Check if two given Strings are Isomorphic to each other

Two strings str1 and str2 are called isomorphic if there is a one-to-one mapping possible for every character of str1 to every character of str2. And all occurrences of every character in ‘str1’ map to the same character in ‘str2’.

Examples: 

Input:  str1 = “aab”, str2 = “xxy”
Output: True
Explanation: ‘a’ is mapped to ‘x’ and ‘b’ is mapped to ‘y’.

Input:  str1 = “aab”, str2 = “xyz”
Output: False
Explanation: One occurrence of ‘a’ in str1 has ‘x’ in str2 and other occurrence of ‘a’ has ‘y’.

We strongly recommend that you click here and practice it, before moving on to the solution.

Naive Approach:

A Simple Solution is to consider every character of ‘str1’ and check if all occurrences of it map to the same character in ‘str2’. 

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

Check if two given strings are isomorphic to each other using Mapping:

The idea is to create an array to store mappings of processed characters. 

Follow the steps below to solve the problem:

• If the lengths of str1 and str2 are not same, return false.
• Do the following for every character in str1 and str2.
  • If this character is seen first time in str1, then-current of str2 must have not appeared before.
    • If the current character of str2 is seen, return false. Mark the current character of str2 as visited.
    • Store mapping of current characters.
  • Else check if the previous occurrence of str1[i] mapped to the same character.

Below is the implementation of the above idea :  

C++

// C++ program to check if two strings are isomorphic
#include <bits/stdc++.h>
using namespace std;
#define MAX_CHARS 256

// This function returns true if str1 and str2 are
// isomorphic
bool areIsomorphic(string str1, string str2)
{

    int m = str1.length(), n = str2.length();

    // Length of both strings must be same for one to one
    // correspondence
    if (m != n)
        return false;

    // To mark visited characters in str2
    bool marked[MAX_CHARS] = { false };

    // To store mapping of every character from str1 to
    // that of str2. Initialize all entries of map as -1.
    int map[MAX_CHARS];
    memset(map, -1, sizeof(map));

    // Process all characters one by one
    for (int i = 0; i < n; i++) {
        // If current character of str1 is seen first
        // time in it.
        if (map[str1[i]] == -1) {
            // If current character of str2 is already
            // seen, one to one mapping not possible
            if (marked[str2[i]] == true)
                return false;

            // Mark current character of str2 as visited
            marked[str2[i]] = true;

            // Store mapping of current characters
            map[str1[i]] = str2[i];
        }

        // If this is not first appearance of current
        // character in str1, then check if previous
        // appearance mapped to same character of str2
        else if (map[str1[i]] != str2[i])
            return false;
    }

    return true;
}

// Driver program
int main()
{
    cout << (areIsomorphic("aab", "xxy") ? "True" : "False")
         << endl;
    return 0;
}

Java

// Java program to check if two strings are isomorphic
import java.io.*;
import java.util.*;
class Isomorphic {
    static int size = 256;

    // Function returns true if str1 and str2 are isomorphic
    static String areIsomorphic(String str1, String str2)
    {
        int m = str1.length();
        int n = str2.length();

        // Length of both strings must be same for one to
        // one correspondence
        if (m != n)
            return "False";

        // To mark visited characters in str2
        Boolean[] marked = new Boolean[size];
        Arrays.fill(marked, Boolean.FALSE);

        // To store mapping of every character from str1 to
        // that of str2. Initialize all entries of map as
        // -1.
        int[] map = new int[size];
        Arrays.fill(map, -1);

        // Process all characters one by one
        for (int i = 0; i < n; i++) {
            // If current character of str1 is seen first
            // time in it.
            if (map[str1.charAt(i)] == -1) {
                // If current character of str2 is already
                // seen, one to one mapping not possible
                if (marked[str2.charAt(i)] == true)
                    return "False";

                // Mark current character of str2 as visited
                marked[str2.charAt(i)] = true;

                // Store mapping of current characters
                map[str1.charAt(i)] = str2.charAt(i);
            }

            // If this is not first appearance of current
            // character in str1, then check if previous
            // appearance mapped to same character of str2
            else if (map[str1.charAt(i)] != str2.charAt(i))
                return "False";
        }

        return "True";
    }
    // driver program
    public static void main(String[] args)
    {
        String res = areIsomorphic("aab", "xxy");
        System.out.println(res);
    }
}

Python

# Python program to check if two strings are isomorphic
MAX_CHARS = 256

# This function returns true if str1 and str2 are isomorphic


def areIsomorphic(string1, string2):
    m = len(string1)
    n = len(string2)

    # Length of both strings must be same for one to one
    # correspondence
    if m != n:
        return False

    # To mark visited characters in str2
    marked = [False] * MAX_CHARS

    # To store mapping of every character from str1 to
    # that of str2. Initialize all entries of map as -1
    map = [-1] * MAX_CHARS

    # Process all characters one by one
    for i in xrange(n):

        # if current character of str1 is seen first
        # time in it.
        if map[ord(string1[i])] == -1:

            # if current character of st2 is already
            # seen, one to one mapping not possible
            if marked[ord(string2[i])] == True:
                return False

            # Mark current character of str2 as visited
            marked[ord(string2[i])] = True

            # Store mapping of current characters
            map[ord(string1[i])] = string2[i]

        # If this is not first appearance of current
        # character in str1, then check if previous
        # appearance mapped to same character of str2
        elif map[ord(string1[i])] != string2[i]:
            return False

    return True


# Driver program
print areIsomorphic("aab", "xxy")
# This code is contributed by Bhavya Jain

C#

// C# program to check if two
// strings are isomorphic
using System;

class GFG {

    static int size = 256;

    // Function returns true if str1
    // and str2 are isomorphic
    static bool areIsomorphic(String str1, String str2)
    {

        int m = str1.Length;
        int n = str2.Length;

        // Length of both strings must be same
        // for one to one correspondence
        if (m != n)
            return false;

        // To mark visited characters in str2
        bool[] marked = new bool[size];

        for (int i = 0; i < size; i++)
            marked[i] = false;

        // To store mapping of every character
        // from str1 to that of str2 and
        // Initialize all entries of map as -1.
        int[] map = new int[size];

        for (int i = 0; i < size; i++)
            map[i] = -1;

        // Process all characters one by one
        for (int i = 0; i < n; i++) {

            // If current character of str1 is
            // seen first time in it.
            if (map[str1[i]] == -1) {

                // If current character of str2
                // is already seen, one to
                // one mapping not possible
                if (marked[str2[i]] == true)
                    return false;

                // Mark current character of
                // str2 as visited
                marked[str2[i]] = true;

                // Store mapping of current characters
                map[str1[i]] = str2[i];
            }

            // If this is not first appearance of current
            // character in str1, then check if previous
            // appearance mapped to same character of str2
            else if (map[str1[i]] != str2[i])
                return false;
        }

        return true;
    }

    // Driver code
    public static void Main()
    {
        bool res = areIsomorphic("aab", "xxy");
        Console.WriteLine(res);
    }
}

// This code is contributed by Sam007.

Javascript

<script>
    // Javascript program to check if two
    // strings are isomorphic
    
    let size = 256;
     
    // Function returns true if str1
    // and str2 are isomorphic
    function areIsomorphic(str1, str2)
    {
         
        let m = str1.length;
        let n = str2.length;
         
        // Length of both strings must be same
        // for one to one correspondence
        if(m != n)
            return false;
             
        // To mark visited characters in str2
        let marked = new Array(size);
         
        for(let i = 0; i < size; i++)
            marked[i]= false;
         
         
        // To store mapping of every character
        // from str1 to that of str2 and
        // Initialize all entries of map as -1.
        let map = new Array(size);
        map.fill(0);
         
        for(let i = 0; i < size; i++)
            map[i]= -1;
     
        // Process all characters one by one
        for (let i = 0; i < n; i++)
        {
             
            // If current character of str1 is
            // seen first time in it.
            if (map[str1[i].charCodeAt()] == -1)
            {
                 
                // If current character of str2
                // is already seen, one to
                // one mapping not possible
                if (marked[str2[i].charCodeAt()] == true)
                    return false;
 
                // Mark current character of
                // str2 as visited
                marked[str2[i].charCodeAt()] = true;
 
                // Store mapping of current characters
                map[str1[i].charCodeAt()] = str2[i].charCodeAt();
            }
 
            // If this is not first appearance of current
            // character in str1, then check if previous
            // appearance mapped to same character of str2
            else if (map[str1[i].charCodeAt()] != str2[i].charCodeAt())
                return 0;
        }
 
        return 1;
    }
    
    let res = areIsomorphic("aab", "xxy");
    document.write(res + "</br>");

    res = areIsomorphic("aab", "xyz");
    document.write(res);
    
    // This code is contributed by decode2207.
</script>

Output

True

Time Complexity: O(N), Traversing over the string of size N
Auxiliary Space: O(1)

Check if two given strings are isomorphic to each other using Single Hashmap:

The idea is to store map the character and check whether the mapping is correct or not

Follow the steps to solve the problem:

• Create a hashmap of (char, char) to store the mapping of str1 and str2.
• Now traverse on the string and check whether the current character is present in the Hashmap.
  • If it is present then the character that is mapped is there at the ith index or not.
  • Else check if str2[i] is not present in the key then add the new mapping.
  • Else return false.

Below is the implementation of the above approach

C++

#include <iostream>
#include <unordered_map>
#include <vector>
#include <algorithm>

using namespace std;

// This function returns true if str1 and str2 are isomorphic
bool areStringsIsomorphic(string str1, string str2) {
    // Initializing an unordered_map to store character mappings from str1 to str2
    unordered_map<char, char> charMapping;
    
    // Iterating over str1 and str2
    for (int i = 0; i < str1.length(); i++) {
        // Check if the character in str1 at index i is already mapped
        if (charMapping.count(str1[i])) {
            // If the mapped value for str1[i] is not equal to str2[i], return false
            if (charMapping[str1[i]] != str2[i]) {
                return false;
            }
        } else {
            // Check if the character in str2 at index i is already used in the mapping
            vector<char> mappedCharacters;
            for (const auto& pair : charMapping) {
                mappedCharacters.push_back(pair.second);
            }
            if (find(mappedCharacters.begin(), mappedCharacters.end(), str2[i]) != mappedCharacters.end()) {
                return false;
            } else {
                // Map str1[i] to str2[i]
                charMapping[str1[i]] = str2[i];
            }
        }
    }
    return true;
}

int main() {
    // Test strings
    string inputString1 = "aac";
    string inputString2 = "xxy";
    
    // Check if the strings are isomorphic
    if (inputString1.length() == inputString2.length() && areStringsIsomorphic(inputString1, inputString2)) {
        cout << "True\n";
    } else {
        cout << "False\n";
    }
    
    return 0;
}

Java

// Java program to check if two strings
// areIsomorphic

import java.io.*;
import java.util.*;

class GFG {

    static boolean areIsomorphic(String str1, String str2)
    {

        HashMap<Character, Character> charCount
            = new HashMap();
        char c = 'a';
        for (int i = 0; i < str1.length(); i++) {
            if (charCount.containsKey(str1.charAt(i))) {
                c = charCount.get(str1.charAt(i));
                if (c != str2.charAt(i))
                    return false;
            }
            else if (!charCount.containsValue(
                         str2.charAt(i))) {
                charCount.put(str1.charAt(i),
                              str2.charAt(i));
            }
            else {
                return false;
            }
        }
        return true;
    }

    /* Driver code*/
    public static void main(String[] args)
    {

        String str1 = "aac";
        String str2 = "xxy";

        // Function Call
        if (str1.length() == str2.length()
            && areIsomorphic(str1, str2))
            System.out.println("True");
        else
            System.out.println("False");
    }
}

// This code is contributed by phasing17

Python3

# Python3 program to check if two strings are IsIsomorphic

# this function returns true if str1
# and str2 are isomorphic


def areIsomorphic(str1, str2):
    # initializing a dictionary
    # to store letters from str1 and str2
    # as key value pairs
    charCount = dict()
    # initially setting c to "a"
    c = "a"
    # iterating over str1 and str2
    for i in range(len(str1)):
        # if str1[i] is a key in charCount
        if str1[i] in charCount:
            c = charCount[str1[i]]
            if c != str2[i]:
                return False
        # if str2[i] is not a value in charCount
        elif str2[i] not in charCount.values():
            charCount[str1[i]] = str2[i]
        else:
            return False
    return True


# Driver Code
str1 = "aac"
str2 = "xxy"

# Function Call
if (len(str1) == len(str2) and areIsomorphic(str1, str2)):
    print("True")
else:
    print("False")


# this code is contributed by phasing17

C#

// C# program to check if two strings
// areIsIsomorphic

using System;
using System.Collections.Generic;

public class GFG {

    static bool areIsomorphic(char[] str1, char[] str2)
    {

        Dictionary<char, char> charCount
            = new Dictionary<char, char>();
        char c = 'a';
        for (int i = 0; i < str1.Length; i++) {
            if (charCount.ContainsKey(str1[i])
                && charCount.TryGetValue(str1[i], out c)) {
                if (c != str2[i])
                    return false;
            }
            else if (!charCount.ContainsValue(str2[i])) {
                charCount.Add(str1[i], str2[i]);
            }
            else {
                return false;
            }
        }
        return true;
    }

    /* Driver code*/
    public static void Main()
    {

        string str1 = "aac";
        string str2 = "xxy";

        // Function Call
        if (str1.Length == str2.Length
            && areIsomorphic(str1.ToCharArray(),
                             str2.ToCharArray()))
            Console.WriteLine("True");
        else
            Console.WriteLine("False");

        Console.ReadLine();
    }
}

Javascript

<script>
// JavaScript program to check if two strings are IsIsomorphic

// this function returns true if str1 
// and str2 are isomorphic
function areIsomorphic(str1, str2)
{
    // initializing an object
    // to store letters from str1 and str2
    // as key value pairs
    var charCount = {};
    
    // initially setting c to "a"
    var c = "a";
    
    // iterating over str1 and str2
    for (var i = 0; i < str1.length; i++)
    {
    
        // if str1[i] is a key in charCount
        if (charCount.hasOwnProperty(str1[i]))
        {
            c = charCount[str1[i]];
            if (c != str2[i])
                return false;
        }
        
        // if str2[i] is not a value in charCount
        else if (!Object.values(charCount).includes(str2[i]))
        {
            charCount[str1[i]] = str2[i];
        }
        else
            return false;
    }
    return true;
}
           
// Driver Code
var str1 = "aac";
var str2 = "xxy";

// Function Call
if (str1.length == str2.length && areIsomorphic(str1, str2))
    document.write(1);
else
    document.write(0);

// This code is contributed by phasing17.
</script>

Output

True

Time Complexity: O(N), traversing over the string of size N.
Auxiliary Space: O(1) 

Thanks to Gaurav and Utkarsh for suggesting the above approach.