What is the optimal time complexity of solving Circular rotation by K positions?

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 Circular rotation by K positions?

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 Circular rotation by K positions?

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 Circular rotation by K positions?

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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Circular rotation by K positions

Learn how to solve the 'Circular rotation by K positions' problem. This detailed resource details brute force and optimized approaches.

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Problem Statement

Easy

Write a function circular_rotate(arr, k) that performs a circular right rotation of the array arr by k positions and returns the result. Elements shifted past the end wrap around to the beginning. For example, rotating [1,2,3,4,5] right by 2 gives [4,5,1,2,3].

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

[4, 5, 1, 2, 3]

Explanation

Right rotate by 2: last 2 elements [4,5] move to the front.

Example 2

Input

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

Output

[40, 10, 20, 30]

Explanation

Right rotate by 1: 40 moves to the front.

Example 3

Input

arr = [1, 2, 3], k = 6

Output

[1, 2, 3]

Explanation

k=6 is a multiple of 3 (array length), so the array returns to its original position.

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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