Isomorphic Strings

Problem Description

Given two strings s and t, determine if they are isomorphic. Two strings s and t are isomorphic if the characters in s can be replaced to get t. All occurrences of a character must be replaced with another character while preserving the order of characters. No two characters may map to the same character, but a character may map to itself.

Key Insights

• Each character in string s must map to a unique character in string t.
• The mapping must be consistent throughout the strings (i.e., the same character in s must always map to the same character in t).
• If a character in s maps to two different characters in t, or if two characters in s map to the same character in t, the strings are not isomorphic.

Space and Time Complexity

Time Complexity: O(n), where n is the length of the strings.
Space Complexity: O(1), as we are using fixed-size data structures (two hash tables).

Solution

To determine if two strings are isomorphic, we can utilize two hash tables (or dictionaries) to maintain the mapping of characters from s to t and from t to s. We iterate through each character in the strings simultaneously and check for the following:

1. If the character from s has already been mapped, ensure it maps to the same character in t.
2. If the character from t has already been mapped, ensure it maps to the same character in s.
3. If neither character has been mapped yet, create a new mapping for both.

If we can traverse both strings without any inconsistencies in the mappings, they are isomorphic.

Code Solutions