"""Independent examples, exhaustive small cases, and deterministic differential checks.""" from copy import deepcopy from itertools import combinations, product from math import comb, lcm import random import unittest from practice.math_lab import ( EXAMPLE, MOD, badge_summary, booth_area2, build_report, choose_sessions, delivery_capacity, demand_report, equipment_budget, packing_unit, registration_code, shortest_busy_window, skills_report, synchronized_launch, team_count, ) class MathLabTests(unittest.TestCase): def test_complete_worked_example(self): report = build_report(EXAMPLE) self.assertEqual(report["badge"], {"digits": 4, "digit_sum": 7, "even": True}) self.assertEqual(report["packing_unit"], 2) # 1204**4 = 2_101_386_547_456; reduce by 1_000_000_007. self.assertEqual(report["registration_code"], 386532749) self.assertEqual(report["team_count_mod"], 6) self.assertEqual(report["skills"], {"available_mask": 7, "missing_mask": 0, "ready": True}) self.assertEqual(report["demand"], {"daily": [2, 6, 4, 6], "total": 18, "range_totals": [8, 16]}) self.assertEqual(report["shortest_busy_window"], 2) self.assertEqual(report["delivery_capacity"], 10) self.assertEqual(report["session_indices"], [0, 2, 3]) self.assertEqual(report["booth_area2"], 24) self.assertEqual(report["launch_time"], 22) self.assertEqual(report["equipment"]["spent"], 11) self.assertEqual(report["equipment"]["remaining"], 0) self.assertEqual(sum(EXAMPLE["equipment_costs"][i] for i in report["equipment"]["indices"]), 11) self.assertTrue(report["can_dispatch"]) def test_badges_zeroes_and_large_decimal(self): self.assertEqual(badge_summary("0000"), {"digits": 4, "digit_sum": 0, "even": True}) self.assertEqual(badge_summary("007"), {"digits": 3, "digit_sum": 7, "even": False}) identifier = "1234567890" * 100 self.assertEqual(registration_code(identifier, 19), pow(int(identifier), 19, MOD)) self.assertEqual(registration_code("000", 2), 0) def test_counts_and_masks(self): for n in range(41): for k in range(n + 1): self.assertEqual(team_count(n, k), comb(n, k) % MOD) self.assertEqual(team_count(2000, 1000), comb(2000, 1000) % MOD) self.assertEqual(packing_unit([12, 18, 30]), 6) self.assertEqual(packing_unit([1]), 1) self.assertEqual(skills_report([1, 2], 7), {"available_mask": 3, "missing_mask": 4, "ready": False}) self.assertTrue(skills_report([0], 0)["ready"]) def test_difference_and_prefix_against_direct_updates(self): rng = random.Random(105) for _ in range(120): n = rng.randint(1, 12) base = [rng.randint(1, 9) for _ in range(n)] original = list(base) expected = list(base) updates = [] for _ in range(rng.randint(0, 12)): left = rng.randrange(n) right = rng.randint(left + 1, n) extra = rng.randint(0, 6) updates.append([left, right, extra]) for i in range(left, right): expected[i] += extra queries = [(left, right) for left in range(n) for right in range(left + 1, n + 1)] actual = demand_report(base, updates, queries) self.assertEqual(actual["daily"], expected) self.assertEqual(actual["range_totals"], [sum(expected[l:r]) for l, r in queries]) self.assertEqual(actual["total"], sum(expected)) self.assertEqual(base, original) def test_windows_against_all_subarrays(self): for n in range(1, 5): for values in product(range(1, 4), repeat=n): for target in range(1, sum(values) + 2): lengths = [r - l for l in range(n) for r in range(l + 1, n + 1) if sum(values[l:r]) >= target] expected = min(lengths, default=0) self.assertEqual(shortest_busy_window(values, target), expected) def test_capacity_against_all_partitions(self): rng = random.Random(107) for _ in range(120): n = rng.randint(1, 8) values = [rng.randint(1, 9) for _ in range(n)] days = rng.randint(1, n) candidates = [] for cut_count in range(days): for cuts in combinations(range(1, n), cut_count): boundaries = (0,) + cuts + (n,) candidates.append(max(sum(values[a:b]) for a, b in zip(boundaries, boundaries[1:]))) self.assertEqual(delivery_capacity(values, days), min(candidates)) def test_greedy_sessions_against_all_subsets(self): rng = random.Random(108) for _ in range(100): sessions = [] for _ in range(rng.randint(0, 8)): start = rng.randrange(10) sessions.append((start, rng.randint(start + 1, 11))) best = 0 for mask in range(1 << len(sessions)): subset = sorted(sessions[i] for i in range(len(sessions)) if mask & (1 << i)) if all(a[1] <= b[0] for a, b in zip(subset, subset[1:])): best = max(best, len(subset)) actual = choose_sessions(sessions) self.assertEqual(len(actual), best) self.assertEqual(len(actual), len(set(actual))) self.assertTrue(all(sessions[a][1] <= sessions[b][0] for a, b in zip(actual, actual[1:]))) def test_geometry_known_shapes_and_degeneracy(self): cases = [([], 0), ([(1, 2)], 0), ([(0, 0), (1, 1), (2, 2)], 0), ([(0, 0), (1, 0), (0, 1)], 1), ([(0, 2), (2, 0), (0, -2), (-2, 0), (0, 0)], 16), ([(0, 0), (4, 0), (4, 3), (0, 3), (2, 1), (0, 0)], 24)] for points, expected in cases: self.assertEqual(booth_area2(points), expected) self.assertEqual(booth_area2(list(reversed(points))), expected) self.assertEqual(booth_area2([(x - 50, y + 19) for x, y in points]), expected) def test_generalized_crt_against_exhaustive_search(self): for modulus1 in range(1, 8): for modulus2 in range(1, 8): cycle = lcm(modulus1, modulus2) for remainder1 in range(modulus1): for remainder2 in range(modulus2): for earliest in (0, 11, 100): expected = next((t for t in range(earliest, earliest + cycle) if t % modulus1 == remainder1 and t % modulus2 == remainder2), None) actual = synchronized_launch([(remainder1, modulus1), (remainder2, modulus2)], earliest) self.assertEqual(actual, expected) self.assertEqual(synchronized_launch([], 19), 19) self.assertEqual(synchronized_launch([(2, 3), (3, 5), (2, 7)], 24), 128) def test_equipment_against_exhaustive_subsets(self): rng = random.Random(111) for _ in range(120): costs = [rng.randint(0, 20) for _ in range(rng.randint(0, 12))] budget = rng.randint(0, 50) totals = [sum(costs[i] for i in range(len(costs)) if mask & (1 << i)) for mask in range(1 << len(costs))] expected = max(total for total in totals if total <= budget) result = equipment_budget(costs, budget) self.assertEqual(result["spent"], expected) self.assertEqual(result["remaining"], budget - expected) self.assertEqual(len(result["indices"]), len(set(result["indices"]))) self.assertEqual(sum(costs[i] for i in result["indices"]), expected) self.assertEqual(equipment_budget([1] * 32, 17)["spent"], 17) def test_dispatch_requires_all_three_conditions_and_preserves_input(self): data = deepcopy(EXAMPLE) snapshot = deepcopy(data) build_report(data) self.assertEqual(data, snapshot) for key, value in (("required_mask", 15), ("booths", [[0, 0]]), ("gate_cycles", [[0, 2], [1, 2]])): altered = deepcopy(data) altered[key] = value self.assertFalse(build_report(altered)["can_dispatch"]) def test_invalid_input_contract(self): cases = [("batch_id", ""), ("batch_id", "১২"), ("batch_id", "1" * 1001), ("base_demand", []), ("base_demand", [0]), ("base_demand", [True]), ("updates", [[1, 5, 2]]), ("updates", [[1, 2, -1]]), ("queries", [[2, 2]]), ("queries", [[-1, 1]]), ("volunteer_masks", []), ("volunteer_masks", [1 << 20]), ("required_mask", -1), ("team_size", 5), ("team_size", -1), ("window_target", 0), ("shipping_days", 0), ("shipping_days", 5), ("sessions", [[4, 4]]), ("booths", [[0, "x"]]), ("gate_cycles", [[0, 0]]), ("gate_cycles", [[3, 3]]), ("earliest_launch", -1), ("equipment_costs", [1] * 33), ("equipment_costs", [-1]), ("budget", -1)] for key, value in cases: data = deepcopy(EXAMPLE) data[key] = value with self.subTest(key=key, value=value), self.assertRaises(ValueError): build_report(data) for data in (None, {}, {**EXAMPLE, "typo": 1}): with self.assertRaises(ValueError): build_report(data) if __name__ == "__main__": unittest.main()