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 same character in ‘str2′

Examples:

Input:  str1 = "aab", str2 = "xxy"
Output: True
'a' is mapped to 'x' and 'b' is mapped to 'y'.

Input:  str1 = "aab", str2 = "xyz"
Output: False
One occurrence of 'a' in str1 has 'x' in str2 and 
other occurrence of 'a' has 'y'.

We strongly recommend you to minimize your browser and try this yourself first.

A Simple Solution is to consider every character of ‘str1′ and check if all occurrences of it map to same character in ‘str2′. Time complexity of this solution is O(n*n).

An Efficient Solution can solve this problem in O(n) time. The idea is to create an array to store mappings of processed characters.

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

Below is C++ implementation of above algorithm.

// 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 ismorphic bool areIsomorphic(string str1, string str2) {       int m = str1.length(), n = str2.length();       // Length of both strings must be same for one to one     // corresponance     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 on     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") << endl;    cout << areIsomorphic("aab", "xyz") << endl;    return 0; }

Output:

1
0

Thanks to Gaurav and Utkarsh for suggesting above approach.

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