Longest Common Subsequence: "ABCBDAB" and "BDCABA"
==================================================

           -   B   D   C   A   B   A
-          0   0   0   0   0   0   0
A          0   0   0   0   1   1   1
B          0   1   1   1   1   2   2
C          0   1   1   2   2   2   2
B          0   1   1   2   2   3   3
D          0   1   2   2   2   3   3
A          0   1   2   2   3   3   4
B          0   1   2   2   3   4   4

length (bottom-right cell)       = 4
reconstructed from the full table = "BCBA"  (a valid subsequence of both strings)
two-row version                   = 4  (length only; cannot rebuild the string)

Calls made on two 15-character strings "ACGTTGCAACGTGCA" and "TGCATGCCGATGACG" (answer 9):
   naive recursion -> 293086 calls
   memoized        -> 247 calls