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I started with the sort-each-word approach and got through it fine, O(n * m log m) and all that.
Start by explaining the sorting-based approach: sort each word and use the sorted string as a key in a hash map. Then optimize to linear time by using a character frequency count (e.g., a 26-length array or a tuple) as the key, avoiding the O(k log k) sort per word. Discuss how to handle collisions (e.g., using a delimiter or fixed-size array) and compare the time/space tradeoffs between the two methods.
Pro tip: Mention that in practice, the sorting approach is often faster for short strings due to lower constant factors, but the frequency approach is asymptotically better for long strings. Also, clarify that the frequency array must be converted to an immutable type (like a tuple) to be used as a dictionary key.
Ask about input size, string length, character set (e.g., lowercase English letters), and whether the output order matters. This helps determine the best approach and edge cases.
Explain that you can sort each string and use the sorted version as a key in a hash map, grouping all strings with the same sorted key. Analyze time complexity: O(n * k log k) where n is number of strings and k is max length.
Describe using a character frequency count (e.g., an array of size 26 for lowercase letters) as the key. Convert the array to a tuple or string to make it hashable. This reduces time to O(n * k) since counting takes O(k) per word.
For the frequency approach, ensure the key uniquely represents the character counts. For example, use a tuple of counts or a string with delimiters. Mention that using a fixed-size array avoids collisions if the character set is known.
Sorting: O(n*k log k) time, O(n*k) space for keys. Frequency: O(n*k) time, O(n*k) space for keys. Note that frequency approach may use more space per key (e.g., 26 integers) but is asymptotically faster. Also mention that for small k, sorting might be faster in practice.
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