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Compute longest palindromic subsequence | J.P. Morgan Coding Question

Quick Overview

This question evaluates understanding of dynamic programming for strings, specifically longest palindromic subsequence concepts such as memoization, bottom-up DP, space optimization and subsequence reconstruction.

Compute longest palindromic subsequence

Company: J.P. Morgan

Role: Software Engineer

Category: Coding & Algorithms

Difficulty: medium

Interview Round: Onsite

Given a string s (1 ≤ |s| ≤ 2000), implement a function that returns the length of the longest subsequence of s that reads the same forward and backward. Provide both a top-down (memoized) and a bottom-up dynamic programming solution, analyze time and space complexity, and explain how to optimize space. Follow up: reconstruct one valid longest palindromic subsequence and discuss how to handle multiple test cases efficiently.

Quick Answer: This question evaluates understanding of dynamic programming for strings, specifically longest palindromic subsequence concepts such as memoization, bottom-up DP, space optimization and subsequence reconstruction.

Part 1: Compute the Length of the Longest Palindromic Subsequence

Given a string s, return the length of its longest palindromic subsequence. A subsequence is formed by deleting zero or more characters without changing the order of the remaining characters. The subsequence does not need to be contiguous.

Constraints

0 <= len(s) <= 2000
Character comparisons are case-sensitive.

Examples

Input: "bbbab"

Expected Output: 4

Explanation: One longest palindromic subsequence is 'bbbb'.

Input: "cbbd"

Expected Output: 2

Explanation: The longest palindromic subsequence is 'bb'.

Hints

Try defining dp[i][j] as the answer for the substring from index i to j.
If s[i] == s[j], those two characters can wrap a smaller palindromic subsequence. Otherwise, try skipping one end.

Part 2: Reconstruct One Longest Palindromic Subsequence

Given a string s, return one longest palindromic subsequence of s. If multiple longest palindromic subsequences exist, use this deterministic tie-break rule while reconstructing from the DP table: when skipping the left character and skipping the right character both keep the optimal length, skip the left character first. This makes the expected output unique.

Constraints

0 <= len(s) <= 2000
The returned value must be both a palindrome and a subsequence of s.
Character comparisons are case-sensitive.

Examples

Input: "bbbab"

Expected Output: "bbbb"

Explanation: The reconstruction picks matching outer b characters and then another matching pair.

Input: "cbbd"

Expected Output: "bb"

Explanation: The longest palindromic subsequence is uniquely 'bb'.

Hints

First compute the LPS length for every substring, then walk inward from both ends to rebuild an answer.
Build the result using a left half and a right half; when both skip choices are equally good, move the left pointer forward.

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