The Programmer's Quest

Tricky DSA Challenge: Palindromic Subarray Product

Problem: Maximum Palindromic Subarray Product

Given an array of positive integers arr, find the maximum product of any contiguous subarray that forms a palindrome. A subarray is palindromic if it reads the same forward and backward (e.g., [2, 3, 2] or [5]). If no palindromic subarray exists, return -1. Return the result modulo 10^9 + 7 to handle large products.

Requirements:

- Subarray must have at least one element.
- Compute the product of all elements in the palindromic subarray.
- Handle edge cases: empty array or no palindromic subarrays.

Example:

Input: arr = [2, 3, 2, 4]
Output: 12
Explanation: Palindromic subarrays are [2], [3], [2], [2, 3, 2]. Products: 2, 3, 2, 12 (2*3*2). Maximum is 12.

Input: arr = [1, 2, 3]
Output: 3
Explanation: Palindromic subarrays are [1], [2], [3]. Products: 1, 2, 3. Maximum is 3.

Input: arr = [4, 5, 4, 5]
Output: 80
Explanation: Palindromic subarrays include [4], [5], [4], [5], [4, 5, 4]. Maximum product is 4*5*4=80.

Input: arr = []
Output: -1

Constraints:

- 0 <= arr.length <= 100
- 1 <= arr[i] <= 100
- Time Complexity: Aim for O(n^2).
- Space Complexity: O(1) excluding input.

Why It’s Tricky: Identifying palindromic subarrays requires checking each subarray’s symmetry while computing products under modulo constraints. The problem is approachable with nested loops but challenges you to handle edge cases and optimize for efficiency.

Resources to Solve It:

- GeeksforGeeks: Palindrome Substring Queries – Explore palindrome checking techniques.
- HackerRank: Palindrome Subarray Problems – Practice similar array-based challenges.
- LeetCode: Maximum Product Subarray – Tackle a related problem for deeper understanding.

Try solving this problem and test your DSA skills! Share your approach or check the linked resources for guidance.