Minimum substring flips required to convert given binary string to another

Given two binary strings A and B, the task is to find the minimum number of times a substring starting from the first character of A needs to be flipped, i.e. convert 1s to 0s and 0s to 1s, to convert A to B.

Examples:

Input: A = “0010”, B = “1011”
Output; 3
Explanation:
Step 1: Flip the entire string A. Therefore, A becomes “1101” .
Step 2: Flip the substring {A[0], A[2]}. Therefore, A becomes "0011" .
Step 3: Flip A[0]. Therefore, A becomes "1011" which is equal to B.
Therefore, the minimum number of operations required is 3.

Input: A = “1010101”, B = “0011100”
Output: 5
Explanation:
Step 1: Flip the entiThehrefore, A becomes “0101010"
Step 2: Flip substring {A[0], A[5]}. Therefore, A becomes “1010100"
Step 3: Flip the substring {A[0], A[3]}. Therefore, A becomes “0101100"
Step 4: Flip the substring {A[0], A[2]}. Therefore, A becomes “1011100"
Step 5: Flip A[0]. Therefore, A becomes "0011100" which is equal to B.
Therefore, the minimum number of operations required is 5.

Approach: The idea is to initialize a variable that holds the last index at which character at A is different from the character at B. Then negate A from the 1st index to the last index. Repeat until both strings become equal. Follow the steps below to solve the problem:

• Initialize a variable last_index that holds the last index at which characters are different in A and B.
• Negate string A from the 1st index to last_index and increment the count of steps.
• Repeat the above steps until string A becomes equal to string B.
• Print the count of steps after both the strings are the same after performing the operations.

Below is the implementation of the above approach:

// C++ program for the above approach

#include <bits/stdc++.h>
using namespace std;

// Function that finds the minimum
// number of operations required such
// that string A and B are the same
void findMinimumOperations(string a,
                           string b)
{

    // Stores the count of steps
    int step = 0;

    // Stores the last index whose
    // bits are not same
    int last_index;

    // Iterate until both string
    // are unequal
    while (a != b) {

        // Check till end of string to
        // find rightmost unequals bit
        for (int i = 0;
             i < a.length(); i++) {

            // Update the last index
            if (a[i] != b[i]) {
                last_index = i;
            }
        }

        // Flipping characters up
        // to the last index
        for (int i = 0;
             i <= last_index; i++) {

            // Flip the bit
            a[i] = (a[i] == '0') ? '1' : '0';
        }

        // Increasing steps by one
        step++;
    }

    // Print the count of steps
    cout << step;
}

// Driver Code
int main()
{
    // Given strings A and B
    string A = "101010", B = "110011";

    // Function Call
    findMinimumOperations(A, B);

    return 0;
}

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

// Function that finds the minimum
// number of operations required such
// that String A and B are the same
static void findMinimumOperations(char[] a,
                                  char[] b)
{
  // Stores the count of steps
  int step = 0;

  // Stores the last index whose
  // bits are not same
  int last_index = 0;

  // Iterate until both String
  // are unequal
  while (!Arrays.equals(a, b))
  {
    // Check till end of String to
    // find rightmost unequals bit
    for (int i = 0;
             i < a.length; i++) 
    {
      // Update the last index
      if (a[i] != b[i]) 
      {
        last_index = i;
      }
    }

    // Flipping characters up
    // to the last index
    for (int i = 0;
             i <= last_index; i++)
    {

      // Flip the bit
      a[i] = (a[i] == '0') ? 
              '1' : '0';
    }
    // Increasing steps by one
    step++;
  }

  // Print the count of steps
  System.out.print(step);
}

// Driver Code
public static void main(String[] args)
{
    // Given Strings A and B
    String A = "101010",
           B = "110011";

    // Function Call
    findMinimumOperations(A.toCharArray(), 
                          B.toCharArray());
}
}

// This code is contributed by 29AjayKumar

# Python3 program for the above approach

# Function that finds the minimum
# number of operations required such
# that string A and B are the same
def findMinimumOperations(a, b):
    
    # Stores the count of steps
    step = 0

    # Stores the last index whose
    # bits are not same
    last_index = 0

    # Iterate until both string
    # are unequal
    while (a != b):
        a = [i for i in a]
        
        # Check till end of string to
        # find rightmost unequals bit
        for i in range(len(a)):
            
            # Update the last index
            if (a[i] != b[i]):
                last_index = i

        # Flipping characters up
        # to the last index
        for i in range(last_index + 1):
            
            # Flip the bit
            if (a[i] == '0'):
                a[i] = '1'
            else:
                a[i] = '0'
                
        a = "".join(a)        

        # Increasing steps by one
        step += 1

    # Print the count of steps
    print(step)

# Driver Code
if __name__ == '__main__':
    
    # Given strings A and B
    A = "101010"
    B = "110011"

    # Function Call
    findMinimumOperations(A, B)

# This code is contributed by mohit kumar 29

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

class GFG{

// Function that finds the minimum
// number of operations required such
// that string A and B are the same
static void findMinimumOperations(string a,
                                  string b)
{
  
  // Stores the count of steps
  int step = 0;

  // Stores the last index whose
  // bits are not same
  int last_index = 0;

  // Iterate until both string
  // are unequal
  while (a.Equals(b) == false)
  {
    
    // Check till end of string to
    // find rightmost unequals bit
    for(int i = 0; i < a.Length; i++) 
    {
      
      // Update the last index
      if (a[i] != b[i]) 
      {
        last_index = i;
      }
    }

    // Flipping characters up
    // to the last index
    char[] ch = a.ToCharArray(); 
    for(int i = 0;
            i <= last_index; i++)
    {
      
      // Flip the bit
      if (ch[i] == '0')
      {
        ch[i] = '1';
      }
      else
      {
        ch[i] = '0';
      }
    }
    a = new string(ch); 
    
    // Increasing steps by one
    step++;
  }

  // Print the count of steps
  Console.WriteLine(step);
}

// Driver Code
public static void Main()
{
  
  // Given strings A and B
  string A = "101010";
  string B = "110011";

  // Function Call
  findMinimumOperations(A,B);
}
}

// This code is contributed by SURENDRA_GANGWAR

<script>

// JavaScript program for the
// above approach

// Function that finds the minimum
// number of operations required such
// that string A and B are the same
function findMinimumOperations(a, b) 
{
    
    // Stores the count of steps
    var step = 0;
    
    // Stores the last index whose
    // bits are not same
    var last_index = 0;
    
    // Iterate until both string
    // are unequal
    while (a !== b)
    {
        
        // Check till end of string to
        // find rightmost unequals bit
        for (var i = 0; i < a.length; i++) 
        {
            
            // Update the last index
            if (a[i] !== b[i]) 
            {
                last_index = i;
            }
        }
    
        // Flipping characters up
        // to the last index
        var ch = a.split("");
        for(var i = 0; i <= last_index; i++)
        {
            
            // Flip the bit
            if (ch[i] === "0")
            {
                ch[i] = "1";
            } 
            else
            {
                ch[i] = "0";
            }
        }
        a = ch.join("");
        
        // Increasing steps by one
        step++;
    }
    
    // Print the count of steps
    document.write(step);
}

// Driver Code

// Given strings A and B
var A = "101010";
var B = "110011";

// Function Call
findMinimumOperations(A, B);

// This code is contributed by rdtank

</script>

4

Time Complexity: O(N²)
Auxiliary Space: O(1)