Given two strings s1 and s2, implement a bottom-up dynamic programming algorithm to identify a longest common subsequence (LCS) between s1 and s2 and determine its length by maintaining only the recent two rows of the direction table.

Function Prototype: pair LCS (string s1, string s2);

I need c++ code for the above problem. (Use vectors)

Output format: length table direction table longest common subsequence obtained length of LCS