K Closest Points to Origin

Each points[i] = [xi, yi] is a point on a flat X-Y plane. Return the k of them that lie nearest to the origin (0, 0).

"Nearest" means straight-line (Euclidean) distance, which for a point measured from the origin is √(x² + y²). The k points can come back in any order.

We want the K smallest distances.

• We can use a Max-Heap of size K.
• Why Max-Heap? Because we want to keep the "smallest" K elements. If the heap gets too big (> K), we want to evict the largest element (the one furthest away) to make room for smaller ones.

Algorithm:

1. Initialize a Max-Heap.
2. Iterate through all points.
3. Calculate squared distance for each point ( x^2 + y^2 ). We don't need sqrt since it preserves order.
4. Push (distance, point) to heap.
5. If size > k, pop the max element.
6. Return the points remaining in the heap.

The plane shows every point. Once the heap holds k, a dashed circle passes through the farthest point kept — a new point has to land inside it to stay. The max-heap beside it is keyed by squared distance.