LeetCode 290: Word Pattern — Python Solution

Solve LeetCode 290: Word Pattern in Python with a bidirectional token 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

Split the sentence into words and enforce a one-to-one mapping between pattern characters and words.

Algorithm

1. Split the sentence into words and enforce a one-to-one mapping between pattern characters and words.
2. Maintain this invariant: Both maps agree for every processed pattern-word 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 wordPattern(self, pattern, s):
        words = s.split()
        if len(pattern) != len(words): return False
        forward, backward = {}, {}
        for char, word in zip(pattern, words):
            if (char in forward and forward[char] != word) or (word in backward and backward[word] != char): return False
            forward[char], backward[word] = word, char
        return True

Why this is correct

The proof follows the maintained state: Both maps agree for every processed pattern-word 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

The number of words must equal the pattern length.

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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