What is the optimal time complexity of solving Maximum Product Subarray?

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 Maximum Product Subarray?

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 Maximum Product Subarray?

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 Maximum Product Subarray?

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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Maximum Product Subarray

Learn how to solve the 'Maximum Product Subarray' problem. This detailed resource details brute force and optimized approaches.

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Problem Statement

Hard

Given an integer array nums, find a contiguous non-empty subarray within the array that has the largest product, and return the product.

The test cases are generated so that the answer will fit in a 32-bit integer.

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

Constraints

•1 <= len(nums) <= 2 * 10^4
•-10 <= nums[i] <= 10
•The product of any prefix or suffix of nums fits in a 32-bit integer

Examples

Example 1

Input

nums = [2,3,-2,4]

Output

Explanation

[2,3] has the largest product 6.

Example 2

Input

nums = [-2,0,-1]

Output

Explanation

The result cannot be larger than 0 because of the negative numbers separated by 0.

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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