161 lines
4.3 KiB
Python
161 lines
4.3 KiB
Python
import heapq
|
|
import sys
|
|
from typing import Callable, Iterator, TypeVar
|
|
|
|
Node = TypeVar("Node")
|
|
|
|
|
|
def dijkstra(
|
|
start: Node,
|
|
neighbors: Callable[[Node], Iterator[Node]],
|
|
cost: Callable[[Node, Node], float],
|
|
) -> tuple[dict[Node, float], dict[Node, Node]]:
|
|
"""
|
|
Compute shortest paths from one node to all reachable ones.
|
|
|
|
Args:
|
|
start: Starting node.
|
|
neighbors: Function returning the neighbors of a node.
|
|
cost: Function to compute the cost of an edge.
|
|
|
|
Returns:
|
|
A tuple (lengths, parents) where lengths is a mapping from Node to distance
|
|
(from the starting node) and parents a mapping from parents Node (in the
|
|
shortest path). If keyset of lengths and parents is the same. If a Node is not
|
|
in the mapping, it cannot be reached from the starting node.
|
|
"""
|
|
|
|
queue: list[tuple[float, Node]] = []
|
|
|
|
visited: set[Node] = set()
|
|
lengths: dict[Node, float] = {start: 0}
|
|
parents: dict[Node, Node] = {}
|
|
|
|
heapq.heappush(queue, (0, start))
|
|
|
|
while queue:
|
|
length, current = heapq.heappop(queue)
|
|
|
|
if current in visited:
|
|
continue
|
|
|
|
visited.add(current)
|
|
|
|
for neighbor in neighbors(current):
|
|
if neighbor in visited:
|
|
continue
|
|
|
|
neighbor_cost = length + cost(current, neighbor)
|
|
|
|
if neighbor_cost < lengths.get(neighbor, float("inf")):
|
|
lengths[neighbor] = neighbor_cost
|
|
parents[neighbor] = current
|
|
|
|
heapq.heappush(queue, (neighbor_cost, neighbor))
|
|
|
|
return lengths, parents
|
|
|
|
|
|
def make_path(parents: dict[Node, Node], start: Node, end: Node) -> list[Node] | None:
|
|
if end not in parents:
|
|
return None
|
|
|
|
path: list[Node] = [end]
|
|
|
|
while path[-1] is not start:
|
|
path.append(parents[path[-1]])
|
|
|
|
return list(reversed(path))
|
|
|
|
|
|
def print_path(path: list[tuple[int, int]], n_rows: int, n_cols: int) -> None:
|
|
end = path[-1]
|
|
|
|
graph = [["." for _c in range(n_cols)] for _r in range(n_rows)]
|
|
graph[end[0]][end[1]] = "E"
|
|
|
|
for i in range(0, len(path) - 1):
|
|
cr, cc = path[i]
|
|
nr, nc = path[i + 1]
|
|
|
|
if cr == nr and nc == cc - 1:
|
|
graph[cr][cc] = "<"
|
|
elif cr == nr and nc == cc + 1:
|
|
graph[cr][cc] = ">"
|
|
elif cr == nr - 1 and nc == cc:
|
|
graph[cr][cc] = "v"
|
|
elif cr == nr + 1 and nc == cc:
|
|
graph[cr][cc] = "^"
|
|
else:
|
|
assert False, "{} -> {} infeasible".format(path[i], path[i + 1])
|
|
|
|
print("\n".join("".join(row) for row in graph))
|
|
|
|
|
|
def neighbors(
|
|
grid: list[list[int]], node: tuple[int, int], up: bool
|
|
) -> Iterator[tuple[int, int]]:
|
|
n_rows = len(grid)
|
|
n_cols = len(grid[0])
|
|
|
|
c_row, c_col = node
|
|
for n_row, n_col in (
|
|
(c_row - 1, c_col),
|
|
(c_row + 1, c_col),
|
|
(c_row, c_col - 1),
|
|
(c_row, c_col + 1),
|
|
):
|
|
if not (n_row >= 0 and n_row < n_rows and n_col >= 0 and n_col < n_cols):
|
|
continue
|
|
|
|
if up and grid[n_row][n_col] > grid[c_row][c_col] + 1:
|
|
continue
|
|
elif not up and grid[n_row][n_col] < grid[c_row][c_col] - 1:
|
|
continue
|
|
|
|
yield n_row, n_col
|
|
|
|
|
|
# === main code ===
|
|
|
|
lines = sys.stdin.read().splitlines()
|
|
|
|
grid = [[ord(cell) - ord("a") for cell in line] for line in lines]
|
|
|
|
start: tuple[int, int]
|
|
end: tuple[int, int]
|
|
|
|
# for part 2
|
|
start_s: list[tuple[int, int]] = []
|
|
|
|
for i_row, row in enumerate(grid):
|
|
for i_col, col in enumerate(row):
|
|
if chr(col + ord("a")) == "S":
|
|
start = (i_row, i_col)
|
|
start_s.append(start)
|
|
elif chr(col + ord("a")) == "E":
|
|
end = (i_row, i_col)
|
|
elif col == 0:
|
|
start_s.append((i_row, i_col))
|
|
|
|
# fix values
|
|
grid[start[0]][start[1]] = 0
|
|
grid[end[0]][end[1]] = ord("z") - ord("a")
|
|
|
|
|
|
lengths_1, parents_1 = dijkstra(
|
|
start=start, neighbors=lambda n: neighbors(grid, n, True), cost=lambda lhs, rhs: 1
|
|
)
|
|
path_1 = make_path(parents_1, start, end)
|
|
assert path_1 is not None
|
|
|
|
print_path(path_1, n_rows=len(grid), n_cols=len(grid[0]))
|
|
|
|
print(f"answer 1 is {lengths_1[end] - 1}")
|
|
|
|
lengths_2, parents_2 = dijkstra(
|
|
start=end, neighbors=lambda n: neighbors(grid, n, False), cost=lambda lhs, rhs: 1
|
|
)
|
|
answer_2 = min(lengths_2.get(start, float("inf")) for start in start_s)
|
|
print(f"answer 2 is {answer_2}")
|