ML CodinghardNumpy~25m

Pairwise Distances

Problem

You are implementing the core distance computation for a K-Nearest Neighbors algorithm. Given N data points in D-dimensional space, you need to compute the Euclidean (L2) distance between every pair of points.

Given a 2D matrix where each row is a point in D-dimensional space, return a symmetric distance matrix D where:

D[i][j] = sqrt(sum((points[i][k] - points[j][k])^2 for k in range(dims)))

The diagonal must be exactly 0.0. Round each value to 6 decimal places.

Key insight: Use the identity ||a-b||² = ||a||² + ||b||² - 2·a·b to express the entire computation as a matrix multiplication — avoiding O(N²·D) nested loops.

Examples

Example 1

Input: [[0, 0], [3, 4]]

Output: [[0.0, 5.0], [5.0, 0.0]]

Classic 3-4-5 right triangle. Distance = sqrt(3²+4²) = 5.0. Matrix is symmetric, diagonal is 0.0.

Example 2

Input: [[1, 0], [0, 1], [-1, 0], [0, -1]]

Output:

[[0.0, 1.414214, 2.0, 1.414214], [1.414214, 0.0, 1.414214, 2.0], [2.0, 1.414214, 0.0, 1.414214], [1.414214, 2.0, 1.414214, 0.0]]

Unit circle: adjacent points √2 apart, opposite points 2.0 apart.

Example 3

Input: [[0, 0, 0], [3, 4, 0], [0, 5, 12]]

Output: [[0.0, 5.0, 13.0], [5.0, 0.0, 12.409674], [13.0, 12.409674, 0.0]]

Pythagorean triples: (3,4,0) is distance 5 from origin, (0,5,12) is distance 13.

Constraints

›2 <= n_points <= 100
›1 <= n_dims <= 100
›-1000 <= points[i][j] <= 1000

Reference solution

Reference solution available after you attempt the question.

Ready to solve it?

Start a session on Mockbit #74. Write your code, run it against hidden tests, and get graded with specific critique on each axis.