This problem comes out of the dynamic programming chapter in The Algorithm Deisgn Manual by Skiena.
Give an algorithm to determine whether you can generate a given string by pasting cutouts from a magazine. You are given a function that will identify the character and its position on the reverse side of the page for any given character position.
I solved this with with backtracking, but since it’s in the dynamic programming chapter I think there must be a recurrence I can’t figure out. Can anyone give me a hint?
You can solve it with maximum bipartite matching.
Each character L of the given string forms the left set. (Note, you repeat the characters if the string has repeated characters).
Each pair of characters (R1,R2) of the magazine forms the right set.
L is connected to (r1,r2) iff L=R1 or L=R2.
Find a maximum matching in the resulting graph. If all left vertices are part of the matching, you have the answer. If not, such a string is not possible.
See Maximum Bipartite Matchings for an algorithm.
Not sure if this is optimal though and sorry for not answering exactly as asked.