What is the optimal time complexity of solving Wave Sort?

The optimized solution achieves a time complexity of O(n log n) by using sorting, mathematical shortcuts, or hash table lookups.

What is the auxiliary space complexity for Wave Sort?

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 Wave Sort?

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 Wave Sort?

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

Wave Sort

Learn how to solve the 'Wave Sort' problem. This detailed resource details brute force and optimized approaches.

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Problem Statement

Easy

Write a function wave_sort(arr) that takes an array of integers arr, sorts it in ascending order, and then swaps every adjacent pair of elements starting from index 0 (i.e., swap arr[0] and arr[1], then arr[2] and arr[3], and so on) to produce a wave-sorted array satisfying the property arr[0] >= arr[1] <= arr[2] >= arr[3] <= arr[4].... Return the resulting array.

Constraints

•1 <= len(arr) <= 10^5
•-10^9 <= arr[i] <= 10^9

Examples

Example 1

Input

wave_sort([3, 6, 5, 10, 7, 20])

Output

[5, 3, 7, 6, 20, 10]

Explanation

First, sort the array to get [3, 5, 6, 7, 10, 20]. Swapping adjacent pairs: swap 3 and 5 -> [5, 3...], swap 6 and 7 -> [..., 7, 6...], swap 10 and 20 -> [..., 20, 10]. Result is [5, 3, 7, 6, 20, 10].

Example 2

Input

wave_sort([10, 90, 49, 2, 1, 5, 23])

Output

[2, 1, 10, 5, 49, 23, 90]

Explanation

Sort array to [1, 2, 5, 10, 23, 49, 90]. Swapping adjacent pairs gives [2, 1, 10, 5, 49, 23, 90].

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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