Linear Algebra-based solution, using linear transformations

katas_santa.py

from numpy import sin, cos, array, pi
from operator import matmul
from functools import reduce

def move(theta, s):
    """Generate a translation and rotation matrix from a given angle theta 
    and displacement s. The transformation rotates the whole coordinate 
    system either left or right, then moves us `s` steps north
    
    Given a vector v = [ x y 1 ], and a tranformation matrix A, 
    We perform one move by computing v' = [ x' y' 1 ] = Av
    """ 
    return array([[cos(theta), -sin(theta), s*cos(theta)],
                  [sin(theta),  cos(theta), s*sin(theta)],
                  [0         , 0          , 1]])

def interpet(instructions):
    """Moves can be composed by simply multiplying them together, 
    so we get all of the transformation matrices for a list of steps
    "L1, R4"... etc and get a final tranformation, the matrix product
    of all of them.
    """
    theta = {'R': pi / 2, 'L': (3 * pi) / 2}
    return reduce(matmul, (move(theta[s[0]], float(s[1:]))
                           for s in instructions.split(', ')))

def travel(instructions):
    """Now to follow a set of instructions we multiply a vector
    representing us being at the origin [0 0 1] by the composite
    tranformation
    
    Our final position is the fist two entries of the resultant
    vector"""
    
    init = array([0, 0, 1])
    transformation = interpet(instructions)
    return (transformation @ init)[:2]

def main():
    """
    To solve this, we then just move to the destination, then take
    the taxicab distance, abs(x) + abs(y)
    """
    moves = ("L4, L3, R1, L4, R2, R2, L1, L2, R1, R1, L3, R5, L2, R5, "
             "L4, L3, R2, R2, L5, L1, R4, L1, R3, L3, R5, R2, L5, R2, "
             "R1, R1, L5, R1, L3, L2, L5, R4, R4, L2, L1, L1, R1, R1, "
             "L185, R4, L1, L1, R5, R1, L1, L3, L2, L1, R2, R2, R2, L1, "
             "L1, R4, R5, R53, L1, R1, R78, R3, R4, L1, R5, L1, L4, R3, "
             "R3, L3, L3, R191, R4, R1, L4, L1, R3, L1, L2, R3, R2, R4, "
             "R5, R5, L3, L5, R2, R3, L1, L1, L3, R1, R4, R1, R3, R4, "
             "R4, R4, R5, R2, L5, R1, R2, R5, L3, L4, R1, L5, R1, L4, "
             "L3, R5, R5, L3, L4, L4, R2, R2, L5, R3, R1, R2, R5, L5, "
             "L3, R4, L5, R5, L3, R1, L1, R4, R4, L3, R2, R5, R1, R2, "
             "L1, R4, R1, L3, L3, L5, R2, R5, L1, L4, R3, R3, L3, R2, "
             "L5, R1, R3, L3, R2, L1, R4, R3, L4, R5, L2, L2, R5, R1, "
             "R2, L4, L4, L5, R3, L4")

    distance = sum(map(abs, travel(moves)))
    print(distance)

if __name__ == '__main__':
    main()