Check if two given Strings are Isomorphic to each other

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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’.

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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++

// C++ program to check if two strings are IsIsomorphic
#include <bits/stdc++.h>
 
using namespace std;
 
// this function returns true if str1 and str2 are
// isomorphic
bool areIsomorphic(string str1, string str2)
{
   
    // initializing an unordered_map to store letters from
    // str1 and str2 as key value pairs
    unordered_map<char, char> charCount;
   
    // iterating over str1 and str2
    for (int i = 0; i < str1.length(); i++) 
    {
       
        // if str1[i] is a key in charCount
        if (charCount.count(str1[i]))
        {
           
            // checking if the value in charCount for key
            // str1[i] is equal to str2[i]
            if (charCount[str1[i]] != str2[i]) {
                return false;
            }
        }
        // if str2[i] is not a value in charCount
        else {
            // checking if str2[i] is already a value in
            // charCount
            vector<char> values;
            for (auto it : charCount) {
                values.push_back(it.second);
            }
            if (find(values.begin(), values.end(), str2[i])
                != values.end()) {
                return false;
            }
            else {
                charCount[str1[i]] = str2[i];
            }
        }
    }
    return true;
}
 
int main()
{
    // Test strings
    string str1 = "aac";
    string str2 = "xxy";
 
    // Function Call
    if (str1.length() == str2.length()
        && areIsomorphic(str1, str2)) {
        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.
Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above

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Last Updated : 20 Mar, 2023