This following project consists of 4 different programs that do the same thing; 
that is find the longest common subsequence.

The four programs starting in order of highest execution times asymptotically begin 
with naive recursive, with memoization, dynamic programming and lastly implementing 
the Hirschberg algorithm to implement the same.

Each of the program has the object file and the executable separate so just 
doing a "./ hirschberg.out > lcs_hirschberg_output.txt" on the bash shell acheives the result.

To create the random input string input one of only binary string that is in 
file binary_seq_input_long.txt and one with characters that is in text 
file dna_input_long.txt, used the program random_input_text.cpp

The programs were compiled and ran using g++ 4.0 on Ubuntu 10.04.