What is the optimal time complexity of solving Counting 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 Counting 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 Counting 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 Counting 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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DSA SectionEasy

Counting Sort

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

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Problem Statement

Easy

Write a function counting_sort(arr) that sorts a list of non-negative integers arr using the Counting Sort algorithm. You may assume that the elements are integers in a small range [0, k]. The function should return the sorted list.

Constraints

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

Examples

Example 1

Input

arr = [4, 2, 2, 8, 3, 3, 1]

Output

[1, 2, 2, 3, 3, 4, 8]

Explanation

Frequencies of each element are counted, and cumulative counts are used to place elements in the sorted output 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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