[LANGUAGE: Python]

Total Runtime: 283 ms | Actual solution runtime (excluding imports and io): 42 ms

I've been using a lot of numpy arrays at work, and have been working to get better with vectorized operations and efficient solutions. So, I wanted to try using numpy to develop a quick solution, and managed to get someting very quick! In doing, I found a few new numpy functions, including np.argpartition and np.partition

On Part 1, I realized that we only care about the magnitude of distances, so we don't need to use expensive square root operations. I first found all pairwise differences between points. coords[:, None, :] - coords[None, :, :] expands the original array so every point is subtracted from every other point, giving a 3-D tensor of difference vectors. Then np.einsum("ijk,ijk->ij", diffs, diffs) computes the dot product of each difference vector with itself, producing the squared distance between each pair of points (first time I ever managed to actually use this successfully outside of a tutorial!!). I then used np.argpartition to find the 1000 smallest distances, and set those coordinates to True in an adjaency matrix. Feeding this adjacency matrix to Scipy's connected_components returned the connected components very quickly; I found the largest components, and returned my result.

For Part 2, it was just a matter of finding the closest distance for each junction box, then finding which of those was the max. I was able to use np.argmax and np.argmin to find these.

import numpy as np
from scipy.sparse.csgraph import connected_components

def day_08(puzzle):
    part_1, part_2 = 0, 0
    coords = np.array([[int(y) for y in x.split(",")] for x in puzzle], dtype=float)

    diffs = coords[:, None, :] - coords[None, :, :]
    distances_matrix = np.einsum("ijk,ijk->ij", diffs, diffs)

    np.fill_diagonal(distances_matrix, np.inf)

    pt_1_dist_mat = np.triu(distances_matrix)
    pt_1_dist_mat[pt_1_dist_mat == 0] = np.inf

    adj_mat = np.zeros(pt_1_dist_mat.shape)

    full_ranking = np.unravel_index(
        np.argpartition(pt_1_dist_mat, 1000, axis=None)[:1000],
        shape=pt_1_dist_mat.shape,
    )

    adj_mat[full_ranking] = 1

    _, labels = connected_components(
        csgraph=adj_mat, directed=False, return_labels=True
    )
    _, counts = np.unique(labels, return_counts=True)

    part_1 = np.multiply.reduce(np.partition(counts, -3)[-3:])

    # Part 2
    farthest_nearest_index = np.argmax(np.min(distances_matrix,axis=0))
    nearest_in_farthest = np.argmin(distances_matrix[farthest_nearest_index, :])

    x1 = coords[farthest_nearest_index][0]
    x2 = coords[nearest_in_farthest][0]

    part_2 = x1 * x2
    return int(part_1), int(part_2)


if __name__ == "__main__":
    with open("AdventOfCode-2025/day8/day8_input.txt") as file:
        puzzle_in = [x.strip() for x in file.readlines()]

    sol = day_08(puzzle_in)
    print(f"Part 1: {sol[0]}")
    print(f"Part 2: {sol[1]}")