# AoC 2016 Day 1: Taxicab Simulator

### Source: No Time for a Taxicab

Part 1: Starting at 0,0 and given a string of L# / R# to turn left / right and move # squares, where do you end up?

location = 0+0j
facing = 1+0j

rotations = {'R': 0+1j, 'L': 0-1j}

with open(args.input_file, 'r') as fin:
facing *= rotations[command[0]]

for step in range(int(command[1:])):
location += facing

def format_location(pt):
return '({}, {}), {} blocks from the origin'.format(
abs(int(pt.real)),
abs(int(pt.imag)),
abs(int(pt.real)) + abs(int(pt.imag)),
)

print('final location:', format_location(location))

We’re going to use a trick I’ve used before and using complex numbers for points. This lets us add them together easily and lets us use complex multiplication for the rotations (multiplying by 0+1i is the same as rotating clockwise).

Part 2: How many blocks away is the first location you visit twice?

For this, we just have to track the points we’ve visited (in a set ) and write down the first duplicate we find.

visited = {0+0j}
first_duplicate = None

with open(args.input_file, 'r') as fin:
facing *= rotations[command[0]]

for step in range(int(command[1:])):
location += facing

if location in visited:
if first_duplicate == None:
first_duplicate = location
else:
print('first duplicate:', format_location(first_duplicate))