What is the optimal time complexity of solving Longest Consecutive Sequence?

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 Longest Consecutive Sequence?

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 Longest Consecutive Sequence?

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 Longest Consecutive Sequence?

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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Longest Consecutive Sequence

Learn how to solve the 'Longest Consecutive Sequence' problem. This detailed resource details brute force and optimized approaches.

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Problem Statement

Easy

Given an unsorted array of integers nums, return the length of the longest consecutive elements sequence.

You must write an algorithm that runs in O(n) time.

Write a function longestConsecutive(nums: List[int]) -> int.

Constraints

•0 <= len(nums) <= 10^5
•-10^9 <= nums[i] <= 10^9

Examples

Example 1

Input

nums = [100, 4, 200, 1, 3, 2]

Output

Explanation

The longest consecutive elements sequence is [1, 2, 3, 4]. Its length is 4.

Example 2

Input

nums = [0, 3, 7, 2, 5, 8, 4, 6, 0, 1]

Output

Explanation

The longest consecutive elements sequence is [0, 1, 2, 3, 4, 5, 6, 7, 8]. Its length is 9.

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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