def tsp1(nodes, dist):
"""
巡回セールスマン問題
入力
nodes: 点(dist未指定時は、座標)のリスト
dist: (i,j)をキー、距離を値とした辞書
出力
距離と点番号リスト
"""
from more_itertools import iterate, take
n = len(nodes)
df = pd.DataFrame(
[(i, j, dist[i, j]) for i in range(n) for j in range(n) if i != j],
columns=["NodeI", "NodeJ", "Dist"],
)
m = LpProblem()
df["VarIJ"] = addbinvars(len(df))
df["VarJI"] = df.sort_values(["NodeJ", "NodeI"]).VarIJ.values
u = [0] + addvars(n - 1)
m += lpDot(df.Dist, df.VarIJ)
for _, v in df.groupby("NodeI"):
m += lpSum(v.VarIJ) == 1 # 出次数制約
m += lpSum(v.VarJI) == 1 # 入次数制約
for i, j, _, vij, vji in df.query("NodeI!=0 & NodeJ!=0").itertuples(False):
m += u[i] + 1 - (n - 1) * (1 - vij) + (n - 3) * vji <= u[
j] # 持ち上げポテンシャル制約(MTZ)
for _, j, _, v0j, vj0 in df.query("NodeI==0").itertuples(False):
m += 1 + (1 - v0j) + (n - 3) * vj0 <= u[j] # 持ち上げ下界制約
for i, _, _, vi0, v0i in df.query("NodeJ==0").itertuples(False):
m += u[i] <= (n - 1) - (1 - vi0) - (n - 3) * v0i # 持ち上げ上界制約
m.solve()
df["ValIJ"] = df.VarIJ.apply(value)
dc = df[df.ValIJ > 0.5].set_index("NodeI").NodeJ.to_dict()
return value(m.objective), list(take(n, iterate(lambda k: dc[k], 0)))
def evolve(state, D):
offset = [o for o in product([-1, 0, +1], repeat=D) if any(o)]
counts = lambda state: (
(p, sum(tuple(a + b for (a, b) in zip(p, q)) in state for q in offset))
for p in product(*[itercoord(state, d) for d in range(D)]))
return iterate(
lambda state: {
p
for (p, c) in counts(state) if (c in {2, 3}
if p in state else c == 3)
}, state)
def part_1(data):
r'''
>>> part_1("""\
... .#.
... ..#
... ###""")
112
'''
grid = GridPart1.parse(data)
final = mit.nth(mit.iterate(GridPart1.next, grid), 6)
return len(final)
def part_2(data):
r'''
>>> part_2("""\
... .#.
... ..#
... ###""")
848
'''
grid = GridPart2.parse(data)
final = mit.nth(mit.iterate(GridPart2.next, grid), 6)
return len(final)
def tsp(nodes, dist=None):
"""
巡回セールスマン問題
入力
nodes: 点(dist未指定時は、座標)のリスト
dist: (i,j)をキー、距離を値とした辞書
出力
距離と点番号リスト
"""
import numpy as np
import pandas as pd
from more_itertools import iterate, take
from pulp import LpProblem, LpVariable, LpBinary, lpDot, lpSum, value
n = len(nodes)
if not dist:
dist = {(i, j): np.linalg.norm(np.subtract(nodes[i], nodes[j]))
for i in range(n) for j in range(i + 1, n)}
dist.update({(j, i): d for (i, j), d in dist.items()})
a = pd.DataFrame(
[(i, j, dist[i, j]) for i in range(n) for j in range(n) if i != j],
columns=["NodeI", "NodeJ", "Dist"],
)
m = LpProblem()
a["VarIJ"] = [LpVariable("x%d" % i, cat=LpBinary) for i in a.index]
a["VarJI"] = a.sort_values(["NodeJ", "NodeI"]).VarIJ.values
u = [0] + [LpVariable("y%d" % i, lowBound=0) for i in range(n - 1)]
m += lpDot(a.Dist, a.VarIJ)
for _, v in a.groupby("NodeI"):
m += lpSum(v.VarIJ) == 1 # 出次数制約
m += lpSum(v.VarJI) == 1 # 入次数制約
for _, (i, j, _, vij, vji) in a.query("NodeI!=0 & NodeJ!=0").iterrows():
m += u[i] + 1 - (n - 1) * (1 - vij) + (n - 3) * vji <= u[
j] # 持ち上げポテンシャル制約(MTZ)
for _, (_, j, _, v0j, vj0) in a.query("NodeI==0").iterrows():
m += 1 + (1 - v0j) + (n - 3) * vj0 <= u[j] # 持ち上げ下界制約
for _, (i, _, _, vi0, v0i) in a.query("NodeJ==0").iterrows():
m += u[i] <= (n - 1) - (1 - vi0) - (n - 3) * v0i # 持ち上げ上界制約
m.solve()
a["ValIJ"] = a.VarIJ.apply(value)
dc = dict(a[a.ValIJ > 0.5][["NodeI", "NodeJ"]].values)
return value(m.objective), list(take(n, iterate(lambda k: dc[k], 0)))
def part_two():
input_lines = get_input()
coordinates = create_coordinates(input_lines, 4)
cycles = iterate(generate_cycle, coordinates)
return len(nth(cycles, 6))
def _walk_parents(command):
"""Walks up a command's parent chain."""
return iter(iterate(operator.attrgetter('parent'), command).__next__, None)
def generate_state(agent, environment):
"""Run a single planning interval for the given number of steps."""
initial_step_data = StepData(environment.initial_state(), None, 0, agent) # Initial state with step_id 0
return iterate(lambda step_data: run_step(step_data, environment), initial_step_data)
def generate_state(agent, environment):
"""Run a single planning interval for the given number of steps."""
initial_step_data = StepData(environment.initial_state(), None, 0,
agent) # Initial state with step_id 0
return iterate(lambda step_data: run_step(step_data, environment),
initial_step_data)
def tsp(nodes, list_of_homes, dist=None):
"""
巡回セールスマン問題
入力
nodes: 点(dist未指定時は、座標)のリスト
dist: (i,j)をキー、距離を値とした辞書
出力
距離と点番号リスト
"""
n = len(nodes)
if not dist:
dist = {(i, j): np.linalg.norm(np.subtract(nodes[i], nodes[j]))
for i in range(n) for j in range(i + 1, n)}
dist.update({(j, i): d for (i, j), d in dist.items()})
# data farme containing distances from node i to node j
print(dist)
a = pd.DataFrame([(nodes[i], i, j, dist[(i, j)]) for i in range(n)
for j in range(n) if i != j],
columns=['Name', 'NodeI', 'NodeJ', 'Dist'])
m = LpProblem()
# creates x_ij for every edge in the graph
a['VarIJ'] = [LpVariable('x%d' % i, cat=LpBinary) for i in a.index]
a['VarJI'] = a.sort_values(['NodeJ', 'NodeI']).VarIJ.values
#
u = [0] + [LpVariable('y%d' % i, lowBound=0) for i in range(n - 1)]
print(a)
# gives the total distance,
m += lpDot(a.Dist, a.VarIJ)
print(list_of_homes)
for _, v in a.groupby('NodeI'):
print(v)
print(v.iloc[0, :].NodeI)
print('*****')
if v.iloc[0, :].Name in list_of_homes:
print('*&&&&', v.iloc[0, :].Name)
m += lpSum(
v.VarIJ) == 1 # constraint for one edge exiting each vertex
m += lpSum(
v.VarJI) == 1 # constraint for one edge entering each vertex
for _, (name, i, j, _, vij,
vji) in a.query('NodeI!=0 & NodeJ!=0').iterrows():
m += u[i] + 1 - (n - 1) * (1 - vij) + (n - 3) * vji <= u[
j] # 持ち上げポテンシャル制約(MTZ)
for _, (name, _, j, _, v0j, vj0) in a.query('NodeI==0').iterrows():
m += 1 + (1 - v0j) + (n - 3) * vj0 <= u[j] # lower bound constraints
for _, (name, i, _, _, vi0, v0i) in a.query('NodeJ==0').iterrows():
m += u[i] <= (n - 1) - (1 -
vi0) - (n - 3) * v0i # upper bound constraints
m.solve()
a['ValIJ'] = a.VarIJ.apply(value)
dc = dict(a[a.ValIJ > 0.5][['NodeI', 'NodeJ']].values)
return value(m.objective), list(take(n, iterate(lambda k: dc[k], 0)))