ML CodinghardNumpy~30m

K-Means Step

Problem

You are implementing the core update step of the K-Means clustering algorithm. K-Means iteratively assigns points to their nearest centroid, then recomputes each centroid as the mean of its assigned points.

Given a list of points and a list of centroids, perform one iteration:

Assign each point to its nearest centroid by L2 (Euclidean) distance
Recompute each centroid as the mean of all points assigned to it
If a centroid has no assigned points, keep it unchanged

Return the new centroids rounded to 6 decimal places.

Note: For ties (equal distances), assign to the lower-indexed centroid.

Examples

Example 1

Input: ([[1], [2], [4], [5]], [[1], [5]])

Output: [[1.5], [4.5]]

Points 1,2 nearest to C0=[1], points 4,5 nearest to C1=[5]. New C0=mean(1,2)=1.5, C1=mean(4,5)=4.5.

Example 2

Input: ([[0, 0], [1, 1], [2, 2]], [[1, 1], [900, 900]])

Output: [[1.0, 1.0], [900.0, 900.0]]

All points assign to C0 (far from C1). C0=mean([0,0],[1,1],[2,2])=[1,1]. C1 empty — kept unchanged.

Example 3

Input: ([[0], [1], [3]], [[0], [10]])

Output: [[1.333333], [10.0]]

All 3 points nearest to C0. Mean = (0+1+3)/3 = 1.333333. C1 empty — kept at 10.0.

Constraints

›2 <= n_points <= 100
›2 <= k <= 10
›1 <= n_dims <= 10
›-1000 <= values <= 1000

Reference solution

Reference solution available after you attempt the question.

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