Check if one string can be converted to another

Given two strings str and str1, the task is to check whether one string can be converted to other by using the following operation: 
 

• Convert all the presence of a character by a different character.

For example, if str = "abacd" and operation is to change character 'a' to 'k', then the resultant str = "kbkcd"
Examples: 
 

Input: str = "abbcaa"; str1 = "bccdbb" 
Output: Yes 
Explanation: The mappings of the characters are: 
c --> d 
b --> c 
a --> b
Input: str = "abbc"; str1 = "bcca" 
Output: No 
Explanation: The mapping of characters are: 
a --> b 
b --> c 
c --> a 
Here, due to the presence of a cycle, a specific order cannot be found. 
 

Approach: 
 

• According to the given operation, every unique character should map to a unique character may be same or different.
• This can easily be checked by a Hashmap.
• However, this fails in cases where there is a cycle in mapping and a specific order cannot be determined.
• One example of such case is Example 2 above.
• Therefore, for mapping, the first and final characters are stored as edges in a hashmap.
• For finding cycle with the edges, these edges are mapped one by one to a parent and are checked for cycle using Union and Find Algorithm.

Below is the implementation of the above approach. 
 

Yes

Time Complexity: O(N * logN), where N is the length of string s1.
Auxiliary Space: O(N)