Maximum number of set bits count in a Ksize substring of a Binary String (original) (raw)

Last Updated : 18 Oct, 2023

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( N 2 ).
**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_**countif ****(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

**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 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

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