13.py

import fileinput

U, D, L, R = (0, -1), (0, 1), (-1, 0), (1, 0)

directions = {'^': U, 'v': D, '<': L, '>': R}
straight = {U: U, D: D, L: L, R: R}
left_turn = {U: L, D: R, L: D, R: U}
right_turn = {U: R, D: L, L: U, R: D}
forward_slash_turn = {U: R, D: L, L: D, R: U}
back_slash_turn = {U: L, D: R, L: U, R: D}

class Cart:
    def __init__(self, p, d):
        self.p = p
        self.d = d
        self.i = 0
        self.ok = True
    def step(self, grid):
        self.p = (self.p[0] + self.d[0], self.p[1] + self.d[1])
        c = grid[self.p]
        if c == '+':
            turn = [left_turn, straight, right_turn][self.i % 3]
            self.d = turn[self.d]
            self.i += 1
        elif c == '/':
            self.d = forward_slash_turn[self.d]
        elif c == '\\':
            self.d = back_slash_turn[self.d]
    def hits(self, other):
        return self != other and self.ok and other.ok and self.p == other.p

grid = {}
carts = []
for y, line in enumerate(fileinput.input()):
    for x, c in enumerate(line):
        grid[(x, y)] = c
        if c in directions:
            carts.append(Cart((x, y), directions[c]))

part1 = part2 = None
while True:
    carts = sorted(carts, key=lambda x: (x.p[1], x.p[0]))
    for cart in carts:
        cart.step(grid)
        for other in carts:
            if cart.hits(other):
                cart.ok = other.ok = False
                part1 = part1 or cart.p
    carts = [x for x in carts if x.ok]
    if len(carts) == 1:
        part2 = carts[0].p
        break

print(part1)
print(part2)