Data Modelling & AI Data Structure & Algorithm

Maximum number of set bits count in a K-size substring of a Binary String

23 June 2025

0

Given a binary string S of size N and an integer K. The task is to find the maximum number of set bit appears in a substring of size K.

Examples:

Input: S = “100111010”, K = 3
Output: 3
Explanation:
The substring “111” contains 3 set bits.

Input:S = “0000000”, K = 4
Output: 0
Explanation: S doesn’t have any set bits in it, so ans is 0.

Naive Approach:

Generate all substring of size K.
Find maximum of count of set bits in all substrings.

Time Complexity: O( N²).
Auxiliary Space: O(1).

Efficient Approach: The problem can be solved using Sliding window technique.

Take maxcount variable to store maximum count of set bit and Count variable to store count set bit of current window.
Traverse string from 1 to K and calculate the count of set bits and store as maxcount.
Traverse string from K + 1 to length of the string.
At every iteration, decrease count if (K – i)^th bit is set. Increase count if i^th bit is set. Compare and update maxcount.
After complete array traversal, finally return maxcount.

Below is the implementation of the above approach:

C++

// C++ program to find the maximum
// set bits in a substring of size K
#include<bits/stdc++.h>
using namespace std;
 
// Function that find Maximum number
// of set bit appears in a substring
// of size K.
int maxSetBitCount(string s, int k)
{
    int maxCount = 0, n = s.length();
    int count = 0;
 
    // Traverse string 1 to k
    for(int i = 0; i < k; i++) 
    {
         
       // Increment count if
       // character is set bit
       if (s[i] == '1')
           count++;
    }
    maxCount = count;
 
    // Traverse string k+1
    // to length of string
    for(int i = k; i < n; i++)
    {
        
       // Remove the contribution of the
       // (i - k)th character which is no
       // longer in the window
       if (s[i - k] == '1')
           count--;
        
       // Add the contribution of
       // the current character
       if (s[i] == '1')
           count++;
            
       // Update maxCount at for
       // each window of size k
       maxCount = max(maxCount, count);
    }
     
    // Return maxCount
    return maxCount;
}
 
// Driver code
int main()
{
    string s = "100111010";
    int k = 3;
 
    cout << (maxSetBitCount(s, k));
    return 0;
}
 
// This code is contributed by Rajput-Ji

Java

// Java program to find the maximum
// set bits in a substring of size K
import java.util.*;
 
class GFG {
 
    // Function that find Maximum number
    // of set bit appears in a substring
    // of size K.
    static int maxSetBitCount(String s, int k)
    {
 
        int maxCount = 0, n = s.length();
        int count = 0;
 
        // Traverse string 1 to k
        for (int i = 0; i < k; i++) {
            // Increment count if
            // character is set bit
            if (s.charAt(i) == '1')
                count++;
        }
 
        maxCount = count;
 
        // Traverse string k+1
        // to length of string
        for (int i = k; i < n; i++) {
 
            // remove the contribution of the
            // (i - k)th character which is no
            // longer in the window
            if (s.charAt(i - k) == '1')
                count--;
 
            // add the contribution of
            // the current character
            if (s.charAt(i) == '1')
                count++;
 
            // update maxCount at for
            // each window of size k
            maxCount = Math.max(maxCount, count);
        }
 
        // return maxCount
        return maxCount;
    }
    // Driver Program
    public static void main(String[] args)
    {
        String s = "100111010";
        int k = 3;
 
        System.out.println(maxSetBitCount(s, k));
    }
}

Python3

# Python3 program to find the maximum
# set bits in a substring of size K
 
# Function that find Maximum number
# of set bit appears in a substring
# of size K.
def maxSetBitCount(s, k):
 
    maxCount = 0
    n = len(s)
    count = 0
 
    # Traverse string 1 to k
    for i in range(k):
         
        # Increment count if
        # character is set bit
        if (s[i] == '1'):
            count += 1
 
    maxCount = count
 
    # Traverse string k+1
    # to length of string
    for i in range(k, n):
 
        # Remove the contribution of the
        # (i - k)th character which is no
        # longer in the window
        if (s[i - k] == '1'):
            count -= 1
 
        # Add the contribution of
        # the current character
        if (s[i] == '1'):
            count += 1
 
        # Update maxCount at for
        # each window of size k
        maxCount = max(maxCount, count)
 
    # Return maxCount
    return maxCount
 
 
# Driver code
if __name__ == '__main__':
     
    s = "100111010"
    k = 3
 
    print(maxSetBitCount(s, k))
     
# This code is contributed by mohit kumar 29

C#

// C# program to find the maximum
// set bits in a substring of size K
using System;
class GFG {
 
// Function that find Maximum number
// of set bit appears in a substring
// of size K.
static int maxSetBitCount(string s, int k)
{
 
    int maxCount = 0, n = s.Length;
    int count = 0;
 
    // Traverse string 1 to k
    for (int i = 0; i < k; i++) 
    {
        // Increment count if
        // character is set bit
        if (s[i] == '1')
            count++;
    }
 
    maxCount = count;
 
    // Traverse string k+1
    // to length of string
    for (int i = k; i < n; i++) 
    {
 
        // remove the contribution of the
        // (i - k)th character which is no
        // longer in the window
        if (s[i - k] == '1')
            count--;
 
        // add the contribution of
        // the current character
        if (s[i] == '1')
            count++;
 
        // update maxCount at for
        // each window of size k
        maxCount = Math.Max(maxCount, count);
    }
 
    // return maxCount
    return maxCount;
}
// Driver Program
public static void Main()
{
    string s = "100111010";
    int k = 3;
 
    Console.Write(maxSetBitCount(s, k));
}
}
 
// This code is contributed by Code_Mech

Javascript

<script>
 
// Javascript program to find the maximum
// set bits in a substring of size K
 
// Function that find Maximum number
// of set bit appears in a substring
// of size K.
function maxSetBitCount(s, k)
{
    var maxCount = 0, n = s.length;
    var count = 0;
 
    // Traverse string 1 to k
    for(var i = 0; i < k; i++) 
    {
         
       // Increment count if
       // character is set bit
       if (s[i] == '1')
           count++;
    }
    maxCount = count;
 
    // Traverse string k+1
    // to length of string
    for(var i = k; i < n; i++)
    {
        
       // Remove the contribution of the
       // (i - k)th character which is no
       // longer in the window
       if (s[i - k] == '1')
           count--;
        
       // Add the contribution of
       // the current character
       if (s[i] == '1')
           count++;
            
       // Update maxCount at for
       // each window of size k
       maxCount = Math.max(maxCount, count);
    }
     
    // Return maxCount
    return maxCount;
}
 
// Driver code
var s = "100111010";
var k = 3;
document.write(maxSetBitCount(s, k));
 
// This code is contributed by famously.
</script>

Output

Time Complexity: O(N).
Auxiliary Space: O(1).

Brute Force in python:

Approach:

One simple approach to solve the problem is to generate all possible substrings of length K from the binary string S and count the number of set bits in each substring. Finally, return the maximum count of set bits among all the substrings.

Define a function count_set_bits(s) that takes a binary string s and returns the count of set bits (i.e., number of ‘1’s) in it.
Define a function max_set_bits(s, k) that takes a binary string s and an integer k and returns the maximum count of set bits in a substring of length k of s.
- Get the length n of the binary string s.
- Initialize a variable ans to 0, which will hold the maximum count of set bits among all the substrings.
- Iterate over all possible substrings of length k in the binary string s. We do this by iterating over all starting positions i from 0 to n-k and taking the substring s[i:i+k].
- For each substring, compute the count of set bits by calling the function count_set_bits(s[i:i+k]).
- Update the ans variable to hold the maximum count of set bits among all the substrings seen so far.
- Return the ans variable as the output.

Example usage: Call the max_set_bits() function with the binary string “100111010” and k=3 as inputs and print the output, which should be 3. Similarly, call the function with the binary string “0000000” and k=4 as inputs and print the output, which should be 0.

C++

#include <iostream>
using namespace std;
 
int countSetBits(string s) {
    int count = 0;
    for (char c : s) {
        if (c == '1') {
            count++;
        }
    }
    return count;
}
int maxSetBits(string s, int k) {
    int n = s.length();
    int ans = 0;
    for (int i = 0; i <= n - k; i++) {
        string subStr = s.substr(i, k);
        int setBitsCount = countSetBits(subStr);
        ans = max(ans, setBitsCount);
    }
    return ans;
}
int main() {
    // Example usage
    cout << maxSetBits("100111010", 3) << endl;
    cout << maxSetBits("0000000", 4) << endl;
    return 0;
}

Java

public class Main {
    // Function to count the number of '1's in a given
    // string.
    public static int countSetBits(String s)
    {
        int count = 0;
        for (char c : s.toCharArray()) {
            if (c == '1') {
                count++;
            }
        }
        return count;
    }
 
    // Function to find the maximum count of '1's in a
    // substring of length 'k'.
    public static int maxSetBits(String s, int k)
    {
        int n = s.length();
        int ans = 0;
        // Iterate through the string to find substrings of
        // length 'k'.
        for (int i = 0; i <= n - k; i++) {
            String subStr = s.substring(i, i + k);
            int setBitsCount = countSetBits(subStr);
            ans = Math.max(ans, setBitsCount);
        }
        return ans;
    }
 
    public static void main(String[] args)
    {
        // Example usage and testing of the maxSetBits
        // function.
        System.out.println(
            "Maximum set bits in '100111010' with k=3: "
            + maxSetBits("100111010", 3));
        System.out.println(
            "Maximum set bits in '0000000' with k=4: "
            + maxSetBits("0000000", 4));
    }
}

Python3

def count_set_bits(s):
    return s.count('1')
 
def max_set_bits(s, k):
    n = len(s)
    ans = 0
    for i in range(n-k+1):
        ans = max(ans, count_set_bits(s[i:i+k]))
    return ans
 
# Example usage
print(max_set_bits("100111010", 3))  # Output: 3
print(max_set_bits("0000000", 4))   # Output: 0

C#

using System;
 
class Program {
    // Function to count the number of set bits in a string
    static int CountSetBits(string s)
    {
        int count = 0;
        foreach(char c in s)
        {
            if (c == '1') {
                count++;
            }
        }
        return count;
    }
 
    // Function to find the maximum number of set bits in a
    // substring of length k
    static int MaxSetBits(string s, int k)
    {
        int n = s.Length;
        int ans = 0;
        for (int i = 0; i <= n - k; i++) {
            string subStr = s.Substring(i, k);
            int setBitsCount = CountSetBits(subStr);
            ans = Math.Max(ans, setBitsCount);
        }
        return ans;
    }
 
    static void Main()
    {
        // Example usage
        Console.WriteLine(MaxSetBits("100111010", 3));
        Console.WriteLine(MaxSetBits("0000000", 4));
    }
}

Javascript

function countSetBits(s) {
    let count = 0;
    for (let i = 0; i < s.length; i++) {
        if (s[i] === '1') {
            count++;
        }
    }
    return count;
}
function maxSetBits(s, k) {
    const n = s.length;
    let ans = 0;
    for (let i = 0; i <= n - k; i++) {
        const subStr = s.substring(i, i + k);
        const setBitsCount = countSetBits(subStr);
        ans = Math.max(ans, setBitsCount);
    }
    return ans;
}
// Example usage
console.log(maxSetBits("100111010", 3));
console.log(maxSetBits("0000000", 4));

Output

3
0

Time Complexity: O(N * K^2), where N is the length of the binary string S.
Space Complexity: O(1)

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Maximum number of set bits count in a K-size substring of a Binary String

C++

Java

Python3

C#

Javascript

Brute Force in python:

C++

Java

Python3

C#

Javascript

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