Better day 16.
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Mikaël Capelle
parent
15b987a590
commit
100df02a09
244
2022/day16.py
244
2022/day16.py
@ -7,10 +7,9 @@ import itertools
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import re
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import sys
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from collections import defaultdict
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from typing import NamedTuple
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from typing import FrozenSet, NamedTuple
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from docplex.mp.model import Model
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from docplex.mp.vartype import BinaryVarType
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from tqdm import tqdm
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class Pipe(NamedTuple):
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@ -55,6 +54,75 @@ def breadth_first_search(pipes: dict[str, Pipe], pipe_1: Pipe, pipe_2: Pipe) ->
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return -1
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def update_with_better(
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node_at_times: dict[FrozenSet[Pipe], int], flow: int, flowing: FrozenSet[Pipe]
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) -> None:
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node_at_times[flowing] = max(node_at_times[flowing], flow)
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def part_1(
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start_pipe: Pipe,
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max_time: int,
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distances: dict[tuple[Pipe, Pipe], int],
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relevant_pipes: FrozenSet[Pipe],
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):
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node_at_times: dict[int, dict[Pipe, dict[FrozenSet[Pipe], int]]] = defaultdict(
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lambda: defaultdict(lambda: defaultdict(lambda: 0))
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)
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node_at_times[0] = {start_pipe: {frozenset(): 0}}
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for time in range(max_time):
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for c_pipe, nodes in node_at_times[time].items():
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for flowing, flow in nodes.items():
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for target in relevant_pipes:
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distance = distances[c_pipe, target] + 1
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if time + distance >= max_time or target in flowing:
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continue
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update_with_better(
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node_at_times[time + distance][target],
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flow + sum(pipe.flow for pipe in flowing) * distance,
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flowing | {target},
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)
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update_with_better(
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node_at_times[max_time][c_pipe],
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flow + sum(pipe.flow for pipe in flowing) * (max_time - time),
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flowing,
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)
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return max(
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flow
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for nodes_of_pipe in node_at_times[max_time].values()
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for flow in nodes_of_pipe.values()
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)
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def part_2(
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start_pipe: Pipe,
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max_time: int,
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distances: dict[tuple[Pipe, Pipe], int],
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relevant_pipes: FrozenSet[Pipe],
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):
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def compute(pipes_for_me: FrozenSet[Pipe]) -> int:
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return part_1(start_pipe, max_time, distances, pipes_for_me) + part_1(
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start_pipe, max_time, distances, relevant_pipes - pipes_for_me
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)
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combs = [
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frozenset(relevant_pipes_1)
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for r in range(2, len(relevant_pipes) // 2 + 1)
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for relevant_pipes_1 in itertools.combinations(relevant_pipes, r)
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]
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return max(compute(comb) for comb in tqdm(combs))
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# === MAIN ===
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lines = sys.stdin.read().splitlines()
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@ -77,171 +145,11 @@ for pipe_1 in pipes.values():
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distances[pipe_1, pipe_2] = breadth_first_search(pipes, pipe_1, pipe_2)
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# valves with flow
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relevant_pipes = [pipe for pipe in pipes.values() if pipe.flow > 0]
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relevant_pipes = frozenset(pipe for pipe in pipes.values() if pipe.flow > 0)
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# nodes: list[tuple[Pipe, int, int, list[Pipe]]] = [(start_pipe, 0, 0, [])]
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# best_flow: int = 0
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# 1651, 1653
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print(part_1(pipes["AA"], 30, distances, relevant_pipes))
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# while nodes:
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# current, time, flow, flowing = nodes.pop(0)
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# if time == max_time:
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# if flow > best_flow:
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# best_flow = flow
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# continue
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# next_nodes: list[tuple[Pipe, int, int, list[Pipe]]] = []
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# for target in relevant_pipes:
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# if target is current or target in flowing:
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# continue
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# distance = distances[current, target] + 1
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# if time + distance >= max_time:
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# continue
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# next_nodes.append(
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# (
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# target,
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# time + distance,
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# flow + distance * sum(pipe.flow for pipe in flowing) + target.flow,
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# flowing + [target],
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# )
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# )
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# # print(time, current, flow, next_nodes)
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# if not next_nodes:
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# next_nodes.append(
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# (
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# current,
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# max_time,
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# flow + sum(pipe.flow for pipe in flowing) * (max_time - time - 1),
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# flowing,
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# )
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# )
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# nodes.extend(next_nodes)
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# # if time >= 4:
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# # break
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# print(best_flow)
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# nodes = [best]
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# while nodes[-1].parent is not None:
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# nodes.append(nodes[-1].parent)
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# nodes = list(reversed(nodes))
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# for node in nodes:
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# print(node.time, node.valve, node.flow, node.flowing)
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#
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start_pipe = pipes["AA"]
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max_time = 30
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ee = [0]
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# max_time = 26
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# ee = [0, 1]
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m = Model()
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var_out: dict[Pipe, dict[Pipe, BinaryVarType]] = {
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pipe: m.binary_var_dict(relevant_pipes) for pipe in relevant_pipes + [start_pipe]
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}
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var_in: dict[Pipe, dict[Pipe, BinaryVarType]] = {pipe: {} for pipe in relevant_pipes}
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for p1 in var_out:
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for p2 in var_out[p1]:
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var_in[p2][p1] = var_out[p1][p2]
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open_at: dict[tuple[int, Pipe], BinaryVarType] = m.continuous_var_dict(
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(
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(t, pipe)
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for t, pipe in itertools.product(range(max_time), [start_pipe] + relevant_pipes)
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),
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lb=0,
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ub=1,
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)
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for time, pipe in itertools.product(range(max_time), relevant_pipes):
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m.add_constraint(open_at[time, pipe] <= m.sum())
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for e in ee:
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m.add_constraint(open_at[e, 0, start_pipe] == 1)
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for e, pipe in itertools.product(ee, relevant_pipes):
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m.add_constraint(open_at[e, 0, pipe] == 0)
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for e, t, p1 in itertools.product(ee, range(max_time), relevant_pipes):
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from_time_and_pipe = [
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(p2, t - distances[p2, p1] - 1)
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for p2 in relevant_pipes + [start_pipe]
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if t - distances[p2, p1] - 1 >= 0 and p2 is not p1
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]
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if from_time_and_pipe:
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m.add_constraint(
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open_at[e, t, p1]
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<= m.sum(open_at[e, t2, p2] for p2, t2 in from_time_and_pipe)
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)
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else:
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m.add_constraint(open_at[e, t, p1] == 0)
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for pipe in relevant_pipes + [start_pipe]:
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m.add_constraint(
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m.sum(open_at[e, t, pipe] for e, t in itertools.product(ee, range(max_time)))
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<= 1
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)
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for e, t in itertools.product(ee, range(max_time)):
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m.add_constraint(
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m.sum(open_at[e, t, pipe] for pipe in relevant_pipes + [start_pipe]) <= 1
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)
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# keeps flowing
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flowing_at = {
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(t, pipe): m.sum(
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open_at[e, t2, pipe] for e, t2 in itertools.product(ee, range(0, t))
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)
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for t, pipe in itertools.product(range(max_time), relevant_pipes)
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}
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# objective
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m.set_objective(
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"max",
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m.sum(
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flowing_at[t, pipe] * pipe.flow
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for t, pipe in itertools.product(range(max_time), relevant_pipes)
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),
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)
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m.log_output = True
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s = m.solve()
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print(s.get_objective_value())
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for t in range(max_time):
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opent = {
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e: [
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pipe
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for pipe in relevant_pipes + [start_pipe]
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if s.get_value(open_at[e, t, pipe]) > 1e-8
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]
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for e in ee
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}
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flowing = [
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pipe
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for pipe in relevant_pipes
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if any(s.get_value(flowing_at[t, pipe]) > 1e-8 for e in ee)
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]
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assert all(len(opent[e]) <= 1 for e in ee)
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o = [opent[e][0] if opent[e] else "-" for e in ee]
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print(f"t={t}, open={o}, flowing={flowing}")
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# 1707, 2223
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print(part_2(pipes["AA"], 26, distances, relevant_pipes))
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