#!/usr/bin/env python import sys from fractions import Fraction from typing import Dict, List, NamedTuple, Optional class Point(NamedTuple): x: int y: int class Line(NamedTuple): p1: Point p2: Point def manhattan_dist(p1: Point, p2: Point = Point(0, 0)) -> int: dx = p2.x - p1.x if p1.x < p2.x else p1.x - p2.x dy = p2.y - p1.y if p1.y < p2.y else p1.y - p2.y return dx + dy def intersect(l1: Line, l2: Line) -> Optional[Point]: (x1, y1), (x2, y2) = l1.p1, l1.p2 (x3, y3), (x4, y4) = l2.p1, l2.p2 den = (x1 - x2) * (y3 - y4) - (y1 - y2) * (x3 - x4) if den == 0: # Parallel lines return None t = Fraction((x1 - x3) * (y3 - y4) - (y1 - y3) * (x3 - x4), den) if t < 0 or t > 1: # Out of l1 return None u = -Fraction((x1 - x2) * (y1 - y3) - (y1 - y2) * (x1 - x3), den) if u < 0 or u > 1: # Out of l2 return None dx = t * (x2 - x1) dy = t * (y2 - y1) assert int(dx) == dx and int(dy) == dy # Sanity checks ix = x1 + int(dx) iy = y1 + int(dy) return Point(ix, iy) def is_on(p: Point, l: Line) -> bool: # Assume that l is horizontal or vertical if l.p1.x == l.p2.x: if l.p1.y < l.p2.y: return p.x == l.p1.x and l.p1.y <= p.y <= l.p2.y elif l.p2.y < l.p1.y: return p.x == l.p1.x and l.p2.y <= p.y <= l.p1.y elif l.p1.y == l.p2.y: if l.p1.x < l.p2.x: return p.y == l.p1.y and l.p1.x <= p.x <= l.p2.x elif l.p2.x < l.p1.x: return p.y == l.p1.y and l.p2.x <= p.x <= l.p1.x assert False # Sanity checks def parse_line(directions: str) -> List[Line]: prev = Point(0, 0) ans = [] for inst in directions.split(","): direction, length = inst[0], int(inst[1:]) new_x, new_y = prev if direction == "U": new_y += length elif direction == "R": new_x += length if direction == "D": new_y -= length elif direction == "L": new_x -= length new = Point(new_x, new_y) ans.append(Line(prev, new)) prev = new return ans def compute_delay(p: Point, lines: List[Line]) -> int: dist = 0 for l in lines: if is_on(p, l): return dist + manhattan_dist(l.p1, p) dist += manhattan_dist(l.p1, l.p2) assert False # Sanity check def main() -> None: wire1, wire2 = tuple(parse_line(l) for l in sys.stdin) intersections = [intersect(l1, l2) for l1 in wire1 for l2 in wire2] print( min( compute_delay(x, wire1) + compute_delay(x, wire2) for x in intersections if x is not None and x != Point(0, 0) # Discard origin ) ) if __name__ == "__main__": main()