Check if two non-duplicate strings can be made equal after at most two swaps in one string

Given two strings A and B consisting of unique lowercase letters, the task is to check if both these strings can be made equal by using at most two swaps. Print Yes if they can. Otherwise, print No.

Example:

Input: A=”abcd”, B=”badc”
Output: Yes
First swap a and b, and then swap c and d, in string A.
Input: A=”abcd”, B=”cbda”
Output: No

Approach: In this problem, string A can only be converted to string B if:

Case 1: If A is already equal to B.
Case 2: If the number of differences in both the strings is less than equal to 3 and both the strings contains same character. Then its always possible to create B from A.
Case 3: If the number of differences is 4 and all the swapping pairs in string A are same and opposite in string B.

Now to solve this problem, follow the below steps:

1. First, check if both the strings are already equal or not. If they are, then print Yes.
2. Also, check if the size of both the string are equal or not. If it isn’t then print No.
3. Create a vector, say b and store the indexes of character in string B.
4. Create two maps, stay mp1 and mp2 to store the frequency of characters in strings A and B respectively.
5. Now, check if the number of differences is less than or equal to 3, and both the maps, mp1 and mp2 have the same entries. If yes, then both the string can be made equal. So, print Yes.
6. Also, both the strings can be made equal if they have 4 differences, but if it is a pair of two mirrored mistakes. So, print Yes if the differences are mirrored in two pairs.
7. Otherwise, print No in the end.

Below is the implementation of the above approach:

C++

// C++ code for the above approach

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

// Function to check if two strings can be made
// equal using at most two swaps
bool canBecomeEqual(string A, string B)
{

    if (A.size() != B.size()) {
        return 0;
    }

    // Case 1:
    if (A == B) {
        return 1;
    }

    // Vector to store the index of characters
    // in B
    vector<int> b(26, -1);

    for (int i = 0; i < A.size(); i++) {
        b[B[i] - 'a'] = i;
    }

    // Map to store the characters
    // with their frequencies
    unordered_map<char, int> mp1, mp2;

    // Variable to store
    // the total number of differences
    int diff = 0;

    // Set to store the pair of indexes
    // having changes in A wrt to B
    set<pair<int, int> > positions;

    for (int i = 0; i < A.size(); ++i) {
        if (A[i] != B[i]) {
            positions.insert({ i, b[A[i] - 'a'] });
            diff++;
        }
        mp1[A[i]]++;
        mp2[B[i]]++;
    }

    // Case 2:
    if (diff <= 3 and mp1 == mp2) {
        return 1;
    }

    // Case 3:
    if (diff == 4 and mp1 == mp2) {
        for (auto x : positions) {
            pair<int, int> search
                = { x.second, x.first };

            if (positions.find(search)
                == positions.end()) {
                return 0;
            }
        }
        return 1;
    }

    return 0;
}

// Driver Code
int main()
{
    string A = "abcd";
    string B = "cbba";

    if (canBecomeEqual(A, B)) {
        cout << "Yes" << endl;
    }
    else {
        cout << "No" << endl;
    }
}

Java

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

class GFG{
    static class pair
    {
        int first, second;
        public pair(int first, int second)
        {
            this.first = first;
            this.second = second;
        }
        @Override
        public int hashCode() {
            final int prime = 31;
            int result = 1;
            result = prime * result + first;
            result = prime * result + second;
            return result;
        }
        @Override
        public boolean equals(Object obj) {
            if (this == obj)
                return true;
            if (obj == null)
                return false;
            if (getClass() != obj.getClass())
                return false;
            pair other = (pair) obj;
            if (first != other.first)
                return false;
            if (second != other.second)
                return false;
            return true;
        }

    }

// Function to check if two Strings can be made
// equal using at most two swaps
static boolean canBecomeEqual(String A, String B)
{

    if (A.length() != B.length()) {
        return false;
    }

    // Case 1:
    if (A == B) {
        return true;
    }

    // Vector to store the index of characters
    // in B
    int []b = new int[26];

    for (int i = 0; i < A.length(); i++) {
        b[B.charAt(i) - 'a'] = i;
    }

    // Map to store the characters
    // with their frequencies
    HashMap<Character,Integer> mp1, mp2;
    mp1 = new HashMap<Character,Integer>();
    mp2 = new HashMap<Character,Integer>();

    // Variable to store
    // the total number of differences
    int diff = 0;

    // Set to store the pair of indexes
    // having changes in A wrt to B
    HashSet<pair> positions = new HashSet<pair>();

    for (int i = 0; i < A.length(); ++i) {
        if (A.charAt(i) != B.charAt(i)) {
            positions.add(new pair(i, b[A.charAt(i) - 'a'] ));
            diff++;
        }
        if(mp1.containsKey(A.charAt(i))){
            mp1.put(A.charAt(i), mp1.get(A.charAt(i))+1);
        }
        else{
            mp1.put(A.charAt(i), 1);
        }
        if(mp2.containsKey(B.charAt(i))){
            mp2.put(B.charAt(i), mp2.get(B.charAt(i))+1);
        }
        else{
            mp2.put(B.charAt(i), 1);
        }
    }

    // Case 2:
    if (diff <= 3 && mp1 == mp2) {
        return true;
    }

    // Case 3:
    if (diff == 4 && mp1 == mp2) {
        for (pair x : positions) {
            pair search
                = new pair( x.second, x.first );

            if (!positions.contains(search)) {
                return false;
            }
        }
        return true;
    }

    return false;
}

// Driver Code
public static void main(String[] args)
{
    String A = "abcd";
    String B = "cdba";

    if (canBecomeEqual(A, B)) {
        System.out.print("Yes" +"\n");
    }
    else {
        System.out.print("No" +"\n");
    }
}
}

// This code is contributed by 29AjayKumar

Python3

# python3 code for the above approach

# Function to check if two strings can be made
# equal using at most two swaps
def canBecomeEqual(A, B):

    if (len(A) != len(B)):
        return 0

        # Case 1:
    if (A == B):
        return 1

        # Vector to store the index of characters
        # in B
    b = [-1 for _ in range(26)]

    for i in range(0, len(A)):
        b[ord(B[i]) - ord('a')] = i

        # Map to store the characters
        # with their frequencies
    mp1 = {}
    mp2 = {}

    # Variable to store
    # the total number of differences
    diff = 0

    # Set to store the pair of indexes
    # having changes in A wrt to B
    positions = set()

    for i in range(0, len(A)):
        if (A[i] != B[i]):
            positions.add((i, b[ord(A[i]) - ord('a')]))
            diff += 1
        if A[i] in mp1:
            mp1[A[i]] += 1
        else:
            mp1[A[i]] = 1

        if B[i] in mp2:
            mp2[B[i]] += 1
        else:
            mp2[B[i]] = 1

        # Case 2:
    if (diff <= 3 and mp1 == mp2):
        return 1

        # Case 3:
    if (diff == 4 and mp1 == mp2):
        for x in positions:
            search = (x[1], x[0])
            if (not (search in positions)):
                return 0

        return 1

    return 0

# Driver Code
if __name__ == "__main__":

    A = "abcd"
    B = "cdba"

    if (canBecomeEqual(A, B)):
        print("Yes")

    else:
        print("No")

    # This code is contributed by rakeshsahni

C#

// C# code for the above approach
using System;
using System.Collections.Generic;

public class GFG{
  class pair : IComparable<pair>
  {
    public int first, second;
    public pair(int first, int second)
    {
      this.first = first;
      this.second = second;
    }
    public int CompareTo(pair p)
    {
      return this.second-p.first;
    }
  }

  // Function to check if two Strings can be made
  // equal using at most two swaps
  static bool canBecomeEqual(String A, String B)
  {

    if (A.Length != B.Length) {
      return false;
    }

    // Case 1:
    if (A == B) {
      return true;
    }

    // List to store the index of characters
    // in B
    int []b = new int[26];

    for (int i = 0; i < A.Length; i++) {
      b[B[i] - 'a'] = i;
    }

    // Map to store the characters
    // with their frequencies
    Dictionary<char,int> mp1, mp2;
    mp1 = new Dictionary<char,int>();
    mp2 = new Dictionary<char,int>();

    // Variable to store
    // the total number of differences
    int diff = 0;

    // Set to store the pair of indexes
    // having changes in A wrt to B
    HashSet<pair> positions = new HashSet<pair>();

    for (int i = 0; i < A.Length; ++i) {
      if (A[i] != B[i]) {
        positions.Add(new pair(i, b[A[i] - 'a'] ));
        diff++;
      }
      if(mp1.ContainsKey(A[i])){
        mp1[A[i]] = mp1[A[i]]+1;
      }
      else{
        mp1.Add(A[i], 1);
      }
      if(mp2.ContainsKey(B[i])){
        mp2[B[i]] = mp2[B[i]]+1;
      }
      else{
        mp2.Add(B[i], 1);
      }
    }

    // Case 2:
    if (diff <= 3 && mp1 == mp2) {
      return true;
    }

    // Case 3:
    if (diff == 4 && mp1 == mp2) {
      foreach (pair x in positions) {
        pair search
          = new pair( x.second, x.first );

        if (!positions.Contains(search)) {
          return false;
        }
      }
      return true;
    }

    return false;
  }

  // Driver Code
  public static void Main(String[] args)
  {
    String A = "abcd";
    String B = "cdba";

    if (canBecomeEqual(A, B)) {
      Console.Write("Yes" +"\n");
    }
    else {
      Console.Write("No" +"\n");
    }
  }
}

// This code is contributed by shikhasingrajput

Javascript

<script>

// JavaScript code for the above approach

// Function to check if two strings can be made
// equal using at most two swaps
function canBecomeEqual(A, B){

    if (A.length != B.length)
        return 0

    // Case 1:
    if (A.B)
        return 1

    // Vector to store the index of characters
    // in B
    let b = new Array(26).fill(-1)

    for(let i=0;i<A.length;i++){
        b[B.charCodeAt(i) - 'a'.charCodeAt(0)] = i
    }

    // Map to store the characters
    // with their frequencies
    let mp1 = new Map()
    let mp2 = new Map()

// Variable to store
// the total number of differences
    diff = 0

// Set to store the pair of indexes
// having changes in A wrt to B
    let positions = new Set()

    for(let i=0;i<A.length;i++){
        if (A[i] != B[i]){
            positions.add([i, b[A.charCodeAt(i) - 'a'.charCodeAt(0)]])
            diff += 1
        }
        if(mp1.has(A[i]))
            mp1.set(A[i],mp1.get(A[i])+1)
        else
            mp1.set(A[i],1)

        if(mp2.has(B[i]))
            mp2.set(B[i],mp2.get(B[i])+1)
        else
            mp2.set(B[i],1)
    }

    // Case 2:
    if (diff <= 3 && mp1 == mp2)
        return 1

    // Case 3:
    if (diff == 4 && mp1 == mp2){
        for(let x of positions){
            search = [x[1], x[0]]
            if (!positions.has(search))
                return 0
        }

        return 1
    }

    return 0
}
// Driver Code

let A = "abcd"
let B = "cdba"

if (canBecomeEqual(A, B))
    document.write("Yes")

else
    document.write("No")

// This code is contributed by shinjanpatra

</script>

Output

No

Time Complexity: O(N*log N)
Auxiliary Space: O(N)

Another Approach:

1. Iterate through the two strings character by character and count the number of mismatches.
2. If the number of mismatches is greater than two, return false as it’s not possible to make the strings equal by using at most two swaps.
3. If there are exactly two mismatches, store the positions of those two mismatches.
4. If there are no mismatches or exactly two mismatches, return true.
5. If there are exactly four mismatches, check if swapping the characters at the two positions will make the strings equal. Return true if they can be made equal, otherwise, return false.
6. If the number of mismatches is not 0, 2, or 4, return false.

Below is the implementation of the above approach:

C++

#include <iostream>
#include <algorithm>
using namespace std;

// Function to check if two strings can be made equal by using at most two swaps
bool canMakeEqual(string A, string B) {
    int N = A.length();
    int count = 0; // Counter for the number of characters that differ between A and B
    int pos1 = -1, pos2 = -1; // Positions of the differing characters
    for (int i = 0; i < N; i++) {
        if (A[i] != B[i]) {
            count++; // Increment counter if characters at the same position are different
            if (count == 1) {
                pos1 = i; // Store position of first differing character
            } else if (count == 2) {
                pos2 = i; // Store position of second differing character
            } else { // If more than 2 characters differ, the strings cannot be made equal
                if (A[pos1] == B[pos2] && A[pos2] == B[pos1]) { // Check if two swaps can make the strings equal
                    return true;
                } else {
                    return false;
                }
            }
        }
    }
    // If only 0 or 2 characters differ, the strings can be made equal with at most two swaps
    if (count == 0 || count == 2) {
        return true;
    } else if (count == 4) { // If 4 characters differ, check if two swaps can make the strings equal
        if (A[pos1] == B[pos2] && A[pos2] == B[pos1]) {
            return true;
        } else {
            return false;
        }
    } else { // If more than 4 characters differ, the strings cannot be made equal with at most two swaps
        return false;
    }
}

int main() {

    string A = "abcd";
    string B = "cbda";
    if (canMakeEqual(A, B)) {
        cout << "Yes\n"; // If the strings can be made equal with at most two swaps, output "Yes"
    } else {
        cout << "No\n"; // If the strings cannot be made equal with at most two swaps, output "No"
    }
    return 0;
}
//This code is contributed by rudra1807raj

Java

/*package whatever //do not write package name here */

import java.util.*;

public class GFG {

    // Function to check if two strings can be made equal by using at most two swaps
    static boolean canMakeEqual(String A, String B) {
        int N = A.length();
        int count = 0; // Counter for the number of characters that differ between A and B
        int pos1 = -1, pos2 = -1; // Positions of the differing characters
        for (int i = 0; i < N; i++) {
            if (A.charAt(i) != B.charAt(i)) {
                count++; // Increment counter if characters at the same position are different
                if (count == 1) {
                    pos1 = i; // Store position of first differing character
                } else if (count == 2) {
                    pos2 = i; // Store position of second differing character
                } else { // If more than 2 characters differ, the strings cannot be made equal
                    if (A.charAt(pos1) == B.charAt(pos2) && A.charAt(pos2) == B.charAt(pos1)) { // Check if two swaps can make the strings equal
                        return true;
                    } else {
                        return false;
                    }
                }
            }
        }
        // If only 0 or 2 characters differ, the strings can be made equal with at most two swaps
        if (count == 0 || count == 2) {
            return true;
        } else if (count == 4) { // If 4 characters differ, check if two swaps can make the strings equal
            if (A.charAt(pos1) == B.charAt(pos2) && A.charAt(pos2) == B.charAt(pos1)) {
                return true;
            } else {
                return false;
            }
        } else { // If more than 4 characters differ, the strings cannot be made equal with at most two swaps
            return false;
        }
    }

    public static void main(String[] args) {

        String A = "abcd";
        String B = "cbda";
        if (canMakeEqual(A, B)) {
            System.out.println("Yes"); // If the strings can be made equal with at most two swaps, output "Yes"
        } else {
            System.out.println("No"); // If the strings cannot be made equal with at most two swaps, output "No"
        }
    }
}

//This code is contributed by aeroabrar_31

Python3

# code

# Function to check if two strings can be made equal by using at most two swaps
def canMakeEqual(A, B):
    N = len(A)
    count = 0  # Counter for the number of characters that differ between A and B
    pos1, pos2 = -1, -1  # Positions of the differing characters

    for i in range(N):
        if A[i] != B[i]:
            count += 1  # Increment counter if characters at the same position are different
            if count == 1:
                pos1 = i  # Store position of first differing character
            elif count == 2:
                pos2 = i  # Store position of second differing character
            else:  # If more than 2 characters differ, the strings cannot be made equal
                if A[pos1] == B[pos2] and A[pos2] == B[pos1]:  # Check if two swaps can make the strings equal
                    return True
                else:
                    return False

    # If only 0 or 2 characters differ, the strings can be made equal with at most two swaps
    if count == 0 or count == 2:
        return True
    elif count == 4:  # If 4 characters differ, check if two swaps can make the strings equal
        if A[pos1] == B[pos2] and A[pos2] == B[pos1]:
            return True
        else:
            return False
    else:  # If more than 4 characters differ, the strings cannot be made equal with at most two swaps
        return False

A = "abcd"
B = "cbda"
if canMakeEqual(A, B):
    print("Yes")  # If the strings can be made equal with at most two swaps, output "Yes"
else:
    print("No")  # If the strings cannot be made equal with at most two swaps, output "No"

#This code is contributed by aeroabrar_31

C#

using System;

public class GFG
{
    // Function to check if two strings can be made equal by using at most two swaps
    static bool CanMakeEqual(string A, string B)
    {
        int N = A.Length;
        int count = 0; // Counter for the number of characters that differ between A and B
        int pos1 = -1, pos2 = -1; // Positions of the differing characters
        for (int i = 0; i < N; i++)
        {
            if (A[i] != B[i])
            {
                count++; // Increment counter if characters at the same position are different
                if (count == 1)
                {
                    pos1 = i; // Store position of first differing character
                }
                else if (count == 2)
                {
                    pos2 = i; // Store position of second differing character
                }
                else
                { // If more than 2 characters differ, the strings cannot be made equal
                    if (A[pos1] == B[pos2] && A[pos2] == B[pos1])
                    { // Check if two swaps can make the strings equal
                        return true;
                    }
                    else
                    {
                        return false;
                    }
                }
            }
        }
        // If only 0 or 2 characters differ, the strings
        // can be made equal with at most two swaps
        if (count == 0 || count == 2)
        {
            return true;
        }
        else if (count == 4)
        { // If 4 characters differ, check if two swaps can make the strings equal
            if (A[pos1] == B[pos2] && A[pos2] == B[pos1])
            {
                return true;
            }
            else
            {
                return false;
            }
        }
        else
        { // If more than 4 characters differ, the strings cannot be
          // made equal with at most two swaps
            return false;
        }
    }

    public static void Main(string[] args)
    {
        string A = "abcd";
        string B = "cbda";
        if (CanMakeEqual(A, B))
        {
            // If the strings can be made equal with at most two swaps, output "Yes"
            Console.WriteLine("Yes");
        }
        else
        {
            // If the strings cannot be made equal with at most two swaps, output "No"
            Console.WriteLine("No");
        }
    }
}

//This code is contributed by aeroabrar_31

Javascript

function canMakeEqual(A, B) {
    const N = A.length;
    let count = 0; // Counter for the number of characters that differ between A and B
    let pos1 = -1, pos2 = -1; // Positions of the differing characters

    for (let i = 0; i < N; i++) {
        if (A[i] !== B[i]) {
            count++; // Increment counter if characters at the same position are different
            if (count === 1) {
                pos1 = i; // Store position of first differing character
            } else if (count === 2) {
                pos2 = i; // Store position of second differing character
            } else { // If more than 2 characters differ, the strings cannot be made equal
                if (A[pos1] === B[pos2] && A[pos2] === B[pos1]) { // Check if two swaps can make the strings equal
                    return true;
                } else {
                    return false;
                }
            }
        }
    }

    // If only 0 or 2 characters differ, the strings can be made equal with at most two swaps
    if (count === 0 || count === 2) {
        return true;
    } else if (count === 4) { // If 4 characters differ, check if two swaps can make the strings equal
        if (A[pos1] === B[pos2] && A[pos2] === B[pos1]) {
            return true;
        } else {
            return false;
        }
    } else { // If more than 4 characters differ, the strings cannot be made equal with at most two swaps
        return false;
    }
}

const A = "abcd";
const B = "cbda";

if (canMakeEqual(A, B)) {
    console.log("Yes"); // If the strings can be made equal with at most two swaps, output "Yes"
} else {
    console.log("No"); // If the strings cannot be made equal with at most two swaps, output "No"
}

Output

No

Time Complexity: The time complexity of the code is O(N), where N is the length of the strings A and B, as the code iterates through the strings once. 
Auxiliary Space: The space complexity is O(1), as the code uses only constant space to store a few variables.