yes fuking shit

tests/test_routing.py

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+"""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）。
+
+要点：
+- Held-Karp 精确开放路径必须**真的**最优（与全排列暴力对拍）；
+- 启发式（NN + 2-opt / Or-opt）必须是可接受的上界，且不劣于 NN；
+- 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）；
+- 路由度量口径可复算：actual == offline 时 gap 为 0，且 gap 不越界。
+"""
+
+import itertools
+import math
+import random
+import unittest
+
+from mcm26b.routing import (EXACT_LIMIT, held_karp_open, improve_open_path,
+                            mst_weight, nearest_neighbor_order,
+                            optimal_open_path, or_opt_open, path_length,
+                            route_metrics, two_opt_open)
+
+
+def _random_points(count: int, seed: int, radius: float = 1500.0):
+    rng = random.Random(seed)
+    return [(rng.uniform(-radius, radius), rng.uniform(-radius, radius))
+            for _ in range(count)]
+
+
+class HeldKarpTests(unittest.TestCase):
+    def test_matches_brute_force_on_small_instances(self):
+        for seed in range(6):
+            points = _random_points(6, seed)
+            order = held_karp_open(points)
+            best = min(path_length(list(perm))
+                       for perm in itertools.permutations(points))
+            self.assertAlmostEqual(path_length(order), best, places=6,
+                                   msg=f"seed={seed}")
+
+    def test_returns_all_points_once(self):
+        points = _random_points(9, 42)
+        order = held_karp_open(points)
+        self.assertEqual(sorted(order), sorted(points))
+
+    def test_single_and_empty(self):
+        self.assertEqual(held_karp_open([]), [])
+        point = [(3.0, 4.0)]
+        self.assertEqual(held_karp_open(point), point)
+
+
+class HeuristicTests(unittest.TestCase):
+    def test_two_opt_and_or_opt_never_worse_than_nn(self):
+        for seed in range(5):
+            points = _random_points(30, seed)
+            base = path_length(nearest_neighbor_order(points))
+            self.assertLessEqual(path_length(two_opt_open(
+                nearest_neighbor_order(points))), base + 1e-9)
+            self.assertLessEqual(path_length(improve_open_path(points)),
+                                 base + 1e-9)
+
+    def test_optimal_open_path_beats_heuristics_small(self):
+        points = _random_points(10, 7)
+        optimal = path_length(optimal_open_path(points))
+        self.assertLessEqual(optimal,
+                             path_length(improve_open_path(points)) + 1e-9)
+
+    def test_or_opt_accepts_only_improvements(self):
+        points = _random_points(20, 3)
+        order = nearest_neighbor_order(points)
+        improved = or_opt_open(order)
+        self.assertLessEqual(path_length(improved), path_length(order) + 1e-9)
+
+
+class LowerBoundTests(unittest.TestCase):
+    def test_mst_is_a_lower_bound(self):
+        for seed in range(8):
+            points = _random_points(24, seed)
+            optimum = path_length(optimal_open_path(points))
+            self.assertLessEqual(mst_weight(points), optimum + 1e-6,
+                                 msg=f"seed={seed}")
+
+    def test_mst_without_start(self):
+        points = _random_points(12, 1)
+        self.assertLessEqual(mst_weight(points, start=None),
+                             path_length(optimal_open_path(points)) + 1e-6)
+
+
+class RouteMetricsTests(unittest.TestCase):
+    def test_gap_zero_when_actual_matches_offline(self):
+        points = _random_points(8, 5)
+        offline = path_length(optimal_open_path(points))
+        metrics = route_metrics(points, offline)
+        self.assertAlmostEqual(metrics["route_gap_vs_offline"], 0.0, places=6)
+        self.assertEqual(metrics["distinct_service_points"], 8)
+
+    def test_dedupes_points(self):
+        points = [(1.0, 1.0), (1.0, 1.0), (2.0, 2.0)]
+        metrics = route_metrics(points, 10.0)
+        self.assertEqual(metrics["distinct_service_points"], 2)
+
+    def test_empty_is_safe(self):
+        metrics = route_metrics([], 0.0)
+        self.assertEqual(metrics["distinct_service_points"], 0)
+        self.assertEqual(metrics["route_gap_vs_offline"], 0.0)
+
+
+if __name__ == "__main__":
+    unittest.main()