Sum of all the levels in a Binary Search Tree
Last Updated :
11 Jul, 2025
Given a Binary Search Tree, the task is to find the horizontal sum of the nodes that are at the same level.
Examples:
Input:
Output:
6
12
24
Input:
Output:
6
12
12
Approach DFS: Find the height of the given binary tree then the number of levels in the tree will be levels = height + 1. Now create an array sum[] of size levels where sum[i] will store the sum of all the nodes at the ith level. To update this array, write a recursive function that adds the current node's data at sum[level] where the level is the level of the current node and then recursively call the same method for the child nodes with level as level + 1.
Below is the implementation of the above approach:
C++
// C++ implementation of the approach
#include <iostream>
#include <queue>
using namespace std;
// A Binary Tree Node
struct Node {
int data;
struct Node *left, *right;
};
// Utility function to create a new tree node
Node* newNode(int data)
{
Node* temp = new Node;
temp->data = data;
temp->left = temp->right = NULL;
return temp;
}
// Utility function to print
// the contents of an array
void printArr(int arr[], int n)
{
for (int i = 0; i < n; i++)
cout << arr[i] << endl;
}
// Function to return the height
// of the binary tree
int getHeight(Node* root)
{
if (root->left == NULL && root->right == NULL)
return 0;
int left = 0;
if (root->left != NULL)
left = getHeight(root->left);
int right = 0;
if (root->right != NULL)
right = getHeight(root->right);
return (max(left, right) + 1);
}
// Recursive function to update sum[] array
// such that sum[i] stores the sum
// of all the elements at ith level
void calculateLevelSum(Node* node, int level, int sum[])
{
if (node == NULL)
return;
// Add current node data to the sum
// of the current node's level
sum[level] += node->data;
// Recursive call for left and right sub-tree
calculateLevelSum(node->left, level + 1, sum);
calculateLevelSum(node->right, level + 1, sum);
}
// Driver code
int main()
{
// Create the binary tree
Node* root = newNode(6);
root->left = newNode(4);
root->right = newNode(8);
root->left->left = newNode(3);
root->left->right = newNode(5);
root->right->left = newNode(7);
root->right->right = newNode(9);
// Count of levels in the
// given binary tree
int levels = getHeight(root) + 1;
// To store the sum at every level
int sum[levels] = { 0 };
calculateLevelSum(root, 0, sum);
// Print the required sums
printArr(sum, levels);
return 0;
}
// Java implementation of the approach
class Sol
{
// A Binary Tree Node
static class Node
{
int data;
Node left, right;
};
// Utility function to create a new tree node
static Node newNode(int data)
{
Node temp = new Node();
temp.data = data;
temp.left = temp.right = null;
return temp;
}
// Utility function to print
// the contents of an array
static void printArr(int arr[], int n)
{
for (int i = 0; i < n; i++)
System.out.print(arr[i]+ " " );
}
// Function to return the height
// of the binary tree
static int getHeight(Node root)
{
if (root.left == null && root.right == null)
return 0;
int left = 0;
if (root.left != null)
left = getHeight(root.left);
int right = 0;
if (root.right != null)
right = getHeight(root.right);
return (Math.max(left, right) + 1);
}
// Recursive function to update sum[] array
// such that sum[i] stores the sum
// of all the elements at ith level
static void calculateLevelSum(Node node, int level, int sum[])
{
if (node == null)
return;
// Add current node data to the sum
// of the current node's level
sum[level] += node.data;
// Recursive call for left and right sub-tree
calculateLevelSum(node.left, level + 1, sum);
calculateLevelSum(node.right, level + 1, sum);
}
// Driver code
public static void main(String args[])
{
// Create the binary tree
Node root = newNode(6);
root.left = newNode(4);
root.right = newNode(8);
root.left.left = newNode(3);
root.left.right = newNode(5);
root.right.left = newNode(7);
root.right.right = newNode(9);
// Count of levels in the
// given binary tree
int levels = getHeight(root) + 1;
// To store the sum at every level
int sum[]=new int[levels];
calculateLevelSum(root, 0, sum);
// Print the required sums
printArr(sum, levels);
}
}
// This code is contributed by andrew1234
# Python3 implementation of above algorithm
# Utility class to create a node
class Node:
def __init__(self, key):
self.data = key
self.left = self.right = None
# Utility function to create a tree node
def newNode( data):
temp = Node(0)
temp.data = data
temp.left = temp.right = None
return temp
# Utility function to print
# the contents of an array
def printArr(arr, n):
i = 0
while ( i < n):
print( arr[i])
i = i + 1
# Function to return the height
# of the binary tree
def getHeight(root):
if (root.left == None and root.right == None):
return 0
left = 0
if (root.left != None):
left = getHeight(root.left)
right = 0
if (root.right != None):
right = getHeight(root.right)
return (max(left, right) + 1)
sum = []
# Recursive function to update sum[] array
# such that sum[i] stores the sum
# of all the elements at ith level
def calculateLevelSum(node, level):
global sum
if (node == None):
return
# Add current node data to the sum
# of the current node's level
sum[level] += node.data
# Recursive call for left and right sub-tree
calculateLevelSum(node.left, level + 1)
calculateLevelSum(node.right, level + 1)
# Driver code
# Create the binary tree
root = newNode(6)
root.left = newNode(4)
root.right = newNode(8)
root.left.left = newNode(3)
root.left.right = newNode(5)
root.right.left = newNode(7)
root.right.right = newNode(9)
# Count of levels in the
# given binary tree
levels = getHeight(root) + 1
# To store the sum at every level
sum = [0] * levels
calculateLevelSum(root, 0)
# Print the required sums
printArr(sum, levels)
# This code is contributed by Arnab Kundu
// C# implementation of the approach
using System;
class GFG
{
// A Binary Tree Node
public class Node
{
public int data;
public Node left, right;
};
// Utility function to create a new tree node
static Node newNode(int data)
{
Node temp = new Node();
temp.data = data;
temp.left = temp.right = null;
return temp;
}
// Utility function to print
// the contents of an array
static void printArr(int []arr, int n)
{
for (int i = 0; i < n; i++)
Console.WriteLine(arr[i]);
}
// Function to return the height
// of the binary tree
static int getHeight(Node root)
{
if (root.left == null &&
root.right == null)
return 0;
int left = 0;
if (root.left != null)
left = getHeight(root.left);
int right = 0;
if (root.right != null)
right = getHeight(root.right);
return (Math.Max(left, right) + 1);
}
// Recursive function to update sum[] array
// such that sum[i] stores the sum
// of all the elements at ith level
static void calculateLevelSum(Node node, int level,
int []sum)
{
if (node == null)
return;
// Add current node data to the sum
// of the current node's level
sum[level] += node.data;
// Recursive call for left and right sub-tree
calculateLevelSum(node.left, level + 1, sum);
calculateLevelSum(node.right, level + 1, sum);
}
// Driver code
public static void Main(String []args)
{
// Create the binary tree
Node root = newNode(6);
root.left = newNode(4);
root.right = newNode(8);
root.left.left = newNode(3);
root.left.right = newNode(5);
root.right.left = newNode(7);
root.right.right = newNode(9);
// Count of levels in the
// given binary tree
int levels = getHeight(root) + 1;
// To store the sum at every level
int []sum = new int[levels];
calculateLevelSum(root, 0, sum);
// Print the required sums
printArr(sum, levels);
}
}
// This code is contributed by 29AjayKumar
<script>
// Javascript implementation of the approach
// A Binary Tree Node
class Node
{
constructor(data)
{
this.data = data;
this.left = this.right = null;
}
}
// Utility function to print
// the contents of an array
function printArr(arr, n)
{
for (let i = 0; i < n; i++)
document.write(arr[i]+ " <br>" );
}
// Function to return the height
// of the binary tree
function getHeight(root)
{
if (root.left == null && root.right == null)
return 0;
let left = 0;
if (root.left != null)
left = getHeight(root.left);
let right = 0;
if (root.right != null)
right = getHeight(root.right);
return (Math.max(left, right) + 1);
}
// Recursive function to update sum[] array
// such that sum[i] stores the sum
// of all the elements at ith level
function calculateLevelSum(node,level,sum)
{
if (node == null)
return;
// Add current node data to the sum
// of the current node's level
sum[level] += node.data;
// Recursive call for left and right sub-tree
calculateLevelSum(node.left, level + 1, sum);
calculateLevelSum(node.right, level + 1, sum);
}
// Driver code
// Create the binary tree
let root = new Node(6);
root.left = new Node(4);
root.right = new Node(8);
root.left.left = new Node(3);
root.left.right = new Node(5);
root.right.left = new Node(7);
root.right.right = new Node(9);
// Count of levels in the
// given binary tree
let levels = getHeight(root) + 1;
// To store the sum at every level
let sum=new Array(levels);
for(let i = 0; i < levels; i++)
sum[i] = 0;
calculateLevelSum(root, 0, sum);
// Print the required sums
printArr(sum, levels);
// This code is contributed by avanitrachhadiya2155
</script>
Time Complexity : O(N)
Auxiliary Space: O(N)
Approach BFS:-Find the height of the given binary tree then the number of levels in the tree will level = height + 1. Now create an array sum[] of size levels where sum[i] will store the sum of all the nodes at the ith level. To update this array Using Breadth-First Search We Will calculate the sum at That Level with Queue and Add their children for future Levels
C++
#include<bits/stdc++.h>
using namespace std;
// A Binary Tree Node
struct Node {
int data;
Node *left, *right;
Node(int data)
{
this->data = data;
left = right = NULL;
}
};
// Utility function to print
// the contents of an array
void printArr(int arr[], int n)
{
for (int i = 0; i < n; i++)
cout << arr[i] << " ";
}
// Function to return the height
// of the binary tree
int getHeight(Node *root)
{
if (root == NULL)
return 0;
int left = 0;
if (root->left != NULL)
left = getHeight(root->left);
int right = 0;
if (root->right != NULL)
right = getHeight(root->right);
return (max(left, right) + 1);
}
// Function to Calculate Level Sum Using BFS
void calculateLevelSum_Using_BFS(Node *root, int sum[])
{
// Queue Through Which We Will Travel Tree Level
// Wise
queue<Node*> q;
// Stores The CurrentLevel for Which is
// Calculating Sum
int current_level = 0;
// Add root Node to queue
q.push(root);
// Travel queue
while (!q.empty()) {
// Stores the No. of Nodes at Current Level
int no_of_nodes_current_level = q.size();
// Will store the LevelSum of CurrentLevel
int current_LevelSum = 0;
// Traveling all node of current level
for (int i = 0; i < no_of_nodes_current_level; i++) {
Node *remove = q.front();
q.pop();
current_LevelSum += remove->data;
// Adding left node of next level if exist
if (remove->left != NULL) {
q.push(remove->left);
}
// Adding right node of next level if exist
if (remove->right != NULL) {
q.push(remove->right);
}
}
// Assign Value of current Level Sum to Sum
// arr
sum[current_level] = current_LevelSum;
// Increasing Level for next Iteration
current_level++;
}
}
int main()
{
// Creating Tree
Node *root = new Node(6);
root->left = new Node(4);
root->right = new Node(8);
root->left->left = new Node(3);
root->left->right = new Node(5);
root->right->left = new Node(7);
root->right->right = new Node(9);
// Finding How Many Level Does The Tree Have
int levels = getHeight(root);
int sum[levels];
// Calling The Function
calculateLevelSum_Using_BFS(root, sum);
// Printing the Array
printArr(sum, levels);
return 0;
}
/*package whatever //do not write package name here */
import java.io.*;
import java.util.LinkedList;
import java.util.Queue;
// A Binary Tree Node
class Node {
int data;
Node left, right;
Node(int data)
{
this.data = data;
left = null;
right = null;
}
}
public class GFG {
// Utility function to create a new tree node
static Node newNode(int data)
{
Node temp = new Node(data);
temp.data = data;
temp.left = temp.right = null;
return temp;
}
// Utility function to print
// the contents of an array
static void printArr(int arr[], int n)
{
for (int i = 0; i < n; i++)
System.out.print(arr[i] + " ");
}
// Function to return the height
// of the binary tree
static int getHeight(Node root)
{
if (root.left == null && root.right == null)
return 0;
int left = 0;
if (root.left != null)
left = getHeight(root.left);
int right = 0;
if (root.right != null)
right = getHeight(root.right);
return (Math.max(left, right) + 1);
}
// Function to Calculate Level Sum Using BFS
static void calculateLevelSum_Using_BFS(Node root,
int sum[])
{
// Queue Through Which We Will Travel Tree Level
// Wise
Queue<Node> queue = new LinkedList<>();
// Stores The CurrentLevel for Which is
// Calculating Sum
int cureentlevel = 0;
// Add root Node to queue
queue.add(root);
// Travel queue
while (queue.size() > 0) {
// Stores the No. of Nodes at Current Level
int no_of_nodes_current_Level = queue.size();
// Will store the LevelSum of CurrentLevel
int current_LevelSum = 0;
// Traveling all node of current level
for (int i = 0; i < no_of_nodes_current_Level;
i++) {
Node remove = queue.poll();
current_LevelSum += remove.data;
// Adding left node of next level if exist
if (remove.left != null) {
queue.add(remove.left);
}
// Adding right node of next level if exist
if (remove.right != null) {
queue.add(remove.right);
}
}
// Assig Value of current Level Sum to Sum
// arr
sum[cureentlevel] = current_LevelSum;
// Increasing Level for next Iteration
cureentlevel++;
}
}
public static void main(String[] args)
{
// Creating Tree
Node root = newNode(6);
root.left = newNode(4);
root.right = newNode(8);
root.left.left = newNode(3);
root.left.right = newNode(5);
root.right.left = newNode(7);
root.right.right = newNode(9);
// Finding How Many Level Does The Tree Have
int levels = getHeight(root) + 1;
int sum[] = new int[levels];
// Calling The Function
calculateLevelSum_Using_BFS(root, sum);
// Printing the Array
printArr(sum, levels);
}
// This Code is Contributed By Vikas Bishnoi
}
#Node constructor
class Node:
def __init__(self, key):
self.data = key
self.left = self.right = None
# Utility function to create a tree node
def newNode( data):
temp = Node(0)
temp.data = data
temp.left = temp.right = None
return temp
#function to print output array
def printArr(arr, n):
i = 0
while ( i < n):
print( arr[i])
i = i + 1
#function to get height at that particular level
def getHeight(root):
if (root.left == None and root.right == None):
return 0
left = 0
if (root.left != None):
left = getHeight(root.left)
right = 0
if (root.right != None):
right = getHeight(root.right)
return (max(left, right) + 1)
def calculateLevelSum_Using_BFS(root, sum):
# Queue Through Which We Will Travel Tree Level
# Wise
queue = []
# Stores The CurrentLevel for Which is
# Calculating Sum
cureentlevel = 0
# Add root Node to queue
queue.append(root)
while len(queue) > 0:
# Stores the No. of Nodes at Current Level
no_of_nodes_current_Level = len(queue)
# Will store the LevelSum of CurrentLevel
current_LevelSum = 0
# Traveling all node of current level
for i in range(no_of_nodes_current_Level):
remove = queue.pop(0)
current_LevelSum += remove.data
# Adding left node of next level if exist
if remove.left is not None:
queue.append(remove.left)
# Adding right node of next level if exist
if remove.right is not None:
queue.append(remove.right)
# Assigning Value of current Level Sum to Sum
# arr
sum[cureentlevel] = current_LevelSum
# Increasing Level for next Iteration
cureentlevel += 1
# Creating Tree
root = newNode(6)
root.left = newNode(4)
root.right = newNode(8)
root.left.left = newNode(3)
root.left.right = newNode(5)
root.right.left = newNode(7)
root.right.right = newNode(9)
# Finding How Many Level Does The Tree Have
levels = getHeight(root) + 1
sum = [0] * levels
# Calling The Function
calculateLevelSum_Using_BFS(root, sum)
# Printing the Array
printArr(sum, levels)
#This code is contributed by Tejas Gundale
// A Binary Tree Node
class Node {
constructor(data) {
this.data = data;
this.left = null;
this.right = null;
}
}
// Utility function to print the contents of an array
function printArr(arr, n) {
for (let i = 0; i < n; i++) {
console.log(arr[i] + " ");
}
}
// Function to return the height of the binary tree
function getHeight(root) {
if (root == null) {
return 0;
}
let left = 0;
if (root.left != null) {
left = getHeight(root.left);
}
let right = 0;
if (root.right != null) {
right = getHeight(root.right);
}
return Math.max(left, right) + 1;
}
// Function to Calculate Level Sum Using BFS
function calculateLevelSum_Using_BFS(root, sum) {
// Queue Through Which We Will Travel Tree Level Wise
let q = [];
// Stores The CurrentLevel for Which is Calculating Sum
let currentLevel = 0;
// Add root Node to queue
q.push(root);
// Travel queue
while (q.length > 0) {
// Stores the No. of Nodes at Current Level
let noOfNodesCurrentLevel = q.length;
// Will store the LevelSum of CurrentLevel
let currentLevelSum = 0;
// Traveling all node of current level
for (let i = 0; i < noOfNodesCurrentLevel; i++) {
let remove = q.shift();
currentLevelSum += remove.data;
// Adding left node of next level if exist
if (remove.left != null) {
q.push(remove.left);
}
// Adding right node of next level if exist
if (remove.right != null) {
q.push(remove.right);
}
}
// Assign Value of current Level Sum to Sum arr
sum[currentLevel] = currentLevelSum;
// Increasing Level for next Iteration
currentLevel++;
}
}
// driver program to test above functions
// Creating Tree
let root = new Node(6);
root.left = new Node(4);
root.right = new Node(8);
root.left.left = new Node(3);
root.left.right = new Node(5);
root.right.left = new Node(7);
root.right.right = new Node(9);
// Finding How Many Level Does The Tree Have
let levels = getHeight(root);
let sum = new Array(levels);
// Calling The Function
calculateLevelSum_Using_BFS(root, sum);
// Printing the Array
printArr(sum, levels);
using System;
using System.Collections.Generic;
// A Binary Tree Node
class Node
{
public int data;
public Node left, right;
public Node(int data)
{
this.data = data;
left = null;
right = null;
}
}
public class GFG
{
// Utility function to create a new tree node
static Node newNode(int data)
{
Node temp = new Node(data);
temp.data = data;
temp.left = temp.right = null;
return temp;
}
// Utility function to print
// the contents of an array
static void printArr(int[] arr, int n)
{
for (int i = 0; i < n; i++)
Console.Write(arr[i] + " ");
}
// Function to return the height
// of the binary tree
static int getHeight(Node root)
{
if (root.left == null && root.right == null)
return 0;
int left = 0;
if (root.left != null)
left = getHeight(root.left);
int right = 0;
if (root.right != null)
right = getHeight(root.right);
return (Math.Max(left, right) + 1);
}
// Function to Calculate Level Sum Using BFS
static void calculateLevelSum_Using_BFS(Node root, int[] sum)
{
// Queue Through Which We Will Travel Tree Level
// Wise
Queue<Node> queue = new Queue<Node>();
// Stores The CurrentLevel for Which is
// Calculating Sum
int currentLevel = 0;
// Add root Node to queue
queue.Enqueue(root);
// Travel queue
while (queue.Count > 0)
{
// Stores the No. of Nodes at Current Level
int no_of_nodes_current_Level = queue.Count;
// Will store the LevelSum of CurrentLevel
int current_LevelSum = 0;
// Traveling all node of current level
for (int i = 0; i < no_of_nodes_current_Level; i++)
{
Node remove = queue.Dequeue();
current_LevelSum += remove.data;
// Adding left node of next level if exist
if (remove.left != null)
{
queue.Enqueue(remove.left);
}
// Adding right node of next level if exist
if (remove.right != null)
{
queue.Enqueue(remove.right);
}
}
// Assig Value of current Level Sum to Sum
// arr
sum[currentLevel] = current_LevelSum;
// Increasing Level for next Iteration
currentLevel++;
}
}
public static void Main(string[] args)
{
// Creating Tree
Node root = newNode(6);
root.left = newNode(4);
root.right = newNode(8);
root.left.left = newNode(3);
root.left.right = newNode(5);
root.right.left = newNode(7);
root.right.right = newNode(9);
// Finding How Many Level Does The Tree Have
int levels = getHeight(root) + 1;
int[] sum = new int[levels];
// Calling The Function
calculateLevelSum_Using_BFS(root, sum);
// Printing the Array
printArr(sum, levels);
}
// This Code is Contributed By Vikas Bishnoi
}
Time Complexity: O(N) Where is the number of Nodes in a tree. As Each Node is only Visited Once so Complexity is O(N)
Auxiliary Space: O(N) Used In queue to store nodes
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Algorithms
Searching AlgorithmsSearching algorithms are essential tools in computer science used to locate specific items within a collection of data. In this tutorial, we are mainly going to focus upon searching in an array. When we search an item in an array, there are two most common algorithms used based on the type of input
2 min read
Sorting AlgorithmsA Sorting Algorithm is used to rearrange a given array or list of elements in an order. For example, a given array [10, 20, 5, 2] becomes [2, 5, 10, 20] after sorting in increasing order and becomes [20, 10, 5, 2] after sorting in decreasing order. There exist different sorting algorithms for differ
3 min read
Introduction to RecursionThe process in which a function calls itself directly or indirectly is called recursion and the corresponding function is called a recursive function. A recursive algorithm takes one step toward solution and then recursively call itself to further move. The algorithm stops once we reach the solution
14 min read
Greedy AlgorithmsGreedy algorithms are a class of algorithms that make locally optimal choices at each step with the hope of finding a global optimum solution. At every step of the algorithm, we make a choice that looks the best at the moment. To make the choice, we sometimes sort the array so that we can always get
3 min read
Graph AlgorithmsGraph is a non-linear data structure like tree data structure. The limitation of tree is, it can only represent hierarchical data. For situations where nodes or vertices are randomly connected with each other other, we use Graph. Example situations where we use graph data structure are, a social net
3 min read
Dynamic Programming or DPDynamic Programming is an algorithmic technique with the following properties.It is mainly an optimization over plain recursion. Wherever we see a recursive solution that has repeated calls for the same inputs, we can optimize it using Dynamic Programming. The idea is to simply store the results of
3 min read
Bitwise AlgorithmsBitwise algorithms in Data Structures and Algorithms (DSA) involve manipulating individual bits of binary representations of numbers to perform operations efficiently. These algorithms utilize bitwise operators like AND, OR, XOR, NOT, Left Shift, and Right Shift.BasicsIntroduction to Bitwise Algorit
4 min read
Advanced
Segment TreeSegment Tree is a data structure that allows efficient querying and updating of intervals or segments of an array. It is particularly useful for problems involving range queries, such as finding the sum, minimum, maximum, or any other operation over a specific range of elements in an array. The tree
3 min read
Pattern SearchingPattern searching algorithms are essential tools in computer science and data processing. These algorithms are designed to efficiently find a particular pattern within a larger set of data. Patten SearchingImportant Pattern Searching Algorithms:Naive String Matching : A Simple Algorithm that works i
2 min read
GeometryGeometry is a branch of mathematics that studies the properties, measurements, and relationships of points, lines, angles, surfaces, and solids. From basic lines and angles to complex structures, it helps us understand the world around us.Geometry for Students and BeginnersThis section covers key br
2 min read
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