Question

Longest common subsequence (LCS) algorithms give a way to decide how similar two given strings are. However, sometimes, we have to filter away some common subsequences that are in some pattern. Here is a problem for you to solve. Given two strings alpha and beta, let gamma to be the longest word satisfying all of the following conditions: gamma is a subsequence of alpha. gamma is a subsequence of beta. gamma does not contain abb. Design an algorithm that finds such a gamma for any given alpha and beta. Also, analyze its time complexity.

Answer 1

function LCSLength(X[1..m], Y[1..n])
C = array(0..m, 0..n)
for i := 0..m
C[i,0] = 0
for j := 0..n
C[0,j] = 0
for i := 1..m
for j := 1..n
if X[i] = Y[j]
C[i,j] := C[i-1,j-1] + 1
else
C[i,j] := max(C[i,j-1], C[i-1,j])
return C[m,n

Screenshot:

after getting the LCS, search for string 'abb'

if 'abb' is substring of obtained LCS

earse 'abb' from LCS.

Note: Please consider my work and give up vote. Thank you :)