Minimum number of steps needed to remove the substring K from given string

Given a binary string S, and a substring K, the task is to find the minimum no of steps required to flip the characters in a binary string such that it doesn’t contain the given substring K. Note: In one step we can change 0 to 1 or vice versa.
Examples:

Input: S = “0111011”, K = “011” 
Output: 2 
Explanation:
In the above string we have the substring 011 for 2 times, hence change the 3rd bit and 7th bit.

Input: S = “010010”, K = “0100” 
Output: 1 
Explanation:
In the above string we have the substring 0100 for 1 time, change the 4th bit of the string to 1. 

Naive Approach: The naive approach is to use the Pattern Searching. Iterate through the string for N! times(N = length of the binary string). In every iteration check for the substring K and if its a match then increment the count. At last, print the count which will be the number of steps required to make the string such that it doesn’t contain the given substring K.

Time Complexity: O(M*N) where M is the length of substring and N is the length of the binary string. 
Auxiliary Space: O(1)

Efficient Approach: To optimize the above method, the idea is to replace the substring with an empty string and subtract the resultant string length from original string length. After this divide the resultant string with the length of the given substring K to get the minimum no of steps required to flip the characters of the given string S so that it doesn’t contain the given substring K.

Below is the implementation of the above approach:

C++

// C++ program for the above approach
#include<bits/stdc++.h>
#include <boost/algorithm/string/replace.hpp>
using namespace std;

// Function that counts the total
// number of character to be flipped
// such the string b doesn't contains
// string sub as a substring
int flipCharacters(string b,
                   string sub)
{

    // Replacing the substring with ""
    // and find the difference between
    // the length of the resultant
    // string and the original
    // string length
    int res = b.size();
    boost::replace_all(b, sub, "");
    res = res - b.size();

    // Divide the result
    // with substring length
    int temp = res / sub.size();

    // Return the final count
    return temp;
}

// Driver Code
int main()
{

    // Given string S and substring K
    string S = "010010";
    string K = "0100";

    // Function call
    int result = flipCharacters(S, K);

    // Print the minimum flip
    cout << (result);
}

// This code is contributed by Amit Katiyar

Java

// Java program for the above approach
import java.util.*;

public class Test {

    // Function that counts the total
    // number of character to be flipped
    // such the string b doesn't contains
    // string sub as a substring
    static int flipCharacters(String b,
                              String sub)
    {

        // Replacing the substring with ""
        // and find the difference between
        // the length of the resultant
        // string and the original
        // string length

        int res = b.length()
                  - b.replaceAll(sub, "")
                        .length();

        // Divide the result
        // with substring length

        int temp = res / sub.length();

        // Return the final count
        return temp;
    }

    // Driver Code
    public static void main(String[] args)
    {

        // Given string S and substring K
        String S = "010010";
        String K = "0100";

        // Function Call
        int result = flipCharacters(S, K);

        // Print the minimum flip
        System.out.println(result);
    }
}

Python3

# Python3 program for the above approach
def flipCharacters(b, sub):

    # Replace the substring with
    # "" (emptryString)
    b1 = b.replace(sub, "")

    n = int((len(b)-len(b1))/len(sub))

    return n

# Driver Code
if __name__ == '__main__':

# Given string S and substring K
    S ="010010"
    X ="0100"

# Function Call
    result = flipCharacters(S, X)

# Print the minimum flip
    print(result)

C#

// C# program for the above approach
using System;
class GFG
{

  // Function that counts the total
  // number of character to be flipped
  // such the string b doesn't contains
  // string sub as a substring
  static int flipCharacters(string b,
                            string sub)
  {

    // Replacing the substring with ""
    // and find the difference between
    // the length of the resultant
    // string and the original
    // string length

    int res = b.Length -
              b.Replace(sub, "").Length;

    // Divide the result
    // with substring length
    int temp = res / sub.Length;

    // Return the final count
    return temp;
  }

  // Driver Code
  public static void Main(string[] args)
  {

    // Given string S and substring K
    string S = "010010";
    string K = "0100";

    // Function Call
    int result = flipCharacters(S, K);

    // Print the minimum flip
    Console.Write(result);
  }
}

// This code is contributed by rutvik_56

Javascript

<script>

// JavaScript program for the above approach

// Function that counts the total
// number of character to be flipped
// such the string b doesn't contains
// string sub as a substring
function flipCharacters(b, sub)
{

    // Replacing the substring with ""
    // and find the difference between
    // the length of the resultant
    // string and the original
    // string length
    var res = b.length - b.replace(sub, "").length;

    // Divide the result
    // with substring length
    var temp = parseInt(res / sub.length);

    // Return the final count
    return temp;
}

// Driver Code

// Given string S and substring K
var S = "010010";
var K = "0100";

// Function call
var result = flipCharacters(S, K);

// Print the minimum flip
document.write(result);


</script>

Output:

1

Time Complexity: O(N), where N is the length of the string. 
Auxiliary Space: O(1)