Product of Array Except Self

🧠 Problem Statement

Given an integer array nums, return an array answer such that
answer[i] equals the product of all elements in nums except nums[i].

The solution must run in O(n) time and use O(1) extra space (excluding the output array).
Division is not allowed in the main approach.

⚙️ Implementations

1️⃣ Prefix–Suffix Approach (No Division)

This approach calculates prefix and suffix products in two passes.

Steps:

1. Compute prefix products from left to right.
2. Compute suffix products from right to left.
3. Multiply corresponding prefix and suffix products for each index.

Complexity:

• Time: O(n)
• Space: O(1) (excluding output)

2️⃣ Optimized Approach (Handles Zeros Efficiently)

This version handles:

• Multiple zeros → all outputs are 0
• Single zero → only that index gets the product of non-zero elements
• No zeros → uses division safely

Reference: LeetCode #238 – Product of Array Except Self

🧩 Checklist

• I have read CONTRIBUTING.md.
• This pull request is all my own work -- I have not plagiarized.
• I know that pull requests will not be merged if they fail the automated tests.
• This PR only changes one algorithm file.
• All new Python files are placed inside an existing directory.
• All filenames are lowercase with no spaces or dashes.
• All function and variable names follow Python naming conventions.
• All functions and parameters have Python type hints.
• All functions have doctests that pass.
• The new algorithm includes a URL for reference.