Data Structure
Networking
RDBMS
Operating System
Java
MS Excel
iOS
HTML
CSS
Android
Python
C Programming
C++
C#
MongoDB
MySQL
Javascript
PHP
Physics
Chemistry
Biology
Mathematics
English
Economics
Psychology
Social Studies
Fashion Studies
Legal Studies
- Selected Reading
- UPSC IAS Exams Notes
- Developer's Best Practices
- Questions and Answers
- Effective Resume Writing
- HR Interview Questions
- Computer Glossary
- Who is Who
Longest Palindromic Subsequence
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
Updated on: 17-Jun-2020
774 Views
Advertisements