What is the optimal time complexity of solving Find maximum product sub-array?

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 Find maximum product sub-array?

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 Find maximum product sub-array?

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 Find maximum product sub-array?

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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Python BasicsHard

Find maximum product sub-array

Learn how to solve the 'Find maximum product sub-array' problem. This detailed resource details brute force and optimized approaches.

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Problem Statement

Hard

Write a function max_product_subarray(arr) that takes a list of integers arr and returns the maximum product of any contiguous subarray. A subarray must contain at least one element.

Constraints

•1 <= len(arr) <= 10^4
•-10 <= arr[i] <= 10

Examples

Example 1

Input

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

Output

Explanation

The subarray [2, 3] has the maximum product: 2 * 3 = 6.

Example 2

Input

arr = [-2, 0, -1]

Output

Explanation

The subarray [0] gives the maximum product of 0, since all other products are negative or zero.

Example 3

Input

arr = [-2, -3, 4]

Output

Explanation

The entire array: (-2) * (-3) * 4 = 24? Wait, that's the subarray [-2,-3,4] = 24. Yes, two negatives multiply to positive.

Need a Hint?

Use simple arithmetic operators (like modulo `%`, division `//`), conditional checks, or loops to inspect number properties.

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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