Longest Palindromic Subsequence in JavaScript

Last Updated : 30 Jan, 2024

A Longest Palindromic Subsequence in JavaScript refers to the longest sequence of characters within a string that reads the same backward and forward. It's a non-contiguous subsequence, and the goal is to find the maximum length of such subsequences in a given input string.

Example:

Input: str = “GEEKSFORGEEKS”
Output: EEKEE, 5
Explanation: The longest palindromic subsequence we can get is of length 5. 
There are more than 1 palindromic subsequences of length 5, for example: EEKEE, EESEE, EEFEE, …etc.

Below approaches can be used to achieve this task

Table of Content

Using dynamic programming
Using Recursive method

Using dynamic programming

In this approach, The palindromicSubsequence function uses dynamic programming to find the longest palindromic subsequence in a given string. It fills the array by comparing characters and their corresponding subsequences. The final result is the longest palindromic subsequence found.

Example: The below code example implements dynamic programming to find the longest palindromic subsequence.

JavaScript

function palindromicSubsequence(str) {
    const n = str.length;
    const dp = Array.from({ length: n },
        () => Array(n).fill(''));

    for (let i = 0; i < n; i++) {
        dp[i][i] = str[i];
    }

    for (let cl = 2; cl <= n; cl++) {
        for (let index = 0; index + cl - 1 < n; index++) {
            const endIndex = index + cl - 1;
            const currentChar = str[index];
            const endChar = str[endIndex];

            if (currentChar === endChar) {
                dp[index][endIndex] =
                    cl === 2 ? currentChar + endChar :
                    currentChar + dp[index + 1][endIndex - 1]
                    + endChar;
            } else {
                const leftSubstring = dp[index][endIndex - 1];
                const bottomSubstring = dp[index + 1][endIndex];

                dp[index][endIndex] = leftSubstring.length > 
                    bottomSubstring.length
                    ? leftSubstring : bottomSubstring;
            }
        }
    }

    return dp[0][n - 1];
}

const inputStr = "GEEKSFORGEEKS";
const result = palindromicSubsequence(inputStr);
console.log(`Longest Palindromic Subsequence: ${result}`);
console.log(`Longest Palindromic Subsequence Length: ${result.length}`);

Output

Longest Palindromic Subsequence: EEGEE
Longest Palindromic Subsequence Length: 5

Using Recursive method

In this approach, we will use recursion to find the Longest Palindromic Subsequence (LPS) of a given string seq. It explores all possible substrings and returns the longest palindromic subsequence found.

Example: The below code explores all possible palindromic subsequences of the input string using the recursive approach.

JavaScript

function max(x, y) {
    return x > y ? x : y;
}

function lps(seq, i, j) {
    if (i === j) {
        return { length: 1, subsequence: seq[i] };
    }

    if (i + 1 === j && seq[i] === seq[j]) {
        return {
            length: 2, subsequence: seq[i]
                + seq[j]
        };
    }

    if (seq[i] === seq[j]) {
        const innerResult = lps(seq, i + 1, j - 1);
        return {
            length: innerResult.length + 2,
            subsequence: seq[i] + innerResult.subsequence
                + seq[j],
        };
    }

    const leftResult = lps(seq, i, j - 1);
    const rightResult = lps(seq, i + 1, j);

    return leftResult.length > rightResult.length ?
        leftResult : rightResult;
}

const seq = "GEEKSFORGEEKS";
const n = seq.length;
const result = lps(seq.split(""), 0, n - 1);
console.log
    ("Longest Palindromic Subsequence: ", result.subsequence);
console.log
    ("Longest Palindromic Subsequence Length: ", result.subsequence.length);

Output

Longest Palindromic Subsequence:  EEGEE
Longest Palindromic Subsequence Length:  5

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Longest Palindromic Subsequence in JavaScript

Example:

Below approaches can be used to achieve this task

Using dynamic programming

Using Recursive method

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