I spent way too long just re-reading the problem.
First, clarify the problem's constraints and assumptions, especially the definition of 'valid English dictionary word' and the size of the dictionary. Then, reason about the combinatorial explosion: if the string length is n, there are O(n^3) subsequences of length 3, and checking each against a dictionary is expensive. Instead, derive necessary conditions: for the property to hold, every length-3 subsequence must be rearrangeable into a word, which implies the string's character multiset must be highly constrained. Finally, propose an efficient algorithm that checks these conditions without enumerating all subsequences.
Pro tip: Demonstrate adaptability by acknowledging the ambiguity in 'valid English dictionary word' and proposing a reasonable formalization (e.g., a fixed set of words) before diving into the algorithm. This shows you can handle underspecified problems, a key trait at Google.
Ask clarifying questions: What is the dictionary? Is it fixed? What is the maximum length of s? Can subsequences be rearranged into any word, or must the rearrangement be a permutation of the subsequence? Confirm that 'rearranged' means the characters can be reordered arbitrarily.
Consider small strings (length < 3) where the condition is vacuously true. For longer strings, note that if any length-3 subsequence cannot be rearranged into a word, the answer is false. Thus, the property must hold for all length-3 subsequences, which is the most restrictive case.
For every triple of characters (with repetition allowed) that appears as a subsequence, their sorted multiset must match the sorted multiset of some dictionary word of length 3. This implies the set of characters in s must be a subset of characters that appear in length-3 words, and their frequencies must be limited.
Preprocess the dictionary to extract all length-3 words and store their sorted character multisets in a hash set. Then, for the given string, check all O(n^3) subsequences? That's too slow. Instead, observe that if the string contains any character not in any length-3 word, return false. Also, if the string contains three characters that cannot form a word, return false. But checking all triples is still O(n^3). We can optimize by noting that the condition must hold for all triples, so we can check the set of distinct characters and their frequencies. If the string has more than 3 distinct characters, then any triple of three distinct characters must be a valid word; if not, return false. Similarly, for repeated characters, check pairs and triples. The key is to reduce the problem to checking a small set of character combinations.
Test with examples: s = 'abc' where 'abc' is not a word, then false. s = 'a' then true. Discuss time complexity: O(n + D) where D is dictionary size, after preprocessing. Space complexity: O(D) for storing length-3 word multisets.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.