = new Node(7);
    root.right.right.right = new Node(8);
    root.right.left.right.left = new Node(9);
     
    // Calculating height of tree
    int levels = height(root);
     
    // Printing the deepest node
    deepestNode(root, levels);
}
}
 
/* This code contributed by PrinciRaj1992 */
 
  

Javascript

   <script>
// A Javascript program to find value of the
// deepest node in a given binary tree
 
// A tree node with constructor
class Node
{
    // constructor
    constructor(key)
    {
        this.data = key;
        this.left = null;
        this.right = null;
    }
}
 
// Utility function to find height
// of a tree, rooted at 'root
function height(root)
{
    if(root == null) return 0;
          
    let leftHt = height(root.left);
    let rightHt = height(root.right);
          
    return Math.max(leftHt, rightHt) + 1;
}
 
// levels : current Level
// Utility function to print all
// nodes at a given level.
function deepestNode(root,levels)
{
    if(root == null) return;
      
    if(levels == 1)
    document.write(root.data + " ");
      
    else if(levels > 1)
    {
        deepestNode(root.left, levels - 1);
        deepestNode(root.right, levels - 1);
    }
}
 
// Driver Codede
let root = new Node(1);
root.left = new Node(2);
root.right = new Node(3);
root.left.left = new Node(4);
root.right.left = new Node(5);
root.right.right = new Node(6);
root.right.left.right = new Node(7);
root.right.right.right = new Node(8);
root.right.left.right.left = new Node(9);
 
// Calculating height of tree
let levels = height(root);
 
// Printing the deepest node
deepestNode(root, levels);
 
 
 
// This code is contributed by avanitrachhadiya2155
</script>
 
  

Output

Time Complexity: O(n)

Space Complexity : O(n)

Method 3: The last node processed from the queue in level order is the deepest node in the binary tree.

Implementation:

C++

   // A C++ program to find value of the
// deepest node in a given binary tree
#include <bits/stdc++.h>
using namespace std;
 
// A tree node with constructor
class Node
{
public:
    int data;
    Node *left, *right;
      
    // constructor   
    Node(int key)
    {
        data = key;
        left = NULL;
        right = NULL;
    }
};
 
// Function to return the deepest node
Node* deepestNode(Node* root)
{
    Node* tmp = NULL;
    if (root == NULL)
        return NULL;
 
    // Creating a Queue
    queue<Node*> q;
    q.push(root);
 
    // Iterates until queue become empty
    while (q.size() > 0)
    {
        tmp = q.front();
        q.pop();
        if (tmp->left != NULL)
            q.push(tmp->left);
        if (tmp->right != NULL)
            q.push(tmp->right);
    }
    return tmp;
}
     
int main()
{
    Node* root = new Node(1);
    root->left = new Node(2);
    root->right = new Node(3);
    root->left->left = new Node(4);
    root->right->left = new Node(5);
    root->right->right = new Node(6);
    root->right->left->right = new Node(7);
    root->right->right->right = new Node(8);
    root->right->left->right->left = new Node(9);
 
    Node* deepNode = deepestNode(root);
    cout << (deepNode->data);
 
    return 0;
}
 
  

Java

   import java.util.*;
 
// A Java program to find value of the
// deepest node in a given binary tree
 
// A tree node with constructor
public class Node 
{
    int data;
    Node left, right;
 
    // constructor
    Node(int key)
    {
        data = key;
        left = null;
        right = null;
    }
};
 
class Gfg 
{
   
    // Function to return the deepest node
    public static Node deepestNode(Node root)
    {
        Node tmp = null;
        if (root == null)
            return null;
 
        // Creating a Queue
        Queue<Node> q = new LinkedList<Node>();
        q.offer(root);
 
        // Iterates until queue become empty
        while (!q.isEmpty()) 
        {
            tmp = q.poll();
            if (tmp.left != null)
                q.offer(tmp.left);
            if (tmp.right != null)
                q.offer(tmp.right);
        }
        return tmp;
    }
 
    public static void main(String[] args)
    {
 
        Node root = new Node(1);
        root.left = new Node(2);
        root.right = new Node(3);
        root.left.left = new Node(4);
        root.right.left = new Node(5);
        root.right.right = new Node(6);
        root.right.left.right = new Node(7);
        root.right.right.right = new Node(8);
        root.right.left.right.left = new Node(9);
 
        Node deepNode = deepestNode(root);
        System.out.println(deepNode.data);
    }
}
 
// Code is contributed by mahi_07
 
  

Python3

   # A Python3 program to find value of the 
# deepest node in a given binary tree by method 3 
from collections import deque
 
class new_Node:
    def __init__(self, key):
        self.data = key
        self.left = self.right = None
 
def deepestNode(root):
    if root == None:
        return 0
    q = deque()
    q.append(root)
    node = None
    while len(q) != 0:
        node = q.popleft()
        if node.left is not None:
            q.append(node.left)
        if node.right is not None:
            q.append(node.right)
    return node.data
  
# Driver Code
if __name__ == '__main__':
  
    root = new_Node(1) 
    root.left = new_Node(2) 
    root.right = new_Node(3) 
    root.left.left = new_Node(4) 
    root.right.left = new_Node(5) 
    root.right.right = new_Node(6) 
    root.right.left.right = new_Node(7) 
    root.right.right.right = new_Node(8) 
    root.right.left.right.left = new_Node(9) 
      
    # Calculating height of tree 
    levels = deepestNode(root) 
      
    # Printing the deepest node 
    print(levels)
     
# This code is contributed by Aprajita Chhawi 
 
  

C#

   // A C# program to find value of the
// deepest node in a given binary tree
using System;
using System.Collections.Generic;
 
// A tree node with constructor
public class Node 
{
  public
    int data;
  public
    Node left, right;
 
  // constructor
  public
    Node(int key)
  {
    data = key;
    left = null;
    right = null;
  }
};
 
class Gfg 
{
 
  // Function to return the deepest node
  public static Node deepestNode(Node root)
  {
    Node tmp = null;
    if (root == null)
      return null;
 
    // Creating a Queue
    Queue<Node> q = new Queue<Node>();
    q.Enqueue(root);
 
    // Iterates until queue become empty
    while (q.Count != 0) 
    {
      tmp = q.Peek();
      q.Dequeue();
      if (tmp.left != null)
        q.Enqueue(tmp.left);
      if (tmp.right != null)
        q.Enqueue(tmp.right);
    }
    return tmp;
  }
 
  // Driver code
  public static void Main(String[] args)
  {
 
    Node root = new Node(1);
    root.left = new Node(2);
    root.right = new Node(3);
    root.left.left = new Node(4);
    root.right.left = new Node(5);
    root.right.right = new Node(6);
    root.right.left.right = new Node(7);
    root.right.right.right = new Node(8);
    root.right.left.right.left = new Node(9);
 
    Node deepNode = deepestNode(root);
    Console.WriteLine(deepNode.data);
  }
}
 
// This code is contributed by gauravrajput1 
 
  

Javascript

   <script>
// A Javascript program to find value of the
// deepest node in a given binary tree
  
// A tree node with constructor
class Node
{
    constructor(key)
    {
        this.data = key;
        this.left = null;
        this.right = null;
    }
}
 
// Function to return the deepest node
function deepestNode(root)
{
    let  tmp = null;
        if (root == null)
            return null;
  
        // Creating a Queue
        let q = [];
        q.push(root);
  
        // Iterates until queue become empty
        while (q.length!=0)
        {
            tmp = q.shift();
            if (tmp.left != null)
                q.push(tmp.left);
            if (tmp.right != null)
                q.push(tmp.right);
        }
        return tmp;
}
 
let root = new Node(1);
root.left = new Node(2);
root.right = new Node(3);
root.left.left = new Node(4);
root.right.left = new Node(5);
root.right.right = new Node(6);
root.right.left.right = new Node(7);
root.right.right.right = new Node(8);
root.right.left.right.left = new Node(9);
 
let deepNode = deepestNode(root);
document.write(deepNode.data);
 
// This code is contributed by unknown2108
</script>
 
  

Output

Time Complexity: O(n)

Auxiliary Space: O(n)

Find Minimum Depth of a Binary Tree

R

Rakesh Kumar

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Practice Tags :

Tree

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