Suppose, we are given a string. We have to find out a palindromic subsequence that is of even length and does not contain two consecutive same characters except in the middle. We have to return the length of this type of substrings as output.
So, if the input is like s = 'efeffe', then the output will be 4
The output is 4 because there is only one palindromic subsequence that is of even length. The string is 'effe' that is of length 4.
To solve this, we will follow these steps −
n := size of s
dp := one n x n 2d array where each item is a pair in the form (0, blank string)
for i in range n-1 to -1, decrease by 1, do
for j in range i+1 to n, do
if s[i] is same as s[j] and string of dp[i+1, j-1] is not s[i], then
dp[i, j] := make a pair (first element of dp[i+1, j-1] + 2, s[i])
otherwise,
dp[i, j] := select among (dp[i+1, j], dp[i, j-1], dp[i+1,j-1]) for which first element of pair is maximum
return first element of pair stored at dp[0, n-1]
Let us see the following implementation to get better understanding −
Example
def solve(s):
n = len(s)
dp = [[(0, '')]*n for _ in range(n)]
for i in range(n-1, -1, -1):
for j in range(i+1, n):
if s[i]== s[j] and dp[i+1][j-1][1] != s[i]:
dp[i][j] = (dp[i+1][j-1][0] + 2, s[i])
else:
dp[i][j] = max(dp[i+1][j], dp[i][j-1], dp[i+1][j-1], key=lambda x: x[0])
return dp[0][n-1][0]
print(solve('efeffe'))Input
'efeffe'
Output
4