Points Clustering: Implement K-Means Clustering from Scratch on 2D Points
Question Details
Problem
Implement the K-Means clustering algorithm for 2D points. Given a list of points and k, initialize centroids using the first k points, then iterate: assign each point to the nearest centroid, recompute centroids as the mean of assigned points. Stop when assignments no longer change or after max_iter iterations.
python
def kmeans(
points: list[tuple[float, float]],
k: int,
max_iter: int = 100
) -> tuple[list[int], list[tuple[float, float]]]:
**Returns** (cluster_labels, final_centroids)
pass
Example:
points = [(1,1),(1,2),(2,1),(8,8),(8,9),(9,8)]
k = 2
-> labels = [0,0,0,1,1,1]
centroids = [(1.33,1.33), (8.33,8.33)] # approx
Follow-ups
- Why does K-Means not guarantee a global optimum, and how does K-Means++ initialization improve convergence?
- What metric would you use to choose
kautomatically (elbow method, silhouette score)? - K-Means assumes spherical clusters of similar size. What algorithm handles elongated or unequal clusters better?
- How would you scale this to 1 million high-dimensional points efficiently (mini-batch K-Means, approximate nearest neighbor)?
Full Details
Problem
Implement the K-Means clustering algorithm for 2D points. Given a list of points and k, initialize centroids using the first k points, then iterate: assign each point to the nearest centroid, recompute centroids as the mean of assigned points. Stop when assignments no longer change or after max_iter iterations.
python
def kmeans(
points: list[tuple[float, float]],
k: int,
max_iter: int = 100
) -> tuple[list[int], list[tuple[float, float]]]:
**Returns** (cluster_labels, final_centroids)
pass
Example:
points = [(1,1),(1,2),(2,1),(8,8),(8,9),(9,8)]
k = 2
-> labels = [0,0,0,1,1,1]
centroids = [(1.33,1.33), (8.33,8.33)] # approx
Follow-ups
- Why does K-Means not guarantee a global optimum, and how does K-Means++ initialization improve convergence?
- What metric would you use to choose
kautomatically (elbow method, silhouette score)? - K-Means assumes spherical clusters of similar size. What algorithm handles elongated or unequal clusters better?
- How would you scale this to 1 million high-dimensional points efficiently (mini-batch K-Means, approximate nearest neighbor)?
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Solve similar problems on LeetCode under timed conditions (25-35 minutes per medium difficulty). The goal is pattern recognition: recognize the underlying technique (sliding window, two-pointer, BFS, memoized recursion, etc.) within 60-90 seconds of reading. Strong candidates verbalize their hypothesis out loud before coding, then iterate based on feedback. Weak candidates dive into implementation immediately, lose time on the wrong approach, and run out of time for follow-ups.
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