What is the optimal time complexity of solving Maximum sum absolute difference?

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 sum absolute difference?

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 Maximum sum absolute difference?

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 sum absolute difference?

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.

Back to Practice Dashboard

Competitive ProgrammingHard

Maximum sum absolute difference

Learn how to solve the 'Maximum sum absolute difference' problem. This detailed resource details brute force and optimized approaches.

Mode Selected

Problem Statement

Hard

Write a function max_sum_abs_diff(arr) that returns the maximum sum of absolute differences of consecutive elements in any circular permutation of the array arr.

Constraints

•2 <= len(arr) <= 1000
•-10^4 <= arr[i] <= 10^4

Examples

Example 1

Input

max_sum_abs_diff([1, 2, 4, 8])

Output

Explanation

The circular permutation [1, 8, 2, 4] yields |1-8| + |8-2| + |2-4| + |4-1| = 7 + 6 + 2 + 3 = 18.

Example 2

Input

max_sum_abs_diff([10, 12])

Output

Explanation

The only circular permutation is [10, 12] yielding |10-12| + |12-10| = 2 + 2 = 4.

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

Ready to Solve?

Open the problem in PyRun's browser-based Python editor. Your code runs fully offline — no server required.

Open in Editor