What is the optimal time complexity of solving Longest Palindromic Subsequence?

The optimized solution achieves a time complexity of O(n) by using sorting, mathematical shortcuts, or hash table lookups.

What is the auxiliary space complexity for Longest Palindromic Subsequence?

The space complexity is O(1) since we only use a minimal/constant amount of extra memory for tracking variables (or auxiliary space if dynamic structures are allocated).

What are the typical edge cases we must handle in Longest Palindromic Subsequence?

Key edge cases include empty collections, negative or large bounds causing integer overflow, arrays with only one element, or inputs where target criteria are not met.

How can we optimize the brute force approach for Longest Palindromic Subsequence?

Brute force methods often inspect all possible combinations. We optimize this by sorting the input list to enable binary search, or tracking processed items in a set to avoid redundant nested loop lookups.

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Competitive ProgrammingEasy

Longest Palindromic Subsequence

Learn how to solve the 'Longest Palindromic Subsequence' problem. This detailed resource details brute force and optimized approaches.

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Problem Statement

Easy

Write a function lps(s) that finds the length of the longest palindromic subsequence in a string s. A subsequence is a sequence that can be derived from another sequence by deleting some or no elements without changing the order of the remaining elements.

Constraints

•1 <= len(s) <= 1000
•s consists of uppercase or lowercase English letters.

Examples

Example 1

Input

lps('BBABCBCAB')

Output

Explanation

The longest palindromic subsequence has length 7, e.g., 'BABCBAB'.

Example 2

Input

lps('GEEKSFORGEEKS')

Output

Explanation

The longest palindromic subsequence has length 5, e.g., 'EEKEE'.

Need a Hint?

Define subproblem states, establish the recurrence relation, and use memoization (top-down) or tabulation (bottom-up).

Edge Cases to Watch

Empty list or null input variables
Single item lists/arrays
Extremely large input bounds causing integer or stack overflow

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