Longest Palindromic Subsequence is the subsequence of a given sequence, and the subsequence is a palindrome.
In this problem, one sequence of characters is given, we have to find the longest length of a palindromic subsequence.
To solve this problem, we can use the recursive formula,
If L (0, n-1) is used to store a length of longest palindromic subsequence, then
L (0, n-1) := L (1, n-2) + 2 (When 0'th and (n-1)'th characters are same).
Input and Output
Input: A string with different letters or symbols. Say the input is “ABCDEEAB” Output: The longest length of the largest palindromic subsequence. Here it is 4. ABCDEEAB. So the palindrome is AEEA.
Algorithm
palSubSeqLen(str)
Input − The given string.
Output − Length of longest palindromic subsequence.
Begin n = length of the string create a table called lenTable of size n x n and fill with 1s for col := 2 to n, do for i := 0 to n – col, do j := i + col – 1 if str[i] = str[j] and col = 2, then lenTable[i, j] := 2 else if str[i] = str[j], then lenTable[i, j] := lenTable[i+1, j-1] + 2 else lenTable[i, j] := maximum of lenTable[i, j-1] and lenTable[i+1, j] done done return lenTable[0, n-1] End
Example
#include<iostream> using namespace std; int max (int x, int y) { return (x > y)? x : y; } int palSubseqLen(string str) { int n = str.size(); int lenTable[n][n]; // Create a table to store results of subproblems for (int i = 0; i < n; i++) lenTable[i][i] = 1; //when string length is 1, it is palindrome for (int col=2; col<=n; col++) { for (int i=0; i<n-col+1; i++) { int j = i+col-1; if (str[i] == str[j] && col == 2) lenTable[i][j] = 2; else if (str[i] == str[j]) lenTable[i][j] = lenTable[i+1][j-1] + 2; else lenTable[i][j] = max(lenTable[i][j-1], lenTable[i+1][j]); } } return lenTable[0][n-1]; } int main() { string sequence = "ABCDEEAB"; int n = sequence.size(); cout << "The length of the longest palindrome subsequence is: " << palSubseqLen(sequence); }
Output
The length of the longest palindrome subsequence is: 4