Breaking a string apart into a sequence of words
I recently came across the following interview question:
Given an input string and a dictionary of words, implement a method that breaks up the input string into a space-separated string of dictionary words that a search engine might use for "Did you mean?" For example, an input of "applepie" should yield an output of "apple pie".
I can't seem to get an optimal solution as far as complexity is concerned. Does anyone have any suggestions on how to do this efficiently?
Answer
Looks like the question is exactly my interview problem, down to the example I used in the post at The Noisy Channel. Glad you liked the solution. Am quite sure you can't beat the O(n^2) dynamic programming / memoization solution I describe for worst-case performance.
You can do better in practice if your dictionary and input aren't pathological. For example, if you can identify in linear time the substrings of the input string are in the dictionary (e.g., with a trie) and if the number of such substrings is constant, then the overall time will be linear. Of course, that's a lot of assumptions, but real data is often much nicer than a pathological worst case.
There are also fun variations of the problem to make it harder, such as enumerating all valid segmentations, outputting a best segmentation based on some definition of best, handling a dictionary too large to fit in memory, and handling inexact segmentations (e.g., correcting spelling mistakes). Feel free to comment on my blog or otherwise contact me to follow up.