# Program to find length of longest palindromic subsequence in Python

PythonServer Side ProgrammingProgramming

Suppose we have a lowercase string s; we have to find the length of the longest palindromic subsequence in s.

So, if the input is like s = "aolpeuvekyl", then the output will be 5, as the palindrome is "level".

To solve this, we will follow these steps −

• n := size of s
• Define a function dp() . This will take i, j
• if i is same as j, then
• return 1
• otherwise when i > j, then
• return 0
• otherwise,
• if s[i] is same as s[j], then
• return 2 + dp(i + 1, j - 1)
• otherwise,
• return maximum of dp(i + 1, j) and dp(i, j - 1)
• return dp(0, n - 1)

## Example (Python)

Let us see the following implementation to get better understanding −

Live Demo

class Solution:
def solve(self, s):
n = len(s)
def dp(i, j):
if i == j:
return 1
elif i > j:
return 0
else:
if s[i] == s[j]:
return 2 + dp(i + 1, j - 1)
else:
return max(dp(i + 1, j), dp(i, j - 1))
return dp(0, n - 1)
ob = Solution()
s = "aolpeuvekyl"
print(ob.solve(s))

## Input

"aolpeuvekyl"

## Output

5
Published on 12-Dec-2020 10:45:08