Problem
Given a string s, find the longest palindromic subsequence’s length in s.
A subsequence is a sequence that can be derived from another sequence by deleting some or no elements without changing the order of the remaining elements.
Algorithm
Dynamic Programming (DP). Define state f(left, right) is the Longest Palindromic Subsequence in s[left…right], so we have
f
(
l
e
f
t
,
r
i
g
h
t
)
=
{
f
(
l
e
f
t
+
1
,
r
i
g
h
t
−
1
)
+
2
if
s
[
l
e
f
t
]
=
=
s
[
r
i
g
h
t
]
max
[
f
(
l
e
f
t
+
1
,
r
i
g
h
t
)
,
f
(
l
e
f
t
,
r
i
g
h
t
−
1
)
]
otherwise
f(left, right) = \begin{cases} f(left+1, right-1) + 2 & \text{if } s[left] == s[right ]\\ \max[f(left+1, right), f(left, right-1)] & \text{otherwise} \end{cases}
f(left,right)={f(left+1,right−1)+2max[f(left+1,right),f(left,right−1)]if s[left]==s[right]otherwise
Code
class Solution:
def longestPalindromeSubseq(self, s: str) -> int:
slen = len(s)
if slen == 0:
return 0
dp = [[0] * slen for i in range(slen)]
for i in range(slen):
dp[i][i] = 1
for L in range(2, slen+1):
for i in range(slen - L + 1):
j = i + L - 1
if s[i] == s[j]:
dp[i][j] = dp[i+1][j-1] + 2
else:
dp[i][j] = max(dp[i+1][j], dp[i][j-1])
return dp[0][slen-1]
