106 lines
2.6 KiB
Python
106 lines
2.6 KiB
Python
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# -*- encoding: utf-8 -*-
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import itertools
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import re
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import sys
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from docplex.mp.model import Model
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lines = sys.stdin.read().splitlines()
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pipes: dict[str, tuple[int, list[str]]] = {}
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for line in lines:
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r = re.match(
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R"Valve ([A-Z]+) has flow rate=([0-9]+); tunnels? leads? to valves? (.+)",
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line,
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).groups()
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pipes[r[0]] = (int(r[1]), r[2].split(", "))
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start_pipe = "AA"
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max_time = 30
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#
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max_time = 26
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ee = [0, 1]
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m = Model()
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present_at = m.binary_var_dict(
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(e, t, pipe) for e, t, pipe in itertools.product(ee, range(max_time), pipes)
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)
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open_at = m.binary_var_dict(
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(e, t, pipe) for e, t, pipe in itertools.product(ee, range(max_time), pipes)
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)
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for e in ee:
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m.add_constraint(present_at[e, 0, start_pipe] == 1)
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for e, pipe in itertools.product(ee, pipes):
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m.add_constraint(open_at[e, 0, pipe] == 0)
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for e, t in itertools.product(ee, range(max_time)):
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m.add_constraint(m.sum(present_at[e, t, pipe] for pipe in pipes) == 1)
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for e, t, pipe in itertools.product(ee, range(1, max_time), pipes):
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m.add_constraint(
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present_at[e, t, pipe]
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<= present_at[e, t - 1, pipe]
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+ m.sum(present_at[e, t - 1, pipe2] for pipe2 in pipes[pipe][1])
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)
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for pipe2 in pipes:
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if pipe2 != pipe:
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m.add_constraint(present_at[e, t, pipe] <= 1 - open_at[e, t - 1, pipe2])
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for e, t, pipe in itertools.product(ee, range(1, max_time), pipes):
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m.add_constraint(open_at[e, t, pipe] <= present_at[e, t, pipe])
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# keeps flowing
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flowing_at = m.binary_var_dict(
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(t, pipe) for t, pipe in itertools.product(range(max_time), pipes)
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)
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for t, pipe in itertools.product(range(max_time), pipes):
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m.add_constraint(
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flowing_at[t, pipe]
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== m.sum(open_at[e, t2, pipe] for e, t2 in itertools.product(ee, range(0, t)))
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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] * pipes[pipe][0]
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for t, pipe in itertools.product(range(max_time), 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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# present = {
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# e: [pipe for pipe in pipes if s.get_value(present_at[e, t, pipe]) > 1e-6]
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# for e in ee
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# }
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# opent = {
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# e: [pipe for pipe in pipes if s.get_value(open_at[e, t, pipe]) > 1e-6]
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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 pipes
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# if any(s.get_value(flowing_at[e, t, pipe]) > 1e-6 for e in ee)
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# ]
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# p = [present[e][0] 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}, at={p}, open={o}, flowing={flowing}")
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