mirror of
https://github.com/TheAlgorithms/Python.git
synced 2024-11-24 21:41:08 +00:00
38 lines
1.1 KiB
Python
38 lines
1.1 KiB
Python
"""
|
|
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))
|