What is the optimal time complexity of solving Maximize the sum of 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 Maximize the sum of array?

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 Maximize the sum of 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 Maximize the sum of 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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Competitive ProgrammingEasy

Maximize the sum of array

Learn how to solve the 'Maximize the sum of array' problem. This detailed resource details brute force and optimized approaches.

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Problem Statement

Easy

Write a function maximize_sum(arr, k) that returns the maximum possible sum of the array after performing exactly k negations. In each negation, you must choose an element and replace it with its negative value. You can negate the same element multiple times.

Constraints

•1 <= len(arr) <= 10^5
•1 <= k <= 10^5
•-10^4 <= arr[i] <= 10^4

Examples

Example 1

Input

maximize_sum([-2, 0, 5, -1, 2], 4)

Output

Explanation

Negate -2 to 2, -1 to 1. The remaining 2 negations can be performed on 0. The array becomes [2, 0, 5, 1, 2], summing to 10.

Example 2

Input

maximize_sum([3, -1, 0, 2], 3)

Output

Explanation

Negate -1 to 1. The remaining 2 negations are performed on 0. Sum is 3 + 1 + 0 + 2 = 6.

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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