Algorithm for checking if a string was built from a list of substrings

Question

You are given a string and an array of strings. How to quickly check, if this string can be built by concatenating some of the strings in the array?

This is a theoretica

Answer 1

What you are looking for is a parser. A parser will check whether a certain word belongs to a certain language. I am not sure of the exact computattional complexity of your problem. Some of the above seems to be correct (there is no need at all for exhaustive search). One thing for sure, it s not NP-Complete.

The alphabet of your language would be all the small substrings. The word you are looking for is the string you have. A regular expression can be a simple Kleene star, or a a very simply context free grammar that is nothing but Or's.

The main issue in the algorithm is: what if the some of the substrings are actually substrings to other substrings ... that is, what if we have substrings: "ab", "abc", "abcd", ... , In this case, the order of checking the substrings will change the complexity. For this, we have LR-parsers. I guess they are the best in solving such problems.

I will find you the exact solution soon.