Minimum flips required to convert given string into concatenation of equal substrings of length K

Given a binary string S and an integer K, the task is to find the minimum number of flips required to convert the given string into a concatenation of K-length equal sub-strings. It is given that the given string can be split into K-length substrings.

Examples: 

Input: S = "101100101", K = 3 
Output: 1 
Explanation: 
Flip the '0' from index 5 to '1'. 
The resultant string is S = "101101101". 
It is the concatenation of substring "101". 
Hence, the minimum number of flips required is 1.

Input: S = "10110111", K = 4 
Output: 2 
Explanation: 
Flip the '0' and '1' at indexes 4 and 5 respectively. 
The resultant string is S = "10111011". 
It is the concatenation of the substring "1011". 
Hence, the minimum number of flips required is 2.

Approach: 
The problem can be solved using Greedy Approach. 
Follow the steps below:

• Iterate the given string with increments of K indices from each index and keep a count of the 0s and 1s.
• The character which occurs the minimum number of times must be flipped and keep incrementing that count.
• Perform the above steps for all the indices from 0 to K-1 to obtain the minimum number of flips required.

Below is the implementation of the above approach:

// C++ Program to implement
// the above approach
#include <bits/stdc++.h>
using namespace std;

// Function that returns the minimum
// number of flips to convert
// the s into a concatenation
// of K-length sub-string
int minOperations(string S, int K)
{
    // Stores the result
    int ans = 0;

    // Iterate through string index
    for (int i = 0; i < K; i++) {

        // Stores count of 0s & 1s
        int zero = 0, one = 0;

        // Iterate making K jumps
        for (int j = i;
             j < S.size(); j += K) {

            // Count 0's
            if (S[j] == '0')
                zero++;

            // Count 1's
            else
                one++;
        }

        // Add minimum flips
        // for index i
        ans += min(zero, one);
    }

    // Return minimum number
    // of flips
    return ans;
}

// Driver Code
int main()
{
    string S = "110100101";

    int K = 3;

    cout << minOperations(S, K);

    return 0;
}

// Java program to implement 
// the above approach 
import java.io.*;

class GFG{

// Function that returns the minimum
// number of flips to convert
// the s into a concatenation
// of K-length sub-string
public static int minOperations(String S, int K)
{
    
    // Stores the result
    int ans = 0;

    // Iterate through string index
    for(int i = 0; i < K; i++)
    {

        // Stores count of 0s & 1s
        int zero = 0, one = 0;

        // Iterate making K jumps
        for(int j = i; j < S.length(); j += K)
        {
            
            // Count 0's
            if (S.charAt(j) == '0')
                zero++;

            // Count 1's
            else
                one++;
        }

        // Add minimum flips
        // for index i
        ans += Math.min(zero, one);
    }

    // Return minimum number
    // of flips
    return ans;
}

// Driver Code
public static void main(String args[])
{
    String S = "110100101";

    int K = 3;

    System.out.println(minOperations(S, K));
}
}

// This code is contributed by grand_master

# Python3 program to implement
# the above approach

# Function that returns the minimum
# number of flips to convert the s
# into a concatenation of K-length
# sub-string
def minOperations(S, K):

    # Stores the result
    ans = 0

    # Iterate through string index
    for i in range(K):

        # Stores count of 0s & 1s
        zero, one = 0, 0

        # Iterate making K jumps
        for j in range(i, len(S), K):

            # Count 0's
            if(S[j] == '0'):
                zero += 1

            # Count 1's
            else:
                one += 1

        # Add minimum flips
        # for index i
        ans += min(zero, one)

    # Return minimum number
    # of flips 
    return ans

# Driver code
if __name__ == '__main__':

    s = "110100101"
    K = 3

    print(minOperations(s, K))

# This code is contributed by Shivam Singh

// C# program to implement 
// the above approach 
using System;

class GFG{

// Function that returns the minimum
// number of flips to convert
// the s into a concatenation
// of K-length sub-string
public static int minOperations(String S, int K)
{
    
    // Stores the result
    int ans = 0;

    // Iterate through string index
    for(int i = 0; i < K; i++)
    {

        // Stores count of 0s & 1s
        int zero = 0, one = 0;

        // Iterate making K jumps
        for(int j = i; j < S.Length; j += K)
        {
            
            // Count 0's
            if (S[j] == '0')
                zero++;

            // Count 1's
            else
                one++;
        }

        // Add minimum flips
        // for index i
        ans += Math.Min(zero, one);
    }

    // Return minimum number
    // of flips
    return ans;
}

// Driver Code
public static void Main(String []args)
{
    String S = "110100101";

    int K = 3;

    Console.WriteLine(minOperations(S, K));
}
}

// This code is contributed by 29AjayKumar 

<script>
      // JavaScript program to implement
      // the above approach
      // Function that returns the minimum
      // number of flips to convert
      // the s into a concatenation
      // of K-length sub-string
      function minOperations(S, K) {
        // Stores the result
        var ans = 0;

        // Iterate through string index
        for (var i = 0; i < K; i++) {
          // Stores count of 0s & 1s
          var zero = 0,
            one = 0;

          // Iterate making K jumps
          for (var j = i; j < S.length; j += K) {
            // Count 0's
            if (S[j] === "0") 
                zero++;
            // Count 1's
            else 
                one++;
          }

          // Add minimum flips
          // for index i
          ans += Math.min(zero, one);
        }

        // Return minimum number
        // of flips
        return ans;
      }

      // Driver Code
      var S = "110100101";
      var K = 3;

      document.write(minOperations(S, K));
</script>

2

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