LeetCode 205: Isomorphic Strings — Python Solution

Solve LeetCode 205: Isomorphic Strings in Python with a bidirectional mapping approach. The key is to make the state invariant explicit, so the implementation and complexity follow naturally.

This guide paraphrases the task and does not reproduce LeetCode’s prompt. Use the official page for the complete statement, examples, constraints, and submission runner.

What the problem is testing

Maintain mappings in both directions so each character corresponds to exactly one partner and no two source characters share a target.

Algorithm

1. Maintain mappings in both directions so each character corresponds to exactly one partner and no two source characters share a target.
2. Maintain this invariant: Both maps describe a one-to-one correspondence for every processed character pair.
3. Continue until every input item or reachable state has been resolved, then return the accumulated result.

Python solution

from collections import Counter, defaultdict, deque, OrderedDict
import random

class Solution:
    def isIsomorphic(self, s, t):
        if len(s) != len(t): return False
        forward, backward = {}, {}
        for a, b in zip(s, t):
            if (a in forward and forward[a] != b) or (b in backward and backward[b] != a): return False
            forward[a], backward[b] = b, a
        return True

Why this is correct

The proof follows the maintained state: Both maps describe a one-to-one correspondence for every processed character pair. Each iteration preserves that claim while permanently resolving at least one position, node, interval, or search state. When the loop or recursion ends, every candidate required by the problem has therefore been included or ruled out, so the returned value is correct.

Complexity

O(n) time and O(k) space. The stated auxiliary space excludes the returned output unless the output is the data structure being built.

Edge cases

Length mismatch fails; repeated patterns must match in both strings.

Tested reference code

This implementation is included in the site’s downloadable 100-solution Python library. The complete suite compiles every solution and runs a behavioral assertion for every problem before publication.

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