"""
LCS Problem Statement: Given two sequences, find the length of longest subsequence present in both of them.
A subsequence is a sequence that appears in the same relative order, but not necessarily continious.
Example:"abc", "abg" are subsequences of "abcdefgh".
"""
from __future__ import print_function
try:
xrange # Python 2
except NameError:
xrange = range # Python 3
def lcs_dp(x, y):
# find the length of strings
m = len(x)
n = len(y)
# declaring the array for storing the dp values
L = [[None] * (n + 1) for i in xrange(m + 1)]
seq = []
for i in range(m + 1):
for j in range(n + 1):
if i == 0 or j == 0:
L[i][j] = 0
elif x[i - 1] == y[ j - 1]:
L[i][j] = L[i - 1][j - 1] + 1
seq.append(x[i -1])
else:
L[i][j] = max(L[i - 1][j], L[i][j - 1])
# L[m][n] contains the length of LCS of X[0..n-1] & Y[0..m-1]
return L[m][n], seq
if __name__=='__main__':
x = 'AGGTAB'
y = 'GXTXAYB'
print(lcs_dp(x, y))