What is the optimal time complexity of solving Array Rotation?

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 Array Rotation?

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 Array Rotation?

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 Array Rotation?

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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DSA SectionEasy

Array Rotation

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

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Problem Statement

Easy

Write a function rotate_array(arr, k) that rotates the array arr to the left by k positions and returns the rotated array. Elements that go past the beginning wrap around to the end. For example, rotating [1,2,3,4,5] left by 2 gives [3,4,5,1,2].

Constraints

•0 <= len(arr) <= 10^5
•0 <= k <= 10^6
•-10^9 <= arr[i] <= 10^9

Examples

Example 1

Input

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

Output

[3, 4, 5, 1, 2]

Explanation

Rotate left by 2: first 2 elements [1,2] move to the end.

Example 2

Input

arr = [10, 20, 30, 40], k = 1

Output

[20, 30, 40, 10]

Explanation

Rotate left by 1: 10 moves to the end.

Example 3

Input

arr = [1, 2, 3], k = 3

Output

[1, 2, 3]

Explanation

Rotating by the array length returns the original array.

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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