129 lines
3.8 KiB
Python
129 lines
3.8 KiB
Python
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#!/usr/bin/env python
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import dataclasses
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import functools
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import sys
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from collections import defaultdict
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@dataclasses.dataclass
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class Valve:
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flow: int
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neighbours: set[str]
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Graph = dict[str, Valve]
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DistanceMatrix = dict[str, dict[str, int]]
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START_ROOM = "AA"
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def solve(input: list[str]) -> int:
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def to_graph(input: list[str]) -> Graph:
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res = {}
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for line in input:
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assert line.startswith("Valve ") # Sanity check
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name = line.split()[1]
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flow = line.split("=")[1].split(";")[0]
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neighbours = line.split(";")[1].replace(", ", " ").split()[4:]
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res[name] = Valve(int(flow), set(neighbours))
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return res
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def useful_valves(g: Graph) -> set[str]:
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return {k for k, v in g.items() if v.flow > 0}
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def floyd_warshall(g: Graph) -> DistanceMatrix:
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points = list(g.keys())
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res: DistanceMatrix = defaultdict(dict)
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for p in points:
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for n in g[p].neighbours:
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res[p][n] = 1
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for p in points:
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for i in points:
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for j in points:
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if (ip := res[i].get(p)) is None:
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continue
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if (pj := res[p].get(j)) is None:
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continue
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dist = ip + pj
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if (ij := res[i].get(j)) is not None:
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dist = min(dist, ij)
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res[i][j] = dist
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return res
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def prune_distances(dist: DistanceMatrix, of_interest: set[str]) -> DistanceMatrix:
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# Only keep non-zero valves for our visits
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pruned = {
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i: {j: dist for j, dist in line.items() if j in of_interest}
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for i, line in dist.items()
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if i in of_interest
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}
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# Explicitly add the starting room, in case it was pruned
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pruned[START_ROOM] = {
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n: dist for n, dist in dist[START_ROOM].items() if n in of_interest
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}
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return pruned
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def max_flow(g: Graph, dist: DistanceMatrix) -> int:
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def pressure_per_minute(opened_valves: frozenset[str]) -> int:
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return sum(g[valve].flow for valve in opened_valves)
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@functools.cache
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def helper(
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start: str, time: int, opened_valves: frozenset[str]
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) -> tuple[int, frozenset[str]]:
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assert time >= 0 # Sanity check
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if time == 0:
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return 0, opened_valves
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pressure = pressure_per_minute(opened_valves)
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# Base-case, don't do anything
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best = pressure * time, opened_valves
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# Try to open the current valve if not done already
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if start not in opened_valves:
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score, valves = helper(start, time - 1, opened_valves | {start})
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score += pressure
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best = max(best, (score, valves))
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# Try to go to each neighbour
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for n, d in dist[start].items():
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if d >= time:
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continue
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score, valves = helper(n, time - d, opened_valves)
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score += pressure * d
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best = max(best, (score, valves))
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return best
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opened_valves = set()
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# If starting room has no flow, consider it open to reduce search space
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if g[START_ROOM].flow == 0:
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opened_valves.add(START_ROOM)
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score, valves = helper(START_ROOM, 26, frozenset(opened_valves))
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elephant_score, _ = helper(START_ROOM, 26, valves)
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elephant_score -= pressure_per_minute(valves) * 26 # Don't double count
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return score + elephant_score
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graph = to_graph(input)
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dist = prune_distances(floyd_warshall(graph), useful_valves(graph))
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return max_flow(graph, dist)
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def main() -> None:
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input = sys.stdin.read().splitlines()
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print(solve(input))
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if __name__ == "__main__":
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main()
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