What is the optimal time complexity of solving Product of Array Except Self?

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 Product of Array Except Self?

The space complexity is O(n) 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 Product of Array Except Self?

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 Product of Array Except Self?

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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Product of Array Except Self

Learn how to solve the 'Product of Array Except Self' problem. This detailed resource details brute force and optimized approaches.

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Problem Statement

Easy

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

The product of any prefix or suffix of nums is guaranteed to fit in a 32-bit integer.

You must write an algorithm that runs in O(n) time and without using the division operation.

Write a function productExceptSelf(nums: List[int]) -> List[int].

Constraints

•2 <= len(nums) <= 10^5
•-30 <= nums[i] <= 30
•The product of any prefix or suffix of nums fits in a 32-bit integer

Examples

Example 1

Input

nums = [1, 2, 3, 4]

Output

[24, 12, 8, 6]

Explanation

answer[0] = 2*3*4 = 24, answer[1] = 1*3*4 = 12, answer[2] = 1*2*4 = 8, answer[3] = 1*2*3 = 6.

Example 2

Input

nums = [-1, 1, 0, -3, 3]

Output

[0, 0, 9, 0, 0]

Explanation

Any product that includes the 0 at index 2 becomes 0. answer[2] = (-1)*1*(-3)*3 = 9.

Need a Hint?

Analyze the input constraints. Try sorting first (O(n log n)) or using a hash map/set to track seen elements in O(n) time.

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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