Minimum Number of Substrings From a String Needed to Piece Together Another String

Revision en3, by vamaddur, 2017-07-11 11:19:40

Given two non-empty strings A and B composed of lowercase Latin letters, what is the minimum number of substrings of A needed to form string B? The lengths of A and B are at most 100000. If the task is not possible for a given input, output a rogue value (a.k.a. -1).

I was thinking about solving this with an O(N^2) DP, but that does not fit into the time limit of 5 seconds.

Please help, and thanks in advance!

EDIT: Note that chosen substrings can overlap. I put some cases below.

Input 1: abcbcd abcd

Output 1: 2

Input 2: iamsmart iamdumb

Output 2: -1

Input 3: asmallmallinmalta atallmallinlima

Output 3: 5

Explanations: "abcd" = "ab" + "cd", no "d"s in the first string of Input 2, "atallmallinlima" = "a" + "ta" + "llmallin" + "li" + "ma"

Tags #strings, dynamic programming

History

 
 
 
 
Revisions
 
 
  Rev. Lang. By When Δ Comment
en5 English vamaddur 2017-07-11 17:30:06 7 Tiny change: ' O(N^2) DP, but that' -> ' O(N^2) DP method, but that'
en4 English vamaddur 2017-07-11 11:20:55 6
en3 English vamaddur 2017-07-11 11:19:40 6
en2 English vamaddur 2017-07-11 11:18:52 371
en1 English vamaddur 2017-07-11 10:36:28 500 Initial revision (published)