Classic problem but I still fumbled the edge cases a bit.
Clarify the definition of isomorphism: a bijective mapping between characters of both strings. Then propose an efficient solution using two hash maps (or a map and a set) to track mappings in both directions, ensuring consistency. Walk through an example and analyze time/space complexity.
Pro tip: Mention that a single map is insufficient because it only enforces one direction; you need to check both directions to prevent two characters mapping to the same character. Also, discuss edge cases like empty strings and Unicode characters.
Confirm that isomorphic means a one-to-one correspondence between characters, and that the mapping must be consistent in both directions. Ask about input constraints (e.g., ASCII vs Unicode, length limits).
Propose using two hash maps: one to map characters from the first string to the second, and another for the reverse mapping. Alternatively, use one map and a set to track mapped characters.
Demonstrate with a simple example like 'egg' and 'add' to show how the mappings are built and checked. Highlight the failure case when a conflict arises.
State that the algorithm runs in O(n) time and O(k) space, where n is the string length and k is the number of distinct characters (bounded by alphabet size).
Mention handling empty strings, strings of different lengths (though problem states equal length), and potential optimizations like early termination on mismatch.
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