Problem Description
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. You may return the answer in any order, and it is guaranteed to be unique (except for the order that it is in).
Key Insights
- The Euclidean distance from the origin can be calculated using the formula: distance = sqrt(x^2 + y^2). However, for comparison purposes, we can use the squared distance to avoid unnecessary computation with square roots.
- Sorting the array based on the squared distance allows us to easily retrieve the k closest points.
- Alternatively, a min-heap (priority queue) can be used to efficiently keep track of the closest k points without fully sorting the array.
Space and Time Complexity
Time Complexity: O(n log n) for sorting, O(n) for using a min-heap. Space Complexity: O(n) for storing the points.
Solution
To solve the problem, we can either sort the points based on their squared distance from the origin or use a min-heap to keep track of the closest k points. The sorting method is straightforward and involves calculating the squared distance for each point, sorting the list, and then selecting the first k points. The min-heap method involves maintaining a heap of size k while iterating through the points, ensuring that we only keep the closest ones.