What is the optimal time complexity of solving Sort first half ascending and second half descending?

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 Sort first half ascending and second half descending?

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 Sort first half ascending and second half descending?

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 Sort first half ascending and second half descending?

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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Sort first half ascending and second half descending

Learn how to solve the 'Sort first half ascending and second half descending' problem. This detailed resource details brute force and optimized approaches.

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Problem Statement

Easy

Write a function sort_half(arr) that takes a list of integers and returns a new list where the first half is sorted in ascending order and the second half is sorted in descending order. If the array has odd length, the middle element belongs to the first half. For example, for length 5, the first 3 elements are sorted ascending and the last 2 are sorted descending.

Constraints

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

Examples

Example 1

Input

arr = [5, 2, 8, 1, 4, 7]

Output

[1, 2, 5, 8, 7, 4]

Explanation

First half [5,2,8] sorted ascending: [1,2,5]. Second half [1,4,7] sorted descending: [8,7,4]. Wait — we split the original array: first 3 elements [5,2,8] sort ascending -> [2,5,8], last 3 [1,4,7] sort descending -> [7,4,1]. Result: [2,5,8,7,4,1].

Example 2

Input

arr = [3, 1, 2, 5, 4]

Output

[1, 2, 3, 5, 4]

Explanation

First half (3 elements) [3,1,2] sorted ascending: [1,2,3]. Second half (2 elements) [5,4] sorted descending: [5,4]. Result: [1,2,3,5,4].

Example 3

Input

arr = [9, 3, 6, 1]

Output

[3, 9, 6, 1]

Explanation

First half [9,3] ascending: [3,9]. Second half [6,1] descending: [6,1]. Result: [3,9,6,1].

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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