Count of Subarrays with sum equals k in given Binary Array
Last Updated :
16 May, 2025
Given a binary array arr[] and an integer k, the task is to find the count of non-empty subarrays with a sum equal to k.
Examples:
Input: arr[] = {1, 0, 1, 1, 0, 1}, k = 2
Output: 6
Explanation: All valid subarrays are: {1, 0, 1}, {0, 1, 1}, {1, 1}, {1, 0, 1}, {0, 1, 1, 0}, {1, 1, 0}.
Input: arr[] = {0, 0, 0, 0, 0}, k = 0
Output: 15
Explanation: All subarrays have a sum equal to 0, and there are a total of 15 subarrays.
[Naive Approach] Checking Each Subarray - O(n^2) time and O(1) space
The idea is to consider each subarray in the array and check if the sum is equal to the target.
C++
// C++ program to find count of Subarrays
// with sum equals k in given Binary Array
#include <iostream>
#include <vector>
using namespace std;
// Function to find count of subarrays
// with sum equal to k
int numberOfSubarrays(vector<int>& arr, int k) {
int ans = 0, n = arr.size();
// Check for each subarray
for (int i=0; i<n; i++) {
int sum = 0;
for (int j=i; j<n; j++) {
sum += arr[j];
if (sum == k) ans++;
}
}
return ans;
}
int main() {
vector<int> arr = { 1, 0, 1, 1, 0, 1 };
int k = 2;
cout << numberOfSubarrays(arr, k) << endl;
return 0;
}
// Java program to find count of Subarrays
// with sum equals k in given Binary Array
class Main {
// Function to find count of subarrays
// with sum equal to k
static int numberOfSubarrays(int[] arr, int k) {
int ans = 0, n = arr.length;
// Check for each subarray
for (int i = 0; i < n; i++) {
int sum = 0;
for (int j = i; j < n; j++) {
sum += arr[j];
if (sum == k) ans++;
}
}
return ans;
}
public static void main(String[] args) {
int[] arr = {1, 0, 1, 1, 0, 1};
int k = 2;
System.out.println(numberOfSubarrays(arr, k));
}
}
# Python program to find count of Subarrays
# with sum equals k in given Binary Array
# Function to find count of subarrays
# with sum equal to k
def numberOfSubarrays(arr, k):
ans = 0
n = len(arr)
# Check for each subarray
for i in range(n):
sum = 0
for j in range(i, n):
sum += arr[j]
if sum == k:
ans += 1
return ans
if __name__ == "__main__":
arr = [1, 0, 1, 1, 0, 1]
k = 2
print(numberOfSubarrays(arr, k))
// C# program to find count of Subarrays
// with sum equals k in given Binary Array
using System;
class GfG {
// Function to find count of subarrays
// with sum equal to k
static int numberOfSubarrays(int[] arr, int k) {
int ans = 0, n = arr.Length;
// Check for each subarray
for (int i = 0; i < n; i++) {
int sum = 0;
for (int j = i; j < n; j++) {
sum += arr[j];
if (sum == k) ans++;
}
}
return ans;
}
static void Main() {
int[] arr = {1, 0, 1, 1, 0, 1};
int k = 2;
Console.WriteLine(numberOfSubarrays(arr, k));
}
}
// JavaScript program to find count of Subarrays
// with sum equals k in given Binary Array
// Function to find count of subarrays
// with sum equal to k
function numberOfSubarrays(arr, k) {
let ans = 0;
let n = arr.length;
// Check for each subarray
for (let i = 0; i < n; i++) {
let sum = 0;
for (let j = i; j < n; j++) {
sum += arr[j];
if (sum === k) ans++;
}
}
return ans;
}
let arr = [1, 0, 1, 1, 0, 1];
let k = 2;
console.log(numberOfSubarrays(arr, k));
[Expected Approach] Using Sliding Window Approach - O(n) time and O(1) space
The idea is to use a sliding window approach with two pointers to efficiently count the number of subarrays with sum equal to k. The key insight is that we can find subarrays with sum exactly equal to k by calculating the difference between the count of subarrays with sum at most k and the count of subarrays with sum at most k-1.
Step by step approach:
- Create a sliding window that expands rightward as long as adding the next element doesn't exceed the target sum.
- For each position of the left pointer, count how many valid subarrays start at that position.
- The number of valid subarrays starting at each position equals the distance between the two pointers.
- Remove the leftmost element from the window and shift the left pointer right.
- Subtract the count of subarrays with sum at most (k-1) from the count of subarrays with sum at most k to get the result.
C++
// C++ program to find count of Subarrays
// with sum equals k in given Binary Array
#include <iostream>
#include <vector>
using namespace std;
// Function to find count of subarrays
// with sum at most k
int atmost(vector<int>& arr, int k){
if (k < 0)
return 0;
int n = arr.size();
int res = 0, sum = 0, j = 0;
for (int i=0; i<n; i++) {
while (j < n && sum+arr[j] <= k) {
sum += arr[j];
j++;
}
// Number of sub-arrays starting from
// index i that have sum atmost k will
// be (j-i).
res += (j - i);
// Remove the i'th index from window.
sum -= arr[i];
}
return res;
}
// Function to find count of subarrays
// with sum equal to k
int numberOfSubarrays(vector<int>& arr, int k) {
// Call atmost(arr, k) and atmost
// (arr, k-1) to get the count of
// subarrays with sum at most k
// and sum at most k-1 respectively,
// then subtract them to get the count
// of subarrays with sum exactly
// equal to k
return atmost(arr, k) - atmost(arr, k - 1);
}
int main() {
vector<int> arr = { 1, 0, 1, 1, 0, 1 };
int k = 2;
cout << numberOfSubarrays(arr, k) << endl;
return 0;
}
// Java program to find count of Subarrays
// with sum equals k in given Binary Array
import java.util.*;
class GfG {
// Function to find count of subarrays
// with sum at most k
static int atmost(int[] arr, int k) {
if (k < 0)
return 0;
int n = arr.length;
int res = 0, sum = 0, j = 0;
for (int i = 0; i < n; i++) {
while (j < n && sum + arr[j] <= k) {
sum += arr[j];
j++;
}
// Number of sub-arrays starting from
// index i that have sum atmost k will
// be (j-i).
res += (j - i);
// Remove the i'th index from window.
sum -= arr[i];
}
return res;
}
// Function to find count of subarrays
// with sum equal to k
static int numberOfSubarrays(int[] arr, int k) {
// Call atmost(arr, k) and atmost
// (arr, k-1) to get the count of
// subarrays with sum at most k
// and sum at most k-1 respectively,
// then subtract them to get the count
// of subarrays with sum exactly
// equal to k
return atmost(arr, k) - atmost(arr, k - 1);
}
public static void main(String[] args) {
int[] arr = {1, 0, 1, 1, 0, 1};
int k = 2;
System.out.println(numberOfSubarrays(arr, k));
}
}
# Python program to find count of Subarrays
# with sum equals k in given Binary Array
# Function to find count of subarrays
# with sum at most k
def atmost(arr, k):
if k < 0:
return 0
n = len(arr)
res, sum_, j = 0, 0, 0
for i in range(n):
while j < n and sum_ + arr[j] <= k:
sum_ += arr[j]
j += 1
# Number of sub-arrays starting from
# index i that have sum atmost k will
# be (j-i).
res += (j - i)
# Remove the i'th index from window.
sum_ -= arr[i]
return res
# Function to find count of subarrays
# with sum equal to k
def numberOfSubarrays(arr, k):
# Call atmost(arr, k) and atmost
# (arr, k-1) to get the count of
# subarrays with sum at most k
# and sum at most k-1 respectively,
# then subtract them to get the count
# of subarrays with sum exactly
# equal to k
return atmost(arr, k) - atmost(arr, k - 1)
if __name__ == "__main__":
arr = [1, 0, 1, 1, 0, 1]
k = 2
print(numberOfSubarrays(arr, k))
// C# program to find count of Subarrays
// with sum equals k in given Binary Array
using System;
class GfG {
// Function to find count of subarrays
// with sum at most k
static int atmost(int[] arr, int k) {
if (k < 0)
return 0;
int n = arr.Length;
int res = 0, sum = 0, j = 0;
for (int i = 0; i < n; i++) {
while (j < n && sum + arr[j] <= k) {
sum += arr[j];
j++;
}
// Number of sub-arrays starting from
// index i that have sum atmost k will
// be (j-i).
res += (j - i);
// Remove the i'th index from window.
sum -= arr[i];
}
return res;
}
// Function to find count of subarrays
// with sum equal to k
static int numberOfSubarrays(int[] arr, int k) {
// Call atmost(arr, k) and atmost
// (arr, k-1) to get the count of
// subarrays with sum at most k
// and sum at most k-1 respectively,
// then subtract them to get the count
// of subarrays with sum exactly
// equal to k
return atmost(arr, k) - atmost(arr, k - 1);
}
static void Main() {
int[] arr = {1, 0, 1, 1, 0, 1};
int k = 2;
Console.WriteLine(numberOfSubarrays(arr, k));
}
}
// JavaScript program to find count of Subarrays
// with sum equals k in given Binary Array
// Function to find count of subarrays
// with sum at most k
function atmost(arr, k) {
if (k < 0)
return 0;
let n = arr.length;
let res = 0, sum = 0, j = 0;
for (let i = 0; i < n; i++) {
while (j < n && sum + arr[j] <= k) {
sum += arr[j];
j++;
}
// Number of sub-arrays starting from
// index i that have sum atmost k will
// be (j-i).
res += (j - i);
// Remove the i'th index from window.
sum -= arr[i];
}
return res;
}
// Function to find count of subarrays
// with sum equal to k
function numberOfSubarrays(arr, k) {
// Call atmost(arr, k) and atmost
// (arr, k-1) to get the count of
// subarrays with sum at most k
// and sum at most k-1 respectively,
// then subtract them to get the count
// of subarrays with sum exactly
// equal to k
return atmost(arr, k) - atmost(arr, k - 1);
}
let arr = [1, 0, 1, 1, 0, 1];
let k = 2;
console.log(numberOfSubarrays(arr, k));
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