How to split a string into words. Ex: "stringintowords" -> "String Into Words"?

Question

What is the right way to split a string into words ? (string doesn't contain any spaces or punctuation marks)

For example: "stringintowords" -> "String Into Words"

Could you please advise what algorithm should be used here ?

! Update: For those who think this question is just for curiosity. This algorithm could be used to camеlcase domain names ("sportandfishing .com" -> "SportAndFishing .com") and this algo is currently used by aboutus dot org to do this conversion dynamically.

Answer 1

Let's assume that you have a function isWord(w), which checks if w is a word using a dictionary. Let's for simplicity also assume for now that you only want to know whether for some word w such a splitting is possible. This can be easily done with dynamic programming.

Let S[1..length(w)] be a table with Boolean entries. S[i] is true if the word w[1..i] can be split. Then set S[1] = isWord(w[1]) and for i=2 to length(w) calculate

S[i] = (isWord[w[1..i] or for any j in {2..i}: S[j-1] and isWord[j..i]).

This takes O(length(w)^2) time, if dictionary queries are constant time. To actually find the splitting, just store the winning split in each S[i] that is set to true. This can also be adapted to enumerate all solution by storing all such splits.

Answer 2

As mentioned by many people here, this is a standard, easy dynamic programming problem: the best solution is given by Falk Hüffner. Additional info though:

(a) you should consider implementing isWord with a trie, which will save you a lot of time if you use properly (that is by incrementally testing for words).

(b) typing "segmentation dynamic programming" yields a score of more detail answers, from university level lectures with pseudo-code algorithm, such as this lecture at Duke's (which even goes so far as to provide a simple probabilistic approach to deal with what to do when you have words that won't be contained in any dictionary).