perfectly spherical houses in a vacuum

approach

a step function turns one arrow into a move on a coordinate pair, and every visited position goes into a set.

part 1 walks a single position through the instructions and returns the size of the set. part 2 keeps two positions in a list and alternates between them with i % 2, adding both paths to the same set.

the trick

two walkers are just two positions indexed by the parity of the instruction.

def part2(instructions):
    dirs = [[0, 0], [0, 0]]
    s = {(0, 0)}

    for i in range(len(instructions)):
        santa = i % 2
        r, c = step(*dirs[santa], instructions[i])
        dirs[santa][0] = r
        dirs[santa][1] = c
        s.add((r, c))

    return len(s)