How to break down a given text into words from the dictionary?

This is an interview question. Suppose you have a string text and a dictionary (a set of strings). How do you break down text into substrings such that each substring is found in the dictionary.

For example you can break down "thisisatext" into ["this", "is", "a", "text"] using /usr/share/dict/words.

I believe backtracking can solve this problem (in pseudo-Java):

void solve(String s, Set<String> dict, List<String> solution) {
   if (s.length == 0)
      return
   for each prefix of s found in dict
      solve(s without prefix, dict, solution + prefix)
}

List<String> solution = new List<String>()
solve(text, dict, solution)

Does it make sense? Would you optimize the step of searching the prefixes in the dictionary? What data structures would you recommend?