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

• Difficulty Level : Medium
• Last Updated : 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:
Explanation:
The substring “111” contains 3 set bits.

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

Naive Approach:

1. Generate all substring of size K.
2. 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.

1. Take maxcount variable to store maximum count of set bit and Count variable to store count set bit of current window.
2. Traverse string from 1 to K and calculate the count of set bits and store as maxcount.
3. Traverse string from K + 1 to length of the string.
4. At every iteration, decrease count if (K – i)th bit is set. Increase count if ith bit is set. Compare and update maxcount.
5. 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``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

 ``
Output:
`3`

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

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