What is the optimal time complexity of solving K Closest Points to Origin?

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 K Closest Points to Origin?

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 K Closest Points to Origin?

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 K Closest Points to Origin?

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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K Closest Points to Origin

Learn how to solve the 'K Closest Points to Origin' problem. This detailed resource details brute force and optimized approaches.

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Problem Statement

Easy

Given an array of points where points[i] = [xi, yi] represents a point on the X-Y plane and an integer k, return the k closest points to the origin (0, 0).

The distance between two points on the X-Y plane is the Euclidean distance (i.e., sqrt((x1 - x2)^2 + (y1 - y2)^2)).

You may return the answer in any order. The answer is guaranteed to be unique (except for the order that it is in).

Write a function kClosest(points: List[List[int]], k: int) -> List[List[int]].

Constraints

•1 <= k <= len(points) <= 10^4
•-10^4 <= xi, yi <= 10^4

Examples

Example 1

Input

points = [[1,3],[-2,2]], k = 1

Output

[[-2,2]]

Explanation

The distance from (1, 3) to the origin is sqrt(10). The distance from (-2, 2) to the origin is sqrt(8). Since sqrt(8) < sqrt(10), (-2, 2) is closer to the origin.

Example 2

Input

points = [[3,3],[5,-1],[-2,4]], k = 2

Output

[[3,3],[-2,4]]

Explanation

The closest two points are (3, 3) and (-2, 4). (Order of elements in the output does not matter).

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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