#!/usr/bin/env python3

from functools import cache

up    = lambda v: (v[0], v[1] + 1)
down  = lambda v: (v[0], v[1] - 1)
left  = lambda v: (v[0] - 1, v[1])
right = lambda v: (v[0] + 1, v[1])

moves = {'U' : up,
         'D' : down,
         'L' : left,
         'R' : right
        }

def iterate(f, x, N):
    for i in range(N):
        yield x
        x = f(x)

@cache
def lines(path):
    pos = (0, 0)
    r = []
    for move in path.split(','):
        dir, steps = move[0], int(move[1:])
        line = list(iterate(moves[dir], pos, steps+1))
        r.append(line)
        pos = line[-1]
    return r

def coordinates(path, corners=True):
    return sum((line[1:len(line) - 1 + corners]
                for line in lines(path)), [])

def crossings(*paths):
    return set.intersection(*(set(coordinates(path, corners=False))
                             for path in paths))

def min_crossing(path1, path2, f):
    return min(f(v) for v in crossings(path1, path2))

def preproc(puzzle_input):
    return puzzle_input.split()

def partI(paths):
    key = lambda v: abs(v[0]) + abs(v[1])

    path1, path2 = paths
    return min_crossing(path1, path2, key)

def partII(paths):
    path1, path2 = paths
    def key(c1, c2):
        r = lambda v: c1.index(v) + c2.index(v) + 2
        return r

    def min_steps(p1, p2):
        c1, c2 = coordinates(p1), coordinates(p2)
        return min_crossing(p1, p2, key(c1, c2))

    return min_steps(path1, path2)

from main import Tests

tests = Tests()
tests.add("R75,D30,R83,U83,L12,D49,R71,U7,L72\n" +
          "U62,R66,U55,R34,D71,R55,D58,R83",
         partI=159,
         partII=610)

tests.add("R98,U47,R26,D63,R33,U87,L62,D20,R33,U53,R51\n" +
          "U98,R91,D20,R16,D67,R40,U7,R15,U6,R7",
         partI=135,
         partII=410)