What is the optimal time complexity of solving Removing Duplicate elements from an array?

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 Removing Duplicate elements from an array?

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 Removing Duplicate elements from an array?

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 Removing Duplicate elements from an array?

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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Removing Duplicate elements from an array

Learn how to solve the 'Removing Duplicate elements from an array' problem. This detailed resource details brute force and optimized approaches.

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Problem Statement

Easy

Write a function remove_duplicates(arr) that takes a list of integers arr and returns a new list with duplicate elements removed, preserving the order of first occurrence of each element.

Constraints

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

Examples

Example 1

Input

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

Output

[1, 2, 3, 4, 5]

Explanation

Remove the second 2 and second 4, keeping first occurrences in order.

Example 2

Input

arr = [5, 5, 5, 5]

Output

[5]

Explanation

All duplicates removed, keeping only one 5.

Example 3

Input

arr = [1, 2, 3]

Output

[1, 2, 3]

Explanation

No duplicates, array unchanged.

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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