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

18 May, 2021
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.
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 ith bit is set. Compare and update maxcount.After complete array traversal, finally return maxcount.
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 ith bit is set. Compare and update maxcount.
After complete array traversal, finally return maxcount.
Below is the implementation of the above approach:  
C++
Java
Python3
C#
Javascript
// 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 codeint main(){    string s = "100111010";    int k = 3;     cout << (maxSetBitCount(s, k));    return 0;} // This code is contributed by Rajput-Ji
// Java program to find the maximum// set bits in a substring of size Kimport 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 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 codeif __name__ == '__main__':         s = "100111010"    k = 3     print(maxSetBitCount(s, k))     # This code is contributed by mohit kumar 29
// C# program to find the maximum// set bits in a substring of size Kusing 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 Programpublic static void Main(){    string s = "100111010";    int k = 3;     Console.Write(maxSetBitCount(s, k));}} // This code is contributed by Code_Mech
<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 codevar s = "100111010";var k = 3;document.write(maxSetBitCount(s, k)); // This code is contributed by famously.</script>
3
 
Time Complexity: O(N). Auxiliary Space: O(1). 
mohit kumar 29
Rajput-Ji
Code_Mech
nidhi_biet
simmytarika5
famously
binary-string
setBitCount
sliding-window
substring
Bit Magic
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sliding-window
Strings
Bit Magic
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