3633：Copying DNA

Evolution is a seemingly random process which works in a way which resembles certain approaches we use to get approximate solutions to hard combinatorial problems. You are now to do something completely different.

Given a DNA string S from the alphabet {A,C,G,T}, find the minimal number of copy operations needed to create another string T. You may reverse the strings you copy, and copy both from S and the pieces of your partial T. You may put these pieces together at any time. You may only copy contiguous parts of your partial T, and all copied strings must be used in your final T. Example: From S = “ACTG” create T = “GTACTATTATA”

1. Get GT......... by copying and reversing "TG" from S.
2. Get GTAC....... by copying "AC" from S.
3. Get GTAC...TA.. by copying "TA" from the partial T.
4. Get GTAC...TAAT by copying and reversing "TA" from the partial T.
5. Get GTACAATTAAT by copying "AAT" from the partial T.