The first/last character constraint is what makes this tractable when vocab has anagram pairs like 'pears' and 'spear'.
Clarify the problem constraints, then propose an efficient algorithm using a hash map keyed by a canonical signature (e.g., sorted characters or character count) to group vocabulary words. For each scrambled word, compute its signature and look up the matching vocab word, leveraging the first/last character constraint to narrow candidates. Discuss time/space complexity and potential trade-offs between preprocessing and online matching.
Pro tip: Mention that the first/last character constraint can be used to quickly filter candidates, but the anagram signature is the primary key; also note that if the vocabulary is large, preprocessing into a hash map is O(N) and each query is O(1) on average, which is optimal.
Ask about input sizes, whether the vocabulary is static or dynamic, and if there are multiple scrambled words to decode. Confirm that each scrambled word maps to exactly one vocab word and that first/last characters match.
Decide on a signature for anagrams, such as sorting the characters or using a character frequency count. Sorting is O(L log L) per word, while counting is O(L) with a fixed alphabet.
Build a hash map from signature to vocab word. Optionally, include the first and last characters in the key to avoid collisions and speed up lookup.
For each scrambled word, compute its signature and look it up in the hash map. If found, return the corresponding vocab word; otherwise, handle as an error (though problem guarantees a match).
Discuss time complexity: O(N * L log L) for preprocessing with sorting, O(M * L log L) for decoding, where N is vocab size, M is number of scrambled words, L is average word length. Space: O(N * L). Compare with alternative approaches like trie or counting sort.
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