p12.py

#!/usr/bin/env python3
# -*- coding: utf8 -*-

import numpy as np 
from re import compile
from math import gcd

def minsta_gemensamma(a, b):
    return abs(a*b) // gcd(a, b)

data = open('12.in','r').read()
x = compile(r"<x=(-?\d+), y=(-?\d+), z=(-?\d+)>")

moons = np.array([[int(a) for a in x.match(m).groups()] for m in data.split("\n") if x.match(m) is not None], dtype=int)
velocities = np.zeros(moons.shape, dtype=int)
initial_position = moons.copy()

# Since the calculation is reversible, then if it repeats it must be a closed loop
# with no branches. Therefore the first repeated step must be the initial step.

steps = 0
p1done = False
p2axes_complete = [False,False,False]
periods = 1

while (not p1done) or (not all(p2axes_complete)):
    for i in range(len(moons)):
        for j in range(i+1, len(moons)):
            diff = np.sign(moons[i,:] - moons[j,:])
            velocities[i,:] = velocities[i,:] - diff
            velocities[j,:] = velocities[j,:] + diff

    steps = steps + 1
    moons = moons + velocities

    if steps == 1000:
        print("Pt 1:", np.sum(np.sum(np.abs(moons), axis=1)*np.sum(np.abs(velocities), axis=1)))
        p1done = True
    for axis in range(3):
        if p2axes_complete[axis]:
            continue
        if np.all(moons[:,axis] == initial_position[:,axis]) and np.all(velocities[:,axis] == 0):
            p2axes_complete[axis] = True
            print("Axis",axis,"complete at", steps,"steps")
            periods = minsta_gemensamma(periods, steps)

        if all(p2axes_complete):
            print("Pt 2:", periods)