Implementing K-Means Clustering | Dataford Interview Questions

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Problem

Implement k-means clustering for a set of 2D points using Lloyd's algorithm. Given points and an integer k, partition the points into k clusters by repeatedly assigning each point to the nearest centroid and recomputing centroids until convergence or a fixed iteration limit.

Formal Specification

Write a function that takes:

points: a list of 2D points, where each point is [x, y]
k: the number of clusters
max_iters: the maximum number of iterations to run

Return a tuple (centroids, labels), where:

centroids is a list of k centroids, each as [x, y]
labels is a list of length len(points), where labels[i] is the cluster index assigned to points[i]

Use Euclidean distance. If a cluster becomes empty, keep its centroid unchanged. Initialize centroids as the first k points.

Constraints

1 <= len(points) <= 10^4
1 <= k <= len(points)
1 <= max_iters <= 100
Each point contains exactly 2 coordinates
-10^4 <= x, y <= 10^4
Return centroids rounded to 2 decimal places for comparison

Function Signature

def k_means(points, k, max_iters):