Find the Deepest Node in a Binary Tree
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 given binary tree. While doing Inorder traversal, we pass level of current node also. We keep track of maximum level seen so far and value of deepest node seen so far.
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 nodestruct Node{ int data; struct Node *left, *right;};// Utility function to create a new nodeNode *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 rootvoid find(Node *root, int level, int &maxLevel, int &res){ if (root != NULL) { find(root->left, ++level, maxLevel, res); // Update level and resue if (level > maxLevel) { res = root->data; maxLevel = level; } find(root->right, level, maxLevel, res); }}// Returns value of deepest nodeint deepestNode(Node *root){ // Initialze 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 programint 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 resue if (level > maxLevel) { res = root.data; maxLevel = level; } find(root.right, level); } } // Returns value of deepest node static int deepestNode(Node root) { // Initialze 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 resue 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) : # Initialze 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 Codeif __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 resue if (level > maxLevel) { res = root.data; maxLevel = level; } find(root.right, level); } } // Returns value of deepest node static int deepestNode(Node root) { // Initialze 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 |
Output:
9
Time Complexity: O(n)
Method 2 : The idea here is to find the height of the given tree and then print the node at the bottom-most level.
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 constructorclass 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 programint 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;} |
Java
// A Java program to find value of the // deepest node in a given binary treeclass GFG{ // A tree node with constructorstatic 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 Codedepublic 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 Codeif __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 treeusing System; class GFG{ // A tree node with constructorpublic 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 Codepublic 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 */ |
Output:
9
Time Complexity: O(n)
Thanks to Parth Patekar for suggesting above method.
Method 3: The last node processed from the queue in level order is the deepest node in the binary tree.
Java
import java.util.*;// A Java program to find value of the// deepest node in a given binary tree// A tree node with constructorpublic class Node { int data; Node left, right; // constructor Node(int key) { data = key; left = null; right = null; }};class Gfg { // Funtion 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 untill 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 |
C#
// A C# program to find value of the// deepest node in a given binary treeusing System;using System.Collections.Generic;// A tree node with constructorpublic class Node { public int data; public Node left, right; // constructor public Node(int key) { data = key; left = null; right = null; }};class Gfg { // Funtion 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 untill 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 |
Output
9
Time Complexity: O(n)
Space Complexity: O(n)
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