Return the K Closest Points with Deterministic Ties

Question

The candidate is asked to implement a function that returns the K closest points to a given origin from a list of points, ensuring that ties are handled deterministically.

Codemia · Accepted Answer

To solve the problem of finding the K closest points to a given origin, we can utilize a sorting approach based on the Euclidean distance from the origin. The basic idea is to compute the distance for each point, sort the points based on this distance, and then select the top K points. We will ensure that ties in distance are handled deterministically by using the coordinates of the points as a secondary sorting criterion.

1. **Calculate Distance:** For each point, calculate the squared distance from the origin to avoid unnecessary square root calculations.  
2. **Sort Points:** Sort the list of points based on their calculated distances. If two points have the same distance, sort them by their x and y coordinates.  
3. **Select K Points:** Return the first K points from the sorted list.

Here is a sample implementation in Python:
```python
from typing import List, Tuple

def k_closest_points(points: List[Tuple[int, int]], origin: Tuple[int, int], K: int) -> List[Tuple[int, int]]:
    # Calculate the squared distance from the origin
    def distance(point):
        return (point[0] - origin[0]) ** 2 + (point[1] - origin[1]) ** 2
    
    # Sort points based on distance and then by coordinates
    points.sort(key=lambda point: (distance(point), point))
    
    # Return the first K points
    return points[:K]
```

The time complexity of this solution is O(N log N) due to the sorting step, where N is the number of points. The space complexity is O(1) if we consider the output list as part of the result, otherwise O(N) if we need to store distances separately.

It is important to consider edge cases, such as when K is larger than the number of available points. In such cases, we should simply return all available points. Additionally, if points are at the same distance, we ensure that our sorting mechanism maintains a consistent order based on coordinates.

Interviewers will be looking for a clear explanation of the thought process, the efficiency of the solution, and the ability to handle edge cases. They will also assess coding style and clarity, as well as the candidate's ability to discuss trade-offs and optimizations.

Return the K Closest Points with Deterministic Ties

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