Find all subarray index ranges in given Array with set bit sum equal to X
Last Updated :
23 Jul, 2025
Given an array arr (1-based indexing) of length N and an integer X, the task is to find and print all index ranges having a set bit sum equal to X in the array.
Examples:
Input: A[] = {1 4 3 5 7}, X = 4
Output: (1, 3), (3, 4)
Explanation: In the above array subarray having set bit sum equal to X (= 4).
Starting from index 1 to 3. {1 4 3} = (001) + (100) + (011) = 4 and
other one is from 3 to 4 {3, 5} = (011) + (101) = 4.
Input: arr[] = {5, 3, 0, 4, 10}, X = 7
Output: (1 5)
Explanation: In the above array subarrays having set bit sum equal to X(= 7) start from 1 to 5 only.
Approach: The problem is solved using two pointer approach.
- Write a function countSetBit to count the number of set bits.
- Initialize a counter c=0, to store the individual count for every number in the array.
- Iterate over the array and check for every set bit and increase the counter.
- replace every number with the count of a number of set bits
- Write a function to print a range of subarrays PrintIndex
Run a loop using two pointers i and j and check for the sum as follow:- If the current index sum is less than X then, add the value at arr[j] in currsum
- else if the sum is equal to X push back the start and end index of the array and increment the counter i.
- else decrement the counter, subtract the value at arr[i] from currsum.
- Repeat the same for all elements.
Below is the implementation of the above method :
C++
// C++ program to Find all range
// Having set bit sum X in array
#include <bits/stdc++.h>
using namespace std;
// Function to replace elements
// With their set bit count
void countSetBit(vector<int>& arr, int n)
{
int c = 0, i;
for (i = 0; i < n; i++) {
int x = arr[i];
while (x) {
int l = x % 10;
if (x & 1)
c++;
x /= 2;
}
// Replace array element
// to set bit count
arr[i] = c;
c = 0;
}
}
// Function to find range of subarrays
// having set bit sum equal to X.
void PrintIndex(vector<int> arr, int N, int X,
vector<int>& v)
{
int i = 0, j = 0, currSum = arr[0];
while (j < N && i < N) {
if (currSum == X) {
// push back index i start
// point ans end point j
// when sum == X
v.push_back(i + 1);
v.push_back(j + 1);
j++;
currSum += arr[j];
}
// when current sum is
// less than X increment j
// and add arr[j]
else if (currSum < X) {
j++;
currSum += arr[j];
}
// when current sum is
// greater than X increment j
// and subtract arr[i]
else {
currSum -= arr[i];
i++;
}
}
}
// Driver code
int main()
{
vector<int> v = { 1, 4, 3, 5, 7 };
int X = 4;
int N = v.size();
// replace all the array element into
// their set bit count value
countSetBit(v, N);
vector<int> ans;
PrintIndex(v, N, X, ans);
for (int i = 0; i < ans.size() - 1; i += 2)
cout << "(" << ans[i] << " "
<< ans[i + 1] << ")"
<< " ";
return 0;
}
// JAVA code to implement the above approach
import java.util.*;
class GFG {
// Function to replace elements
// With their set bit count
static void countSetBit(int[] arr, int n)
{
int c = 0, i;
for (i = 0; i < n; i++) {
int x = arr[i];
while (x > 0) {
int l = x % 10;
if ((x & 1) == 1)
c++;
x /= 2;
}
// Replace array element
// to set bit count
arr[i] = c;
c = 0;
}
}
// Function to find range of subarrays
// having set bit sum equal to X.
static void PrintIndex(int[] arr, int N, int X,
ArrayList<Integer> v)
{
int i = 0, j = 0, currSum = arr[0];
while (j < N && i < N) {
if (currSum == X) {
// push back index i start
// point ans end point j
// when sum == X
v.add(i + 1);
v.add(j + 1);
j++;
if (j < N)
currSum += arr[j];
}
// when current sum is
// less than X increment j
// and add arr[j]
else if (currSum < X) {
j++;
if (j < N)
currSum += arr[j];
}
// when current sum is
// greater than X increment j
// and subtract arr[i]
else {
currSum -= arr[i];
i++;
}
}
}
// Driver Code
public static void main(String[] args)
{
int[] v = { 1, 4, 3, 5, 7 };
int X = 4;
int N = v.length;
// replace all the array element into
// their set bit count value
countSetBit(v, N);
ArrayList<Integer> ans = new ArrayList<Integer>();
PrintIndex(v, N, X, ans);
for (int i = 0; i < ans.size() - 1; i += 2)
System.out.print("(" + ans.get(i) + " " + ans.get(i + 1)
+ ")"
+ " ");
}
}
// This code is contributed by sanjoy_62.
# Python program to Find all range
# Having set bit sum X in array
# Function to replace elements
# With their set bit count
def countSetBit(arr, n):
c = 0
for i in range(n):
x = arr[i]
while (x):
l = x % 10
if (x & 1):
c += 1
x = x // 2
# Replace array element
# to set bit count
arr[i] = c
c = 0
# Function to find range of subarrays
# having set bit sum equal to X.
def PrintIndex(arr, N, X, v):
i,j,currSum = 0,0,arr[0]
while (j < N and i < N):
if (currSum == X):
# append back index i start
# point ans end point j
# when sum == X
v.append(i + 1)
v.append(j + 1)
j += 1
if(j<N):
currSum += arr[j]
# when current sum is
# less than X increment j
# and add arr[j]
elif (currSum < X):
j += 1
if(j<N):
currSum += arr[j]
# when current sum is
# greater than X increment j
# and subtract arr[i]
else:
currSum -= arr[i]
i += 1
# Driver code
v = [1, 4, 3, 5, 7]
X = 4
N = len(v)
# replace all the array element into
# their set bit count value
countSetBit(v, N)
ans = []
PrintIndex(v, N, X, ans)
for i in range(0,len(ans) - 1,2):
print(f"({ans[i]} {ans[i + 1]})",end=" ")
# This code is contributed by shinjanpatra
// C# program to Find all range
// Having set bit sum X in array
using System;
using System.Collections;
class GFG {
// Function to replace elements
// With their set bit count
static void countSetBit(int[] arr, int n)
{
int c = 0, i;
for (i = 0; i < n; i++) {
int x = arr[i];
while (x > 0) {
int l = x % 10;
if ((x & 1) == 1)
c++;
x /= 2;
}
// Replace array element
// to set bit count
arr[i] = c;
c = 0;
}
}
// Function to find range of subarrays
// having set bit sum equal to X.
static void PrintIndex(int[] arr, int N, int X,
ArrayList v)
{
int i = 0, j = 0, currSum = arr[0];
while (j < N && i < N) {
if (currSum == X) {
// push back index i start
// point ans end point j
// when sum == X
v.Add(i + 1);
v.Add(j + 1);
j++;
if (j < N)
currSum += arr[j];
}
// when current sum is
// less than X increment j
// and add arr[j]
else if (currSum < X) {
j++;
if (j < N)
currSum += arr[j];
}
// when current sum is
// greater than X increment j
// and subtract arr[i]
else {
currSum -= arr[i];
i++;
}
}
}
// Driver code
public static void Main()
{
int[] v = { 1, 4, 3, 5, 7 };
int X = 4;
int N = v.Length;
// replace all the array element into
// their set bit count value
countSetBit(v, N);
ArrayList ans = new ArrayList();
PrintIndex(v, N, X, ans);
for (int i = 0; i < ans.Count - 1; i += 2)
Console.Write("(" + ans[i] + " " + ans[i + 1]
+ ")"
+ " ");
}
}
// This code is contributed by Samim Hossain Mondal.
<script>
// JavaScript program to Find all range
// Having set bit sum X in array
// Function to replace elements
// With their set bit count
const countSetBit = (arr, n) => {
let c = 0, i;
for (i = 0; i < n; i++) {
let x = arr[i];
while (x) {
let l = x % 10;
if (x & 1)
c++;
x = parseInt(x / 2);
}
// Replace array element
// to set bit count
arr[i] = c;
c = 0;
}
}
// Function to find range of subarrays
// having set bit sum equal to X.
const PrintIndex = (arr, N, X, v) => {
let i = 0, j = 0, currSum = arr[0];
while (j < N && i < N)
{
if (currSum == X)
{
// push back index i start
// point ans end point j
// when sum == X
v.push(i + 1);
v.push(j + 1);
j++;
currSum += arr[j];
}
// when current sum is
// less than X increment j
// and add arr[j]
else if (currSum < X) {
j++;
currSum += arr[j];
}
// when current sum is
// greater than X increment j
// and subtract arr[i]
else {
currSum -= arr[i];
i++;
}
}
}
// Driver code
let v = [1, 4, 3, 5, 7];
let X = 4;
let N = v.length;
// replace all the array element into
// their set bit count value
countSetBit(v, N);
let ans = [];
PrintIndex(v, N, X, ans);
for (let i = 0; i < ans.length - 1; i += 2)
document.write(`(${ans[i]} ${ans[i + 1]}) `);
// This code is contributed by rakeshsahni
</script>
Time Complexity: O(N * d) where d is the count of bits in an array element
Auxiliary Space: O(N)
Another Approach:
- The code defines a function called countSetBit that takes an integer x and returns the number of set bits in its binary representation.
- The code also defines another function called printSubarraysWithSetBitSumX that takes a vector of integers arr and an integer X. This function prints all the subarrays of arr whose sum of set bits is equal to X.
- Inside the printSubarraysWithSetBitSumX function, the code initializes some variables: n is the size of the input vector arr, i and j are two pointers initially set to 0, and currSum is the current sum of set bits.
- The code enters a while loop with a condition of j < n. This loop iterates through all the elements of the input vector arr.
- Inside the while loop, the code adds the count of set bits of the current element to the currSum variable and increments j by 1.
- The code then enters another while loop with a condition of currSum > X. This loop removes the set bit count of the element pointed by i from the currSum variable and increments i by 1 until the currSum becomes less than or equal to X.
- If the currSum is equal to X after the above while loop, the code prints the indices of the subarray whose sum of set bits is equal to X.
- The while loop in step 4 continues until j reaches the end of the input vector arr.
- Finally, the main function creates a vector arr containing integers {1, 4, 3, 5, 7} and sets X to 4. It then calls the printSubarraysWithSetBitSumX function with these arguments, which prints "(1, 3) (3, 4)" to the console.
Below is the implementation of the above approach:
C++
#include <iostream>
#include <vector>
using namespace std;
int countSetBit(int x) {
int count = 0;
while (x > 0) {
count += x & 1;
x >>= 1;
}
return count;
}
void printSubarraysWithSetBitSumX(vector<int>& arr, int X) {
int n = arr.size();
int i = 0, j = 0, currSum = 0;
while (j < n) {
currSum += countSetBit(arr[j]);
j++;
while (currSum > X) {
currSum -= countSetBit(arr[i]);
i++;
}
if (currSum == X) {
cout << "(" << i + 1 << ", " << j << ") ";
}
}
}
int main() {
vector<int> arr = {1, 4, 3, 5, 7};
int X = 4;
printSubarraysWithSetBitSumX(arr, X); // prints (1, 3) (3, 4)
return 0;
}
import java.util.*;
public class SubarraysWithSetBitSum {
public static int countSetBit(int x) {
int count = 0;
while (x > 0) {
count += x & 1;
x >>= 1;
}
return count;
}
public static void printSubarraysWithSetBitSumX(ArrayList<Integer> arr, int X) {
int n = arr.size();
int i = 0, j = 0, currSum = 0;
while (j < n) {
currSum += countSetBit(arr.get(j));
j++;
while (currSum > X) {
currSum -= countSetBit(arr.get(i));
i++;
}
if (currSum == X) {
System.out.print("(" + (i + 1) + ", " + j + ") ");
}
}
}
public static void main(String[] args) {
ArrayList<Integer> arr = new ArrayList<Integer>(Arrays.asList(1, 4, 3, 5, 7));
int X = 4;
printSubarraysWithSetBitSumX(arr, X); // prints (1, 3) (3, 4)
}
}
def count_set_bits(x):
# Function to count the number of set bits (1s) in a binary representation of 'x'
count = 0
while x > 0:
count += x & 1 # Add the least significant bit of 'x' to the count
x >>= 1 # Right shift 'x' to check the next bit
return count
def print_subarrays_with_set_bit_sum_x(arr, X):
n = len(arr) # Get the length of the input array 'arr'
i, j, curr_sum = 0, 0, 0 # Initialize variables for subarray tracking
while j < n: # Iterate through the array using a sliding window (j moves forward)
curr_sum += count_set_bits(arr[j]) # Add the count of set bits in 'arr[j]' to 'curr_sum'
j += 1
while curr_sum > X: # If 'curr_sum' exceeds the target 'X', move the window's left end (i) forward
curr_sum -= count_set_bits(arr[i]) # Subtract the count of set bits in 'arr[i]' from 'curr_sum'
i += 1
if curr_sum == X: # If 'curr_sum' matches the target 'X', print the subarray
print(f"({i + 1}, {j}) ", end='')
# Main function
if __name__ == "__main__":
arr = [1, 4, 3, 5, 7] # Input array
X = 4 # Target sum of set bits
print_subarrays_with_set_bit_sum_x(arr, X) # Call the function to find and print subarrays with the target sum
using System;
using System.Collections.Generic;
public class SubarraysWithSetBitSum {
// Function to count the number of set bits in a number
public static int CountSetBit(int x) {
int count = 0;
while (x > 0) {
count += x & 1; // Increment count if the last bit is 1
x >>= 1; // Right shift the number to check the next bit
}
return count;
}
// Function to find and print subarrays with a given set bit sum
public static void PrintSubarraysWithSetBitSumX(List<int> arr, int X) {
int n = arr.Count;
int i = 0, j = 0, currSum = 0;
while (j < n) {
currSum += CountSetBit(arr[j]); // Calculate set bit sum for the current element
j++;
// Slide the window to the right while current set bit sum is greater than X
while (currSum > X) {
currSum -= CountSetBit(arr[i]); // Remove set bit count of the left element
i++;
}
// If the current set bit sum matches X, print the subarray indices
if (currSum == X) {
Console.Write("(" + (i + 1) + ", " + j + ") ");
}
}
}
public static void Main(string[] args) {
List<int> arr = new List<int> { 1, 4, 3, 5, 7 };
int X = 4;
PrintSubarraysWithSetBitSumX(arr, X); // prints (1, 3) (3, 4)
}
}
function countSetBit(x) {
let count = 0;
while (x > 0) {
count += x & 1;
x >>= 1;
}
return count;
}
function printSubarraysWithSetBitSumX(arr, X) {
const n = arr.length;
let i = 0, j = 0, currSum = 0;
while (j < n) {
currSum += countSetBit(arr[j]);
j++;
while (currSum > X) {
currSum -= countSetBit(arr[i]);
i++;
}
if (currSum === X) {
console.log(`(${i + 1}, ${j})`);
}
}
}
const arr = [1, 4, 3, 5, 7];
const X = 4;
printSubarraysWithSetBitSumX(arr, X); // prints (1, 3) (3, 4)
Time complexity: O(n*logx)
Auxiliary Space: O(n)
Similar Reads
Basics & Prerequisites
Data Structures
Array Data StructureIn this article, we introduce array, implementation in different popular languages, its basic operations and commonly seen problems / interview questions. An array stores items (in case of C/C++ and Java Primitive Arrays) or their references (in case of Python, JS, Java Non-Primitive) at contiguous
3 min read
String in Data StructureA string is a sequence of characters. The following facts make string an interesting data structure.Small set of elements. Unlike normal array, strings typically have smaller set of items. For example, lowercase English alphabet has only 26 characters. ASCII has only 256 characters.Strings are immut
2 min read
Hashing in Data StructureHashing is a technique used in data structures that efficiently stores and retrieves data in a way that allows for quick access. Hashing involves mapping data to a specific index in a hash table (an array of items) using a hash function. It enables fast retrieval of information based on its key. The
2 min read
Linked List Data StructureA linked list is a fundamental data structure in computer science. It mainly allows efficient insertion and deletion operations compared to arrays. Like arrays, it is also used to implement other data structures like stack, queue and deque. Here’s the comparison of Linked List vs Arrays Linked List:
2 min read
Stack Data StructureA Stack is a linear data structure that follows a particular order in which the operations are performed. The order may be LIFO(Last In First Out) or FILO(First In Last Out). LIFO implies that the element that is inserted last, comes out first and FILO implies that the element that is inserted first
2 min read
Queue Data StructureA Queue Data Structure is a fundamental concept in computer science used for storing and managing data in a specific order. It follows the principle of "First in, First out" (FIFO), where the first element added to the queue is the first one to be removed. It is used as a buffer in computer systems
2 min read
Tree Data StructureTree Data Structure is a non-linear data structure in which a collection of elements known as nodes are connected to each other via edges such that there exists exactly one path between any two nodes. Types of TreeBinary Tree : Every node has at most two childrenTernary Tree : Every node has at most
4 min read
Graph Data StructureGraph Data Structure is a collection of nodes connected by edges. It's used to represent relationships between different entities. If you are looking for topic-wise list of problems on different topics like DFS, BFS, Topological Sort, Shortest Path, etc., please refer to Graph Algorithms. Basics of
3 min read
Trie Data StructureThe Trie data structure is a tree-like structure used for storing a dynamic set of strings. It allows for efficient retrieval and storage of keys, making it highly effective in handling large datasets. Trie supports operations such as insertion, search, deletion of keys, and prefix searches. In this
15+ min read
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
Binary Indexed Tree or Fenwick TreeBinary Indexed Trees are used for problems where we have following types of multiple operations on a fixed sized.Prefix Operation (Sum, Product, XOR, OR, etc). Note that range operations can also be solved using prefix. For example, range sum from index L to R is prefix sum till R (included minus pr
15 min read
Square Root (Sqrt) Decomposition AlgorithmSquare Root Decomposition Technique is one of the most common query optimization techniques used by competitive programmers. This technique helps us to reduce Time Complexity by a factor of sqrt(N) The key concept of this technique is to decompose a given array into small chunks specifically of size
15+ min read
Binary LiftingBinary Lifting is a Dynamic Programming approach for trees where we precompute some ancestors of every node. It is used to answer a large number of queries where in each query we need to find an arbitrary ancestor of any node in a tree in logarithmic time.The idea behind Binary Lifting:1. Preprocess
15+ 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
Interview Preparation
Practice Problem