/* Dynamic Prgramming:
 * Longest Common Subsequence
 * input: two ascii strings within length of 100
 * output: the longest length that match
 * 		   all the subsequence that satisfied the LCS
 *
 * Debug parameter:
 * 		-DEBUG_MATRIX
 * 			this will output the table we calculated.
 *
 *
 * Problem Solved:
 * 		1. how to search for all the feasible path that matches
 * 		2. how to output the path in order
 * 		(I use a simple stack, not considering its exception
 * 		because it will not cause any exception:
 * 		a push followed by a pop, never overflow or underflow)
 */