106 lines
4.1 KiB
Python
106 lines
4.1 KiB
Python
"""图论 / DP 工具箱验收（docs/第三四问图论与动态规划优化方案.md §3.2、§3.4）。
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要点：
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- Held-Karp 精确开放路径必须**真的**最优（与全排列暴力对拍）；
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- 启发式（NN + 2-opt / Or-opt）必须是可接受的上界，且不劣于 NN；
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- MST 权重必须是最优开放路径的合法下界（在线后悔值审计依赖它）；
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- 路由度量口径可复算：actual == offline 时 gap 为 0，且 gap 不越界。
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"""
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import itertools
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import math
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import random
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import unittest
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from mcm26b.routing import (EXACT_LIMIT, held_karp_open, improve_open_path,
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mst_weight, nearest_neighbor_order,
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optimal_open_path, or_opt_open, path_length,
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route_metrics, two_opt_open)
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def _random_points(count: int, seed: int, radius: float = 1500.0):
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rng = random.Random(seed)
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return [(rng.uniform(-radius, radius), rng.uniform(-radius, radius))
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for _ in range(count)]
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class HeldKarpTests(unittest.TestCase):
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def test_matches_brute_force_on_small_instances(self):
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for seed in range(6):
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points = _random_points(6, seed)
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order = held_karp_open(points)
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best = min(path_length(list(perm))
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for perm in itertools.permutations(points))
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self.assertAlmostEqual(path_length(order), best, places=6,
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msg=f"seed={seed}")
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def test_returns_all_points_once(self):
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points = _random_points(9, 42)
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order = held_karp_open(points)
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self.assertEqual(sorted(order), sorted(points))
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def test_single_and_empty(self):
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self.assertEqual(held_karp_open([]), [])
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point = [(3.0, 4.0)]
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self.assertEqual(held_karp_open(point), point)
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class HeuristicTests(unittest.TestCase):
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def test_two_opt_and_or_opt_never_worse_than_nn(self):
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for seed in range(5):
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points = _random_points(30, seed)
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base = path_length(nearest_neighbor_order(points))
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self.assertLessEqual(path_length(two_opt_open(
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nearest_neighbor_order(points))), base + 1e-9)
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self.assertLessEqual(path_length(improve_open_path(points)),
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base + 1e-9)
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def test_optimal_open_path_beats_heuristics_small(self):
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points = _random_points(10, 7)
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optimal = path_length(optimal_open_path(points))
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self.assertLessEqual(optimal,
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path_length(improve_open_path(points)) + 1e-9)
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def test_or_opt_accepts_only_improvements(self):
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points = _random_points(20, 3)
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order = nearest_neighbor_order(points)
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improved = or_opt_open(order)
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self.assertLessEqual(path_length(improved), path_length(order) + 1e-9)
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class LowerBoundTests(unittest.TestCase):
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def test_mst_is_a_lower_bound(self):
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for seed in range(8):
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points = _random_points(24, seed)
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optimum = path_length(optimal_open_path(points))
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self.assertLessEqual(mst_weight(points), optimum + 1e-6,
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msg=f"seed={seed}")
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def test_mst_without_start(self):
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points = _random_points(12, 1)
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self.assertLessEqual(mst_weight(points, start=None),
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path_length(optimal_open_path(points)) + 1e-6)
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class RouteMetricsTests(unittest.TestCase):
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def test_gap_zero_when_actual_matches_offline(self):
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points = _random_points(8, 5)
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offline = path_length(optimal_open_path(points))
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metrics = route_metrics(points, offline)
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self.assertAlmostEqual(metrics["route_gap_vs_offline"], 0.0, places=6)
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self.assertEqual(metrics["distinct_service_points"], 8)
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def test_dedupes_points(self):
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points = [(1.0, 1.0), (1.0, 1.0), (2.0, 2.0)]
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metrics = route_metrics(points, 10.0)
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self.assertEqual(metrics["distinct_service_points"], 2)
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def test_empty_is_safe(self):
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metrics = route_metrics([], 0.0)
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self.assertEqual(metrics["distinct_service_points"], 0)
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self.assertEqual(metrics["route_gap_vs_offline"], 0.0)
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if __name__ == "__main__":
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unittest.main()
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