I tested functional programming vs a for loop and it seems like the for loop can be about 100ms faster than the functional programming approach. Not too sure why

Agreed, I remember reading that somewhere -- but why? because of the lambda function, right?

Actually not the best practice. List comprehension would be more fitting

okay....i figured it out completely....thank god....

testing with test.assert_equals(lcs("8a4" , "8b4"), "84") and it works, however im having trouble to understand why it works, this code return lcs(x[:-1], y[:-1]) + x[-1] was returned 3times as follows: "4","8","8", so shouldn't the result be like '844'? why is it 84 instead....

The complexity is 2^n. if string length is very large, this method maybe very slow