Implement `k_closest_points(points, origin, k)` for two-dimensional integer points. Return the `k` points closest to the query location `origin`. Rank points by squared Euclidean distance, then by `x`, then by `y`; return the selected points in that order. This tie-breaking rule makes the answer deterministic. `k` will not exceed the number of points. Avoid square roots. When `k` is much smaller than the number of points, target `O(n log k)` time and `O(k)` auxiliary space. ```hint Keep only the current winners Maintain a size-`k` max-heap ordered by the same distance and coordinate key used for the final result. ``` ```hint Preserve deterministic ties The heap's notion of the worst retained point must reverse the complete ranking key, not only the distance. ``` ### Discussion Extensions - How could quickselect reduce expected running time when all points are available as one batch? - For millions of moving points, compare a uniform grid, a quadtree, and a hierarchical spatial cell index. - If final ranking uses road-network travel distance, where can straight-line distance still provide a safe candidate filter?