Minimum substring reversals required to make given Binary String alternating

Given a binary string S of length N, the task is to count the minimum number substrings of S that is required to be reversed to make the string S alternating. If it is not possible to make string alternating, then print "-1".

Examples:

Input: S = "10001110"
Output: 2
Explanation:
In the first operation, reversing the substring {S[3], .., S[6]} modifies the string to "10110010".
In the second operation, reversing the substring {S[4], .. S[5]}modifies the string to "10101010", which is alternating.

Input: S = "100001"
Output: -1
Explanation: Not possible to obtain an alternating binary string.

Approach: The idea is based on the observation that when a substring s[L, R] is reversed, then no more than two pairs s[L - 1], s[L] and s[R], S[R + 1] are changed. Moreover, one pair should be a consecutive pair of 00 and the other 11. So, the minimum number of operations can be obtained by pairing 00 with 11 or with the left/right border of S. Thus, the required number of operations is half of the number of consecutive pairs of the same character. Follow the steps below to solve the problem:

• Traverse the string S to count the number of 1s and 0s and store them in sum1 and sum0 respectively.
• If the absolute difference of sum1 and sum0 > 1, then print "-1".
• Otherwise, find the count of consecutive characters that are the same in the string S. Let that count be K for 1 and L for 0.
• After completing the above steps, print the value of K as the result.

Below is the implementation of the above approach:

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

// Function to count the minimum number
// of substrings required to be reversed
// to make the string S alternating
int minimumReverse(string s, int n)
{
    // Store count of consecutive pairs
    int k = 0 , l = 0 ;

    // Stores the count of 1s and 0s
    int sum1 = 0, sum0 = 0;

    // Traverse through the string
    for (int i = 1; i < n; i++) {

        if (s[i] == '1')

            // Increment 1s count
            sum1++;
        else

            // Increment 0s count
            sum0++;

        // Increment K if consecutive
        // same elements are found
        if (s[i] == s[i - 1]&& s[i] == '0')
            k++;
      else if( s[i] == s[i - 1]&& s[i] == '1')
        l++;
    }
  
    // Increment 1s count
    if(s[0]=='1')     
       sum1++;
    else  // Increment 0s count
       sum0++;

    // Check if it is possible or not
    if (abs(sum1 - sum0) > 1)
        return -1;

    // Otherwise, print the number
    // of required operations
    return max(k , l );
}

// Driver Code
int main()
{
    string S = "10001";
    int N = S.size();

    // Function Call
    cout << minimumReverse(S, N);

    return 0;
}

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

class GFG 
{

  // Function to count the minimum number
  // of substrings required to be reversed
  // to make the string S alternating
  static int minimumReverse(String s, int n)
  {

    // Store count of consecutive pairs
    int k = 0 , l = 0 ;

    // Stores the count of 1s and 0s
    int sum1 = 0, sum0 = 0;

    // Traverse through the string
    for (int i = 1; i < n; i++) 
    {

      if (s.charAt(i) == '1')

        // Increment 1s count
        sum1++;
      else

        // Increment 0s count
        sum0++;

      // Increment K if consecutive
      // same elements are found
      if (s.charAt(i) == s.charAt(i - 1) && s.charAt(i) == '0')
        k++;
      else if( s.charAt(i) == s.charAt(i - 1) && s.charAt(i) == '1')
        l++;
    }

    // Increment 1s count
    if(s.charAt(0)=='1')     
      sum1++;
    else  // Increment 0s count
      sum0++;

    // Check if it is possible or not
    if (Math.abs(sum1 - sum0) > 1)
      return -1;

    // Otherwise, print the number
    // of required operations
    return Math.max(k , l);
  }

  // Driver code
  public static void main (String[] args) 
  {
    String S = "10001";
    int N = S.length();

    // Function Call
    System.out.print(minimumReverse(S, N));

  }
}

// This code is contributed by offbeat

# Python program for the above approach

# Function to count the minimum number
# of substrings required to be reversed
# to make the string S alternating
def minimumReverse(s, n):
  
    # Store count of consecutive pairs
    k = 0;
    l = 0;

    # Stores the count of 1s and 0s
    sum1 = 0;
    sum0 = 0;

    # Traverse through the string
    for i in range(1, n):
        if (s[i] == '1'):

            # Increment 1s count
            sum1 += 1;
        else:

            # Increment 0s count
            sum0 += 1;

        # Increment K if consecutive
        # same elements are found
        if (s[i] == s[i - 1] and s[i] == '0'):
            k += 1;
        elif (s[i] == s[i - 1] and s[i] == '1'):
            l += 1;

    # Increment 1s count
    if (s[0] == '1'):
        sum1 += 1;
    else:  # Increment 0s count
        sum0 += 1;

    # Check if it is possible or not
    if (abs(sum1 - sum0) > 1):
        return -1;

    # Otherwise, print the number
    # of required operations
    return max(k, l);

# Driver code
if __name__ == '__main__':
    S = "10001";
    N = len(S);

    # Function Call
    print(minimumReverse(S, N));

# This code is contributed by shikhasingrajput 

// C# program for the above approach
using System;

public class GFG 
{

  // Function to count the minimum number
  // of substrings required to be reversed
  // to make the string S alternating
  static int minimumReverse(String s, int n)
  {

    // Store count of consecutive pairs
    int k = 0 , l = 0 ;

    // Stores the count of 1s and 0s
    int sum1 = 0, sum0 = 0;

    // Traverse through the string
    for (int i = 1; i < n; i++) 
    {

      if (s[i] == '1')

        // Increment 1s count
        sum1++;
      else

        // Increment 0s count
        sum0++;

      // Increment K if consecutive
      // same elements are found
      if (s[i] == s[i-1] && s[i] == '0')
        k++;
      else if( s[i] == s[i-1] && s[i] == '1')
        l++;
    }

    // Increment 1s count
    if(s[0] == '1')     
      sum1++;
    else  // Increment 0s count
      sum0++;

    // Check if it is possible or not
    if (Math.Abs(sum1 - sum0) > 1)
      return -1;

    // Otherwise, print the number
    // of required operations
    return Math.Max(k , l);
  }

  // Driver code
  public static void Main(String[] args) 
  {
    String S = "10001";
    int N = S.Length;

    // Function Call
    Console.Write(minimumReverse(S, N));
  }
}


// This code is contributed by shikhasingrajput 

<script>

// JavaScript program to implement
// the above approach

  // Function to count the minimum number
  // of substrings required to be reversed
  // to make the string S alternating
  function minimumReverse(s, n)
  {
 
    // Store count of consecutive pairs
    let k = 0 , l = 0 ;
 
    // Stores the count of 1s and 0s
    let sum1 = 0, sum0 = 0;
 
    // Traverse through the string
    for (let i = 1; i < n; i++)
    {
 
      if (s[i] == '1')
 
        // Increment 1s count
        sum1++;
      else
 
        // Increment 0s count
        sum0++;
 
      // Increment K if consecutive
      // same elements are found
      if (s[i] == s[i-1] && s[i] == '0')
        k++;
      else if( s[i] == s[i-1] && s[i] == '1')
        l++;
    }
 
    // Increment 1s count
    if(s[0] == '1')    
      sum1++;
    else  // Increment 0s count
      sum0++;
 
    // Check if it is possible or not
    if (Math.abs(sum1 - sum0) > 1)
      return -1;
 
    // Otherwise, print the number
    // of required operations
    return Math.max(k , l);
  }
     
// Driver code
        
    let S = "10001";
    let N = S.length;
 
    // Function Call
    document.write(minimumReverse(S, N));

</script>

2

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