advent-of-code/2019/d18/ex2/ex2.py

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2020-12-02 16:43:49 +01:00
#!/usr/bin/env python
import heapq
import sys
from collections import defaultdict, deque
from dataclasses import dataclass
from functools import lru_cache
from math import inf
from typing import DefaultDict, Deque, Dict, FrozenSet, Iterator, List, Tuple, Union
RawGrid = List[str]
GraphInfo = List[Tuple[str, int]]
Graph = Dict[str, GraphInfo]
@dataclass(eq=True, frozen=True) # Hash-able
class Position:
x: int
y: int
def neighbours(grid: RawGrid, pos: Position) -> Iterator[Position]:
for dx, dy in ((1, 0), (-1, 0), (0, 1), (0, -1)):
new_pos = Position(pos.x + dx, pos.y + dy)
if not (0 <= new_pos.x < len(grid) and 0 <= new_pos.y < len(grid[0])):
continue
if grid[new_pos.x][new_pos.y] == "#":
continue
yield new_pos
def find_adjacent(grid: RawGrid, pos: Position) -> GraphInfo:
queue: Deque[Tuple[Position, int]] = deque()
visited = {pos}
adjacent: GraphInfo = []
for n in neighbours(grid, pos):
queue.append((n, 1)) # Distance is 1
while queue:
n, d = queue.popleft()
if n in visited:
continue
visited |= {n}
cell = grid[n.x][n.y]
if cell not in "#.1234": # We don't care about those
adjacent.append((cell, d))
continue # Do not go through doors and keys
for neighbour in neighbours(grid, n):
queue.append((neighbour, d + 1))
return adjacent
def build_graph(grid: RawGrid) -> Graph:
graph = {}
for x, row in enumerate(grid):
for y, cell in enumerate(row):
if cell not in "#.":
graph[cell] = find_adjacent(grid, Position(x, y))
return graph
def solve(G: Graph, start: str) -> int:
@lru_cache(2 ** 20)
def reachable_keys(src: str, found: FrozenSet[str]) -> GraphInfo:
queue = []
distance: DefaultDict[str, Union[float, int]] = defaultdict(lambda: inf)
reachable: GraphInfo = []
for neighbor, weight in G[src]:
queue.append((weight, neighbor)) # Weight first for heap comparisons
heapq.heapify(queue)
while queue:
dist, node = heapq.heappop(queue)
# Do key, add it to reachable if not found previously
if node.islower() and node not in found:
reachable.append((node, dist))
continue
# Do door, if not opened by a key that was found in the search
if node.lower() not in found:
continue
# If not a key and not a closed door
for neighbor, weight in G[node]:
new_dist = dist + weight
if new_dist < distance[neighbor]:
distance[neighbor] = new_dist
heapq.heappush(queue, (new_dist, neighbor))
return reachable
@lru_cache(2 ** 20)
def min_steps(
sources: str, keys_to_find: int, found: FrozenSet[str] = frozenset()
) -> Union[float, int]:
if keys_to_find == 0:
return 0
best = inf
for src in sources:
for key, dist in reachable_keys(src, found):
new_keys = found | {key}
new_sources = sources.replace(src, key)
new_dist = dist + min_steps(new_sources, keys_to_find - 1, new_keys)
if new_dist < best:
best = new_dist
return best
total_keys = sum(node.islower() for node in G)
return int(min_steps(start, total_keys)) # Throw if we kept the infinite float
def main() -> None:
G = build_graph(list(line.strip() for line in sys.stdin.readlines()))
print(solve(G, "1234"))
if __name__ == "__main__":
main()