Check if a string can be converted to another by swapping of adjacent characters of given type

Given two strings str1 and str2 of size N consisting of only three characters A, B, and C, the task is to check whether the string str1 can be changed to str2 using the below operations:

• Replacing one occurrence of “BC” with “CB” i.e swap adjacent ‘B’ and ‘C’.
• Replacing one occurrence of “CA” with “AC” i.e swap adjacent ‘C’ and ‘A’.

Print “Yes” if we can transform the string else print “No”.
Examples:

Input: str1 = “BCCABCBCA”, str2 = “CBACCBBAC” 
Output: Yes 
Explanation:
Transform the strings using following these steps: 
BCCABCBCA -> CBCABCBCA -> CBACBCBCA -> CBACCBBCA -> CBACCBBAC.
Input: str1 = “BAC”, str2 = “CAB” 
Output: False

Naive Approach: The idea is to generate all possible strings recursively from the start of the string str1 by performing the given operations and store it in a set of strings. Then check if any string from the set is equal to the string str2 or not. If string str2 is found in the set then print “Yes” else print “No”.

Time Complexity: O(2^N) 
Auxiliary Space: O(1)
Efficient Approach: The idea is to transverse the two strings simultaneously and check if it’s possible to transform the string str1 to str2 till a particular index. Below are the steps:

1. Check for the sequence ‘A’ and ‘B’ in the strings str1 and str2, if it’s the same, then proceed to the second step. Otherwise, print “No” as the desired conversion is not possible.
2. The index of ‘A’ in str1 should be greater than and equal to the index of the corresponding ‘A’ in str2, since “CA” can be converted only to “AC”.
3. Similarly, the index of ‘B’ in str1 string should be less than or equal to the corresponding index of ‘B’ in str2, since “BC” can only be converted to “CB”.
4. If the above two conditions are not satisfied, then print “No”. Otherwise, print “Yes”.

Below is the implementation of the above approach:

C++

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

// Function to check if it is possible
// to transform start to end
bool canTransform(string str1,
                string str2)
{
    string s1 = "";
    string s2 = "";

    // Check the sequence of A, B in
    // both strings str1 and str2
    for (char c : str1) {
        if (c != 'C') {
            s1 += c;
        }
    }

    for (char c : str2) {
        if (c != 'C') {
            s2 += c;
        }
    }

    // If both the strings
    // are not equal
    if (s1 != s2)
        return false;

    int i = 0;
    int j = 0;
    int n = str1.length();

    // Traverse the strings
    while (i < n and j < n) {
        if (str1[i] == 'C') {
            i++;
        }

        else if (str2[j] == 'C') {
            j++;
        }

        // Check for indexes of A and B
        else {
            if ((str1[i] == 'A'
                and i < j)
                or (str1[i] == 'B'
                    and i > j)) {
                return false;
            }
            i++;
            j++;
        }
    }

    return true;
}

// Driver Code
int main()
{
    string str1 = "BCCABCBCA";
    string str2 = "CBACCBBAC";

    // Function Call
    if (canTransform(str1, str2)) {
        cout << "Yes";
    }
    else {
        cout << "No";
    }
    return 0;
}

Java

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

    // Function to check if it is possible
    // to transform start to end
    static boolean canTransform(String str1, String str2)
    {
        String s1 = "";
        String s2 = "";

        // Check the sequence of A, B in
        // both Strings str1 and str2
        for (char c : str1.toCharArray())
        {
            if (c != 'C')
            {
                s1 += c;
            }
        }

        for (char c : str2.toCharArray())
        {
            if (c != 'C')
            {
                s2 += c;
            }
        }

        // If both the Strings
        // are not equal
        if (!s1.equals(s2))
            return false;

        int i = 0;
        int j = 0;
        int n = str1.length();

        // Traverse the Strings
        while (i < n && j < n)
        {
            if (str1.charAt(i) == 'C')
            {
                i++;
            }
            else if (str2.charAt(j) == 'C')
            {
                j++;
            }

            // Check for indexes of A and B
            else
            {
                if ((str1.charAt(i) == 'A' && i < j) ||
                    (str1.charAt(i) == 'B' && i > j))
                {
                    return false;
                }
                i++;
                j++;
            }
        }
        return true;
    }

    // Driver Code
    public static void main(String[] args)
    {
        String str1 = "BCCABCBCA";
        String str2 = "CBACCBBAC";

        // Function Call
        if (canTransform(str1, str2))
        {
            System.out.print("Yes");
        }
        else
        {
            System.out.print("No");
        }
    }
}

// This code is contributed by Rajput-Ji

Python3

# Python3 program for the above approach

# Function to check if it is possible
# to transform start to end
def canTransform(str1, str2):

    s1 = ""
    s2 = ""

    # Check the sequence of A, B in
    # both strings str1 and str2
    for c in str1:
        if (c != 'C'):
            s1 += c

    for c in str2:
        if (c != 'C'):
            s2 += c

    # If both the strings
    # are not equal
    if (s1 != s2):
        return False

    i = 0
    j = 0
    n = len(str1)

    # Traverse the strings
    while (i < n and j < n):
        if (str1[i] == 'C'):
            i += 1

        elif (str2[j] == 'C'):
            j += 1

        # Check for indexes of A and B
        else:
            if ((str1[i] == 'A' and i < j) or
                (str1[i] == 'B' and i > j)):
                return False

            i += 1
            j += 1

    return True

# Driver Code
if __name__ == '__main__':

    str1 = "BCCABCBCA"
    str2 = "CBACCBBAC"

    # Function call
    if (canTransform(str1, str2)):
        print("Yes")
    else:
        print("No")

# This code is contributed by mohit kumar 29

C#

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

class GFG{

// Function to check if it is possible
// to transform start to end
static bool canTransform(string str1, string str2)
{
    string s1 = "";
    string s2 = "";

    // Check the sequence of A, B in
    // both Strings str1 and str2
    foreach(char c in str1.ToCharArray())
    {
        if (c != 'C')
        {
            s1 += c;
        }
    }

    foreach(char c in str2.ToCharArray())
    {
        if (c != 'C')
        {
            s2 += c;
        }
    }

    // If both the Strings
    // are not equal
    if (s1 != s2)
        return false;

    int i = 0;
    int j = 0;
    int n = str1.Length;

    // Traverse the Strings
    while (i < n && j < n)
    {
        if (str1[i] == 'C')
        {
            i++;
        }
        else if (str2[j] == 'C')
        {
            j++;
        }

        // Check for indexes of A and B
        else
        {
            if ((str1[i] == 'A' && i < j) ||
                (str1[i] == 'B' && i > j))
            {
                return false;
            }
            i++;
            j++;
        }
    }
    return true;
}

// Driver Code
public static void Main(string[] args)
{
    string str1 = "BCCABCBCA";
    string str2 = "CBACCBBAC";

    // Function call
    if (canTransform(str1, str2))
    {
        Console.Write("Yes");
    }
    else
    {
        Console.Write("No");
    }
}
}

// This code is contributed by rutvik_56

Javascript

<script>
      // JavaScript program for the above approach
      // Function to check if it is possible
      // to transform start to end
      function canTransform(str1, str2) {
        var s1 = "";
        var s2 = "";

        // Check the sequence of A, B in
        // both Strings str1 and str2
        for (const c of str1) {
          if (c !== "C") {
            s1 += c;
          }
        }

        for (const c of str2) {
          if (c !== "C") {
            s2 += c;
          }
        }

        // If both the Strings
        // are not equal
        if (s1 !== s2) return false;

        var i = 0;
        var j = 0;
        var n = str1.length;

        // Traverse the Strings
        while (i < n && j < n) {
          if (str1[i] === "C") {
            i++;
          } else if (str2[j] === "C") {
            j++;
          }

          // Check for indexes of A and B
          else {
            if ((str1[i] === "A" && i < j) || (str1[i] === "B" && i > j)) {
              return false;
            }
            i++;
            j++;
          }
        }
        return true;
      }

      // Driver Code
      var str1 = "BCCABCBCA";
      var str2 = "CBACCBBAC";

      // Function call
      if (canTransform(str1.split(""), str2.split(""))) {
        document.write("Yes");
      } else {
        document.write("No");
      }
    </script>

Output:

Yes

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