day12b.py

inp = """<x=15, y=-2, z=-6>
<x=-5, y=-4, z=-11>
<x=0, y=-6, z=0>
<x=5, y=9, z=6>"""

inp = inp.split("\n")

coords = [
    line[1:-1].split(", ")
    for line in inp
]

posns = [
    tuple([int(coord[2:]) for coord in line])
    for line in coords
]

vels = [
    (0, 0, 0)
] * len(posns)

# Find the interval along each axis as each one is indepenent
intervals = {}
for axis in range(3):
    seen = set()
    step = 0

    vals = [pos[axis] for pos in posns]
    speeds = [0] * len(vals)

    while True:
        key = tuple(vals) + tuple(speeds)
        if key in seen:
            intervals[axis] = step
            break
        else:
            seen.add(key)

        new_speeds = []
        for i, (pos_a, vel_a) in enumerate(zip(vals, speeds)):
            for j, pos_b, in enumerate(vals):
                if pos_a < pos_b:
                    vel_a += 1
                elif pos_a > pos_b:
                    vel_a -= 1
            new_speeds.append(vel_a)

        speeds = new_speeds

        vals = [
            val + speed
            for val, speed in zip(vals, speeds)
        ]

        step += 1

def gcd(a, b):
    if a < b:
        a, b = b, a
    while b:
        a, b = b, a % b
    return a

print intervals

def compute_lcm(x, y):
   lcm = (x*y)//gcd(x,y)
   return lcm

print compute_lcm(intervals[0], compute_lcm(intervals[1], intervals[2]))