FA-94696 / Exam timetabling constraints / Open access

Online exam candidates consume hall seats · case 01

Periods with online exams appear over capacity.

Verified by executionVariant 1 · 8 checks per implementationDownload source bundle ↓JSON ↗

ROOT CAUSE

Online sittings are not excluded from seat counts.

VERIFIED REPAIR

Skip online exams when counting seats.

Unsuccessful approach: Defaulting unknown modes to online drops paper exams missing from the mode table.

Case contract

sits [student, exam, period, access]; cap period -> seats (missing = 0); mode exam -> paper/online (missing = paper). Each distinct (student, exam) uses one seat, two with an access arrangement, and none for online exams. Return [period, used, capacity] for periods over capacity, by period.

Why this case matters

Seat capacity per period is a hard constraint on which periods can take large exams.

1 / The failure

Exit 1

"""Failure Map reference implementation. Python standard library only."""
import json

N = 1
observations = []
def solve(sits, cap, mode):
    seen = set()
    used = {}
    for st, ex, p, acc in sits:
        if (st, ex) in seen:
            continue
        seen.add((st, ex))
        used[p] = used.get(p, 0) + (2 if acc else 1)
    return [[p, used[p], cap.get(p, 0)] for p in sorted(used) if used[p] > cap.get(p, 0)]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('regression: online seats 1', [[['s1', 'A', 0, False], ['s2', 'A', 0, False]], {0: 1}, {'A': 'online'}],
   []),
  ('regression variant: online seats 2',
   [[['s1', 'MATH101', 1, True], ['s1', 'CHEM120', 0, False], ['s5', 'PHYS110', 0, False],
     ['s5', 'CHEM120', 0, False], ['s3', 'PHYS110', 1, False], ['s3', 'MATH101H', 0, False],
     ['s1', 'CHEM120', 1, False], ['s1', 'CHEM120', 0, False], ['s3', 'CHEM120', 2, False],
     ['s3', 'PHYS110', 2, False], ['s3', 'PHYS110', 1, False]],
    {0: 3, 1: 2, 2: 4}, {'MATH101': 'online', 'MATH101H': 'online', 'CHEM120': 'online', 'BIO130': 'paper'}],
   []),
  ('partial repair guard 3',
   [[['s3', 'MATH101', 0, False], ['s3', 'BIO130', 2, False], ['s2', 'MATH101H', 0, False],
     ['s2', 'MATH101H', 2, False], ['s3', 'BIO130', 2, False]],
    {0: 1, 1: 2, 2: 3}, {'MATH101': 'paper', 'PHYS110': 'paper', 'BIO130': 'online'}],
   [[0, 2, 1]]),
  ('boundary control 4', [[['s1', 'A', 0, False], ['s1', 'B', 0, False]], {0: 1}, {}], [[0, 2, 1]]),
  ('boundary control 5', [[['s1', 'A', 0, False], ['s1', 'A', 0, False]], {0: 1}, {'A': 'paper'}], []),
  ('normal control 6',
   [[['s1', 'BIO130', 1, False], ['s2', 'PHYS110', 1, False]], {0: 1, 1: 1, 2: 2},
    {'MATH101H': 'paper', 'PHYS110': 'paper', 'CHEM120': 'online', 'BIO130': 'paper'}],
   [[1, 2, 1]]),
  ('normal control 7',
   [[['s2', 'PHYS110', 0, False], ['s5', 'PHYS110', 2, False], ['s5', 'BIO130', 2, True],
     ['s1', 'MATH101H', 1, False], ['s5', 'BIO130', 2, True]],
    {0: 4, 1: 3, 2: 3},
    {'MATH101': 'paper', 'MATH101H': 'online', 'PHYS110': 'paper', 'CHEM120': 'paper', 'BIO130': 'paper'}],
   []),
  ('normal control 8',
   [[['s3', 'BIO130', 1, False], ['s5', 'PHYS110', 2, False], ['s3', 'MATH101H', 1, False],
     ['s3', 'MATH101H', 0, False], ['s4', 'MATH101H', 1, True], ['s1', 'CHEM120', 2, False],
     ['s3', 'MATH101H', 1, False], ['s1', 'BIO130', 1, False]],
    {0: 3, 1: 4, 2: 1}, {'MATH101': 'paper', 'MATH101H': 'paper', 'PHYS110': 'online', 'CHEM120': 'online'}],
   [[1, 5, 4]])],
 [('regression: online seats 1',
   [[['s4', 'MATH101H', 0, False], ['s5', 'CHEM120', 1, False], ['s5', 'MATH101H', 1, False],
     ['s5', 'MATH101H', 2, False], ['s4', 'MATH101H', 2, False], ['s2', 'CHEM120', 1, False],
     ['s3', 'MATH101', 0, False], ['s2', 'MATH101', 2, False], ['s2', 'BIO130', 1, False],
     ['s2', 'MATH101H', 0, False]],
    {0: 3, 1: 1, 2: 3},
    {'MATH101': 'online', 'MATH101H': 'online', 'PHYS110': 'online', 'CHEM120': 'paper'}],
   [[1, 3, 1]]),
  ('regression variant: online seats 2',
   [[['s1', 'PHYS110', 2, False], ['s4', 'MATH101H', 0, False], ['s1', 'MATH101H', 2, False],
     ['s5', 'MATH101', 1, True], ['s5', 'PHYS110', 2, False], ['s3', 'BIO130', 2, True],
     ['s4', 'MATH101H', 2, False]],
    {1: 2, 2: 1}, {'MATH101': 'paper', 'MATH101H': 'online'}],
   [[2, 4, 1]]),
  ('partial repair guard 3',
   [[['s2', 'MATH101H', 2, True], ['s4', 'MATH101', 0, False], ['s3', 'CHEM120', 0, True],
     ['s1', 'MATH101', 2, False], ['s2', 'PHYS110', 1, True], ['s4', 'BIO130', 0, True],
     ['s3', 'CHEM120', 2, False], ['s4', 'BIO130', 0, True]],
    {0: 2, 1: 3}, {'MATH101': 'paper', 'MATH101H': 'online', 'CHEM120': 'paper'}],
   [[0, 5, 2], [2, 1, 0]]),
  ('boundary control 4', [[['s1', 'A', 0, False], ['s2', 'A', 0, False]], {0: 2}, {'A': 'paper'}], []),
  ('boundary control 5', [[['s1', 'A', 0, False], ['s2', 'A', 0, False]], {0: 1}, {'A': 'online'}], []),
  ('normal control 6',
   [[['s1', 'PHYS110', 2, False], ['s4', 'MATH101', 1, False], ['s4', 'MATH101', 1, False]], {1: 1, 2: 3},
    {'MATH101': 'online', 'MATH101H': 'paper', 'PHYS110': 'paper', 'CHEM120': 'paper', 'BIO130': 'paper'}],
   []),
  ('normal control 7',
   [[['s5', 'BIO130', 0, False], ['s5', 'PHYS110', 1, False], ['s1', 'PHYS110', 0, False],
     ['s5', 'MATH101', 1, False], ['s3', 'MATH101', 2, False]],
    {0: 4, 1: 4, 2: 3}, {'MATH101': 'paper', 'MATH101H': 'online', 'PHYS110': 'paper', 'CHEM120': 'online'}],
   []),
  ('normal control 8',
   [[['s2', 'PHYS110', 1, False], ['s4', 'MATH101', 2, False], ['s5', 'MATH101', 0, True],
     ['s4', 'MATH101', 0, True], ['s1', 'MATH101', 2, True], ['s2', 'MATH101', 0, False],
     ['s2', 'BIO130', 2, True], ['s4', 'BIO130', 2, False], ['s2', 'MATH101H', 2, False],
     ['s3', 'BIO130', 1, False]],
    {0: 1, 1: 2, 2: 1}, {'PHYS110': 'paper', 'CHEM120': 'paper', 'BIO130': 'paper'}],
   [[0, 3, 1], [2, 7, 1]])],
 [('regression: online seats 1',
   [[['s3', 'MATH101H', 2, False], ['s3', 'MATH101H', 0, False], ['s5', 'PHYS110', 0, False],
     ['s2', 'MATH101H', 0, False], ['s4', 'MATH101H', 0, False], ['s3', 'PHYS110', 1, False],
     ['s2', 'MATH101', 1, False], ['s5', 'PHYS110', 0, False], ['s4', 'CHEM120', 0, False],
     ['s3', 'MATH101H', 1, True]],
    {0: 1, 2: 1},
    {'MATH101': 'online', 'MATH101H': 'online', 'PHYS110': 'paper', 'CHEM120': 'paper', 'BIO130': 'online'}],
   [[0, 2, 1], [1, 1, 0]]),
  ('regression variant: online seats 2',
   [[['s4', 'PHYS110', 1, False], ['s1', 'MATH101H', 1, True], ['s3', 'BIO130', 1, False],
     ['s1', 'MATH101H', 1, False], ['s4', 'MATH101H', 1, False], ['s1', 'MATH101H', 1, True]],
    {0: 2, 1: 2, 2: 4},
    {'MATH101': 'online', 'MATH101H': 'online', 'PHYS110': 'online', 'CHEM120': 'paper'}],
   []),
  ('partial repair guard 3',
   [[['s1', 'PHYS110', 2, False], ['s4', 'MATH101H', 0, False], ['s1', 'MATH101H', 2, False],
     ['s5', 'MATH101', 1, True], ['s5', 'PHYS110', 2, False], ['s3', 'BIO130', 2, True],
     ['s4', 'MATH101H', 2, False]],
    {1: 2, 2: 1}, {'MATH101': 'paper', 'MATH101H': 'online'}],
   [[2, 4, 1]]),
  ('boundary control 4', [[['s1', 'A', 0, False], ['s1', 'B', 0, False]], {0: 1}, {}], [[0, 2, 1]]),
  ('boundary control 5', [[['s1', 'A', 0, False], ['s1', 'A', 0, False]], {0: 1}, {'A': 'paper'}], []),
  ('normal control 6',
   [[['s4', 'CHEM120', 1, True], ['s5', 'CHEM120', 0, False], ['s3', 'MATH101', 0, False],
     ['s4', 'BIO130', 0, False], ['s4', 'MATH101', 1, False], ['s3', 'MATH101H', 1, False],
     ['s4', 'MATH101', 1, False], ['s1', 'MATH101', 0, True]],
    {0: 4, 1: 4, 2: 1},
    {'MATH101': 'paper', 'MATH101H': 'paper', 'PHYS110': 'online', 'CHEM120': 'online', 'BIO130': 'paper'}],
   []),
  ('normal control 7',
   [[['s5', 'PHYS110', 0, True], ['s2', 'MATH101', 0, False], ['s3', 'PHYS110', 0, False],
     ['s4', 'BIO130', 2, False], ['s2', 'MATH101', 0, False]],
    {1: 4, 2: 3},
    {'MATH101': 'online', 'MATH101H': 'paper', 'PHYS110': 'paper', 'CHEM120': 'paper', 'BIO130': 'paper'}],
   [[0, 3, 0]]),
  ('normal control 8',
   [[['s3', 'PHYS110', 2, True], ['s5', 'MATH101', 1, True], ['s5', 'CHEM120', 0, True],
     ['s4', 'CHEM120', 2, False], ['s4', 'PHYS110', 0, False], ['s2', 'MATH101H', 0, True],
     ['s3', 'PHYS110', 1, True], ['s5', 'MATH101', 1, True]],
    {0: 3, 1: 3, 2: 3},
    {'MATH101': 'paper', 'MATH101H': 'paper', 'PHYS110': 'paper', 'CHEM120': 'online', 'BIO130': 'online'}],
   [])],
 [('regression: online seats 1',
   [[['s5', 'CHEM120', 0, False], ['s2', 'MATH101H', 2, True], ['s5', 'PHYS110', 2, False],
     ['s3', 'PHYS110', 0, False], ['s3', 'MATH101', 1, False], ['s1', 'MATH101H', 1, True],
     ['s2', 'MATH101H', 0, True], ['s3', 'MATH101', 2, False], ['s4', 'PHYS110', 2, False],
     ['s3', 'MATH101', 2, False]],
    {0: 3, 1: 2, 2: 1}, {'MATH101': 'online', 'PHYS110': 'paper', 'CHEM120': 'paper', 'BIO130': 'paper'}],
   [[2, 4, 1]]),
  ('regression variant: online seats 2',
   [[['s4', 'PHYS110', 1, False], ['s1', 'CHEM120', 2, False], ['s1', 'CHEM120', 0, True],
     ['s2', 'MATH101H', 1, False], ['s3', 'CHEM120', 0, False], ['s5', 'PHYS110', 0, True],
     ['s1', 'PHYS110', 1, True], ['s1', 'MATH101H', 0, True], ['s1', 'BIO130', 0, True],
     ['s4', 'MATH101', 1, False]],
    {0: 3, 1: 2, 2: 1}, {'MATH101': 'online', 'MATH101H': 'paper', 'CHEM120': 'paper', 'BIO130': 'online'}],
   [[0, 5, 3], [1, 4, 2]]),
  ('partial repair guard 3',
   [[['s2', 'BIO130', 1, False], ['s2', 'BIO130', 0, False], ['s2', 'MATH101', 2, False],
     ['s4', 'MATH101H', 2, False], ['s2', 'MATH101', 2, False], ['s3', 'CHEM120', 0, False],
     ['s3', 'MATH101H', 1, False], ['s2', 'MATH101H', 1, False], ['s5', 'BIO130', 2, False],
     ['s4', 'MATH101', 1, True]],
    {0: 1, 1: 4, 2: 1}, {'MATH101': 'paper', 'MATH101H': 'online', 'CHEM120': 'paper'}],
   [[2, 2, 1]]),
  ('boundary control 4', [[['s1', 'A', 0, False], ['s2', 'A', 0, False]], {0: 2}, {'A': 'paper'}], []),
  ('boundary control 5', [[['s1', 'A', 0, False], ['s2', 'A', 0, False]], {0: 1}, {'A': 'online'}], []),
  ('normal control 6',
   [[['s1', 'CHEM120', 2, False], ['s3', 'BIO130', 0, True], ['s1', 'MATH101', 1, True],
     ['s5', 'BIO130', 1, False], ['s3', 'BIO130', 0, True]],
    {0: 1, 1: 2}, {'MATH101': 'online', 'CHEM120': 'online', 'BIO130': 'online'}],
   []),
  ('normal control 7',
   [[['s3', 'BIO130', 1, False], ['s2', 'PHYS110', 0, False], ['s2', 'MATH101H', 2, False],
     ['s5', 'CHEM120', 0, False], ['s4', 'MATH101', 1, False], ['s3', 'CHEM120', 0, True],
     ['s1', 'PHYS110', 1, False]],
    {0: 2, 2: 4},
    {'MATH101': 'paper', 'MATH101H': 'online', 'PHYS110': 'paper', 'CHEM120': 'paper', 'BIO130': 'online'}],
   [[0, 4, 2], [1, 2, 0]]),
  ('normal control 8',
   [[['s1', 'PHYS110', 1, False], ['s3', 'CHEM120', 2, False], ['s4', 'MATH101H', 1, False],
     ['s3', 'MATH101H', 0, False]],
    {0: 2, 1: 2, 2: 4},
    {'MATH101': 'paper', 'MATH101H': 'paper', 'PHYS110': 'online', 'CHEM120': 'online', 'BIO130': 'paper'}],
   [])],
 [('regression: online seats 1',
   [[['s5', 'BIO130', 1, False], ['s2', 'MATH101H', 2, False], ['s5', 'BIO130', 1, False],
     ['s3', 'MATH101H', 2, False], ['s2', 'MATH101', 2, False], ['s2', 'PHYS110', 0, False],
     ['s3', 'PHYS110', 1, False], ['s1', 'BIO130', 1, False], ['s2', 'CHEM120', 1, True],
     ['s1', 'PHYS110', 2, False], ['s1', 'PHYS110', 2, False]],
    {0: 2, 1: 2},
    {'MATH101': 'paper', 'MATH101H': 'online', 'PHYS110': 'paper', 'CHEM120': 'online', 'BIO130': 'paper'}],
   [[1, 3, 2], [2, 2, 0]]),
  ('regression variant: online seats 2',
   [[['s1', 'PHYS110', 0, False], ['s2', 'CHEM120', 1, False], ['s1', 'PHYS110', 2, False],
     ['s1', 'CHEM120', 2, False], ['s1', 'CHEM120', 1, False], ['s2', 'PHYS110', 0, False],
     ['s4', 'MATH101H', 0, False]],
    {0: 1, 1: 3, 2: 2},
    {'MATH101': 'online', 'MATH101H': 'online', 'PHYS110': 'online', 'CHEM120': 'paper', 'BIO130': 'paper'}],
   []),
  ('partial repair guard 3',
   [[['s1', 'PHYS110', 0, True], ['s1', 'PHYS110', 1, False], ['s3', 'MATH101H', 0, True],
     ['s4', 'MATH101', 1, True], ['s4', 'BIO130', 2, False], ['s3', 'MATH101', 2, False],
     ['s1', 'PHYS110', 1, False]],
    {0: 1, 1: 2}, {'MATH101': 'paper', 'MATH101H': 'online', 'PHYS110': 'paper', 'CHEM120': 'online'}],
   [[0, 2, 1], [2, 2, 0]]),
  ('boundary control 4', [[['s1', 'A', 0, False], ['s1', 'B', 0, False]], {0: 1}, {}], [[0, 2, 1]]),
  ('boundary control 5', [[['s1', 'A', 0, False], ['s1', 'A', 0, False]], {0: 1}, {'A': 'paper'}], []),
  ('normal control 6',
   [[['s2', 'PHYS110', 0, False], ['s1', 'MATH101H', 1, False], ['s2', 'MATH101', 1, False],
     ['s4', 'CHEM120', 0, False]],
    {0: 1, 1: 3, 2: 2}, {'MATH101': 'online', 'MATH101H': 'paper', 'PHYS110': 'paper', 'CHEM120': 'paper'}],
   [[0, 2, 1]]),
  ('normal control 7',
   [[['s3', 'PHYS110', 2, False], ['s2', 'MATH101', 2, False]], {0: 1, 1: 4},
    {'MATH101': 'paper', 'MATH101H': 'online', 'PHYS110': 'paper', 'BIO130': 'online'}],
   [[2, 2, 0]]),
  ('normal control 8',
   [[['s1', 'MATH101H', 2, False], ['s3', 'MATH101H', 1, True], ['s1', 'BIO130', 1, False],
     ['s5', 'MATH101H', 2, False], ['s2', 'PHYS110', 0, False], ['s5', 'CHEM120', 1, True],
     ['s1', 'MATH101', 1, False]],
    {0: 2, 1: 2, 2: 2},
    {'MATH101': 'online', 'MATH101H': 'online', 'PHYS110': 'paper', 'CHEM120': 'paper', 'BIO130': 'paper'}],
   [[1, 3, 2]])]]
for label, args, expected in fixtures[N-1]:
    check(label, solve(*args), expected)
print(json.dumps({"observations": observations, "passed": all(x["passed"] for x in observations)}, ensure_ascii=False))
raise SystemExit(0 if all(x["passed"] for x in observations) else 1)

Boundary fixture	Actual	Expected	Outcome
regression: online seats 1	`[[0, 2, 1]]`	`[]`	Failed
regression variant: online seats 2	`[[0, 4, 3], [1, 3, 2]]`	`[]`	Failed
partial repair guard 3	`[[0, 2, 1]]`	`[[0, 2, 1]]`	Passed
boundary control 4	`[[0, 2, 1]]`	`[[0, 2, 1]]`	Passed
boundary control 5	`[]`	`[]`	Passed
normal control 6	`[[1, 2, 1]]`	`[[1, 2, 1]]`	Passed
normal control 7	`[]`	`[]`	Passed
normal control 8	`[[1, 5, 4], [2, 2, 1]]`	`[[1, 5, 4]]`	Failed

SHA-256 / 16177774624d7b1ecad98fabd5dcc9ae0356f7d6bbdb0afe47a82a40ad70dce1

2 / The unsuccessful fix

Exit 1

"""Failure Map reference implementation. Python standard library only."""
import json

N = 1
observations = []
def solve(sits, cap, mode):
    seen = set()
    used = {}
    for st, ex, p, acc in sits:
        if (st, ex) in seen:
            continue
        seen.add((st, ex))
        if mode.get(ex, 'online') == 'online':
            continue
        used[p] = used.get(p, 0) + (2 if acc else 1)
    return [[p, used[p], cap.get(p, 0)] for p in sorted(used) if used[p] > cap.get(p, 0)]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('regression: online seats 1', [[['s1', 'A', 0, False], ['s2', 'A', 0, False]], {0: 1}, {'A': 'online'}],
   []),
  ('regression variant: online seats 2',
   [[['s1', 'MATH101', 1, True], ['s1', 'CHEM120', 0, False], ['s5', 'PHYS110', 0, False],
     ['s5', 'CHEM120', 0, False], ['s3', 'PHYS110', 1, False], ['s3', 'MATH101H', 0, False],
     ['s1', 'CHEM120', 1, False], ['s1', 'CHEM120', 0, False], ['s3', 'CHEM120', 2, False],
     ['s3', 'PHYS110', 2, False], ['s3', 'PHYS110', 1, False]],
    {0: 3, 1: 2, 2: 4}, {'MATH101': 'online', 'MATH101H': 'online', 'CHEM120': 'online', 'BIO130': 'paper'}],
   []),
  ('partial repair guard 3',
   [[['s3', 'MATH101', 0, False], ['s3', 'BIO130', 2, False], ['s2', 'MATH101H', 0, False],
     ['s2', 'MATH101H', 2, False], ['s3', 'BIO130', 2, False]],
    {0: 1, 1: 2, 2: 3}, {'MATH101': 'paper', 'PHYS110': 'paper', 'BIO130': 'online'}],
   [[0, 2, 1]]),
  ('boundary control 4', [[['s1', 'A', 0, False], ['s1', 'B', 0, False]], {0: 1}, {}], [[0, 2, 1]]),
  ('boundary control 5', [[['s1', 'A', 0, False], ['s1', 'A', 0, False]], {0: 1}, {'A': 'paper'}], []),
  ('normal control 6',
   [[['s1', 'BIO130', 1, False], ['s2', 'PHYS110', 1, False]], {0: 1, 1: 1, 2: 2},
    {'MATH101H': 'paper', 'PHYS110': 'paper', 'CHEM120': 'online', 'BIO130': 'paper'}],
   [[1, 2, 1]]),
  ('normal control 7',
   [[['s2', 'PHYS110', 0, False], ['s5', 'PHYS110', 2, False], ['s5', 'BIO130', 2, True],
     ['s1', 'MATH101H', 1, False], ['s5', 'BIO130', 2, True]],
    {0: 4, 1: 3, 2: 3},
    {'MATH101': 'paper', 'MATH101H': 'online', 'PHYS110': 'paper', 'CHEM120': 'paper', 'BIO130': 'paper'}],
   []),
  ('normal control 8',
   [[['s3', 'BIO130', 1, False], ['s5', 'PHYS110', 2, False], ['s3', 'MATH101H', 1, False],
     ['s3', 'MATH101H', 0, False], ['s4', 'MATH101H', 1, True], ['s1', 'CHEM120', 2, False],
     ['s3', 'MATH101H', 1, False], ['s1', 'BIO130', 1, False]],
    {0: 3, 1: 4, 2: 1}, {'MATH101': 'paper', 'MATH101H': 'paper', 'PHYS110': 'online', 'CHEM120': 'online'}],
   [[1, 5, 4]])],
 [('regression: online seats 1',
   [[['s4', 'MATH101H', 0, False], ['s5', 'CHEM120', 1, False], ['s5', 'MATH101H', 1, False],
     ['s5', 'MATH101H', 2, False], ['s4', 'MATH101H', 2, False], ['s2', 'CHEM120', 1, False],
     ['s3', 'MATH101', 0, False], ['s2', 'MATH101', 2, False], ['s2', 'BIO130', 1, False],
     ['s2', 'MATH101H', 0, False]],
    {0: 3, 1: 1, 2: 3},
    {'MATH101': 'online', 'MATH101H': 'online', 'PHYS110': 'online', 'CHEM120': 'paper'}],
   [[1, 3, 1]]),
  ('regression variant: online seats 2',
   [[['s1', 'PHYS110', 2, False], ['s4', 'MATH101H', 0, False], ['s1', 'MATH101H', 2, False],
     ['s5', 'MATH101', 1, True], ['s5', 'PHYS110', 2, False], ['s3', 'BIO130', 2, True],
     ['s4', 'MATH101H', 2, False]],
    {1: 2, 2: 1}, {'MATH101': 'paper', 'MATH101H': 'online'}],
   [[2, 4, 1]]),
  ('partial repair guard 3',
   [[['s2', 'MATH101H', 2, True], ['s4', 'MATH101', 0, False], ['s3', 'CHEM120', 0, True],
     ['s1', 'MATH101', 2, False], ['s2', 'PHYS110', 1, True], ['s4', 'BIO130', 0, True],
     ['s3', 'CHEM120', 2, False], ['s4', 'BIO130', 0, True]],
    {0: 2, 1: 3}, {'MATH101': 'paper', 'MATH101H': 'online', 'CHEM120': 'paper'}],
   [[0, 5, 2], [2, 1, 0]]),
  ('boundary control 4', [[['s1', 'A', 0, False], ['s2', 'A', 0, False]], {0: 2}, {'A': 'paper'}], []),
  ('boundary control 5', [[['s1', 'A', 0, False], ['s2', 'A', 0, False]], {0: 1}, {'A': 'online'}], []),
  ('normal control 6',
   [[['s1', 'PHYS110', 2, False], ['s4', 'MATH101', 1, False], ['s4', 'MATH101', 1, False]], {1: 1, 2: 3},
    {'MATH101': 'online', 'MATH101H': 'paper', 'PHYS110': 'paper', 'CHEM120': 'paper', 'BIO130': 'paper'}],
   []),
  ('normal control 7',
   [[['s5', 'BIO130', 0, False], ['s5', 'PHYS110', 1, False], ['s1', 'PHYS110', 0, False],
     ['s5', 'MATH101', 1, False], ['s3', 'MATH101', 2, False]],
    {0: 4, 1: 4, 2: 3}, {'MATH101': 'paper', 'MATH101H': 'online', 'PHYS110': 'paper', 'CHEM120': 'online'}],
   []),
  ('normal control 8',
   [[['s2', 'PHYS110', 1, False], ['s4', 'MATH101', 2, False], ['s5', 'MATH101', 0, True],
     ['s4', 'MATH101', 0, True], ['s1', 'MATH101', 2, True], ['s2', 'MATH101', 0, False],
     ['s2', 'BIO130', 2, True], ['s4', 'BIO130', 2, False], ['s2', 'MATH101H', 2, False],
     ['s3', 'BIO130', 1, False]],
    {0: 1, 1: 2, 2: 1}, {'PHYS110': 'paper', 'CHEM120': 'paper', 'BIO130': 'paper'}],
   [[0, 3, 1], [2, 7, 1]])],
 [('regression: online seats 1',
   [[['s3', 'MATH101H', 2, False], ['s3', 'MATH101H', 0, False], ['s5', 'PHYS110', 0, False],
     ['s2', 'MATH101H', 0, False], ['s4', 'MATH101H', 0, False], ['s3', 'PHYS110', 1, False],
     ['s2', 'MATH101', 1, False], ['s5', 'PHYS110', 0, False], ['s4', 'CHEM120', 0, False],
     ['s3', 'MATH101H', 1, True]],
    {0: 1, 2: 1},
    {'MATH101': 'online', 'MATH101H': 'online', 'PHYS110': 'paper', 'CHEM120': 'paper', 'BIO130': 'online'}],
   [[0, 2, 1], [1, 1, 0]]),
  ('regression variant: online seats 2',
   [[['s4', 'PHYS110', 1, False], ['s1', 'MATH101H', 1, True], ['s3', 'BIO130', 1, False],
     ['s1', 'MATH101H', 1, False], ['s4', 'MATH101H', 1, False], ['s1', 'MATH101H', 1, True]],
    {0: 2, 1: 2, 2: 4},
    {'MATH101': 'online', 'MATH101H': 'online', 'PHYS110': 'online', 'CHEM120': 'paper'}],
   []),
  ('partial repair guard 3',
   [[['s1', 'PHYS110', 2, False], ['s4', 'MATH101H', 0, False], ['s1', 'MATH101H', 2, False],
     ['s5', 'MATH101', 1, True], ['s5', 'PHYS110', 2, False], ['s3', 'BIO130', 2, True],
     ['s4', 'MATH101H', 2, False]],
    {1: 2, 2: 1}, {'MATH101': 'paper', 'MATH101H': 'online'}],
   [[2, 4, 1]]),
  ('boundary control 4', [[['s1', 'A', 0, False], ['s1', 'B', 0, False]], {0: 1}, {}], [[0, 2, 1]]),
  ('boundary control 5', [[['s1', 'A', 0, False], ['s1', 'A', 0, False]], {0: 1}, {'A': 'paper'}], []),
  ('normal control 6',
   [[['s4', 'CHEM120', 1, True], ['s5', 'CHEM120', 0, False], ['s3', 'MATH101', 0, False],
     ['s4', 'BIO130', 0, False], ['s4', 'MATH101', 1, False], ['s3', 'MATH101H', 1, False],
     ['s4', 'MATH101', 1, False], ['s1', 'MATH101', 0, True]],
    {0: 4, 1: 4, 2: 1},
    {'MATH101': 'paper', 'MATH101H': 'paper', 'PHYS110': 'online', 'CHEM120': 'online', 'BIO130': 'paper'}],
   []),
  ('normal control 7',
   [[['s5', 'PHYS110', 0, True], ['s2', 'MATH101', 0, False], ['s3', 'PHYS110', 0, False],
     ['s4', 'BIO130', 2, False], ['s2', 'MATH101', 0, False]],
    {1: 4, 2: 3},
    {'MATH101': 'online', 'MATH101H': 'paper', 'PHYS110': 'paper', 'CHEM120': 'paper', 'BIO130': 'paper'}],
   [[0, 3, 0]]),
  ('normal control 8',
   [[['s3', 'PHYS110', 2, True], ['s5', 'MATH101', 1, True], ['s5', 'CHEM120', 0, True],
     ['s4', 'CHEM120', 2, False], ['s4', 'PHYS110', 0, False], ['s2', 'MATH101H', 0, True],
     ['s3', 'PHYS110', 1, True], ['s5', 'MATH101', 1, True]],
    {0: 3, 1: 3, 2: 3},
    {'MATH101': 'paper', 'MATH101H': 'paper', 'PHYS110': 'paper', 'CHEM120': 'online', 'BIO130': 'online'}],
   [])],
 [('regression: online seats 1',
   [[['s5', 'CHEM120', 0, False], ['s2', 'MATH101H', 2, True], ['s5', 'PHYS110', 2, False],
     ['s3', 'PHYS110', 0, False], ['s3', 'MATH101', 1, False], ['s1', 'MATH101H', 1, True],
     ['s2', 'MATH101H', 0, True], ['s3', 'MATH101', 2, False], ['s4', 'PHYS110', 2, False],
     ['s3', 'MATH101', 2, False]],
    {0: 3, 1: 2, 2: 1}, {'MATH101': 'online', 'PHYS110': 'paper', 'CHEM120': 'paper', 'BIO130': 'paper'}],
   [[2, 4, 1]]),
  ('regression variant: online seats 2',
   [[['s4', 'PHYS110', 1, False], ['s1', 'CHEM120', 2, False], ['s1', 'CHEM120', 0, True],
     ['s2', 'MATH101H', 1, False], ['s3', 'CHEM120', 0, False], ['s5', 'PHYS110', 0, True],
     ['s1', 'PHYS110', 1, True], ['s1', 'MATH101H', 0, True], ['s1', 'BIO130', 0, True],
     ['s4', 'MATH101', 1, False]],
    {0: 3, 1: 2, 2: 1}, {'MATH101': 'online', 'MATH101H': 'paper', 'CHEM120': 'paper', 'BIO130': 'online'}],
   [[0, 5, 3], [1, 4, 2]]),
  ('partial repair guard 3',
   [[['s2', 'BIO130', 1, False], ['s2', 'BIO130', 0, False], ['s2', 'MATH101', 2, False],
     ['s4', 'MATH101H', 2, False], ['s2', 'MATH101', 2, False], ['s3', 'CHEM120', 0, False],
     ['s3', 'MATH101H', 1, False], ['s2', 'MATH101H', 1, False], ['s5', 'BIO130', 2, False],
     ['s4', 'MATH101', 1, True]],
    {0: 1, 1: 4, 2: 1}, {'MATH101': 'paper', 'MATH101H': 'online', 'CHEM120': 'paper'}],
   [[2, 2, 1]]),
  ('boundary control 4', [[['s1', 'A', 0, False], ['s2', 'A', 0, False]], {0: 2}, {'A': 'paper'}], []),
  ('boundary control 5', [[['s1', 'A', 0, False], ['s2', 'A', 0, False]], {0: 1}, {'A': 'online'}], []),
  ('normal control 6',
   [[['s1', 'CHEM120', 2, False], ['s3', 'BIO130', 0, True], ['s1', 'MATH101', 1, True],
     ['s5', 'BIO130', 1, False], ['s3', 'BIO130', 0, True]],
    {0: 1, 1: 2}, {'MATH101': 'online', 'CHEM120': 'online', 'BIO130': 'online'}],
   []),
  ('normal control 7',
   [[['s3', 'BIO130', 1, False], ['s2', 'PHYS110', 0, False], ['s2', 'MATH101H', 2, False],
     ['s5', 'CHEM120', 0, False], ['s4', 'MATH101', 1, False], ['s3', 'CHEM120', 0, True],
     ['s1', 'PHYS110', 1, False]],
    {0: 2, 2: 4},
    {'MATH101': 'paper', 'MATH101H': 'online', 'PHYS110': 'paper', 'CHEM120': 'paper', 'BIO130': 'online'}],
   [[0, 4, 2], [1, 2, 0]]),
  ('normal control 8',
   [[['s1', 'PHYS110', 1, False], ['s3', 'CHEM120', 2, False], ['s4', 'MATH101H', 1, False],
     ['s3', 'MATH101H', 0, False]],
    {0: 2, 1: 2, 2: 4},
    {'MATH101': 'paper', 'MATH101H': 'paper', 'PHYS110': 'online', 'CHEM120': 'online', 'BIO130': 'paper'}],
   [])],
 [('regression: online seats 1',
   [[['s5', 'BIO130', 1, False], ['s2', 'MATH101H', 2, False], ['s5', 'BIO130', 1, False],
     ['s3', 'MATH101H', 2, False], ['s2', 'MATH101', 2, False], ['s2', 'PHYS110', 0, False],
     ['s3', 'PHYS110', 1, False], ['s1', 'BIO130', 1, False], ['s2', 'CHEM120', 1, True],
     ['s1', 'PHYS110', 2, False], ['s1', 'PHYS110', 2, False]],
    {0: 2, 1: 2},
    {'MATH101': 'paper', 'MATH101H': 'online', 'PHYS110': 'paper', 'CHEM120': 'online', 'BIO130': 'paper'}],
   [[1, 3, 2], [2, 2, 0]]),
  ('regression variant: online seats 2',
   [[['s1', 'PHYS110', 0, False], ['s2', 'CHEM120', 1, False], ['s1', 'PHYS110', 2, False],
     ['s1', 'CHEM120', 2, False], ['s1', 'CHEM120', 1, False], ['s2', 'PHYS110', 0, False],
     ['s4', 'MATH101H', 0, False]],
    {0: 1, 1: 3, 2: 2},
    {'MATH101': 'online', 'MATH101H': 'online', 'PHYS110': 'online', 'CHEM120': 'paper', 'BIO130': 'paper'}],
   []),
  ('partial repair guard 3',
   [[['s1', 'PHYS110', 0, True], ['s1', 'PHYS110', 1, False], ['s3', 'MATH101H', 0, True],
     ['s4', 'MATH101', 1, True], ['s4', 'BIO130', 2, False], ['s3', 'MATH101', 2, False],
     ['s1', 'PHYS110', 1, False]],
    {0: 1, 1: 2}, {'MATH101': 'paper', 'MATH101H': 'online', 'PHYS110': 'paper', 'CHEM120': 'online'}],
   [[0, 2, 1], [2, 2, 0]]),
  ('boundary control 4', [[['s1', 'A', 0, False], ['s1', 'B', 0, False]], {0: 1}, {}], [[0, 2, 1]]),
  ('boundary control 5', [[['s1', 'A', 0, False], ['s1', 'A', 0, False]], {0: 1}, {'A': 'paper'}], []),
  ('normal control 6',
   [[['s2', 'PHYS110', 0, False], ['s1', 'MATH101H', 1, False], ['s2', 'MATH101', 1, False],
     ['s4', 'CHEM120', 0, False]],
    {0: 1, 1: 3, 2: 2}, {'MATH101': 'online', 'MATH101H': 'paper', 'PHYS110': 'paper', 'CHEM120': 'paper'}],
   [[0, 2, 1]]),
  ('normal control 7',
   [[['s3', 'PHYS110', 2, False], ['s2', 'MATH101', 2, False]], {0: 1, 1: 4},
    {'MATH101': 'paper', 'MATH101H': 'online', 'PHYS110': 'paper', 'BIO130': 'online'}],
   [[2, 2, 0]]),
  ('normal control 8',
   [[['s1', 'MATH101H', 2, False], ['s3', 'MATH101H', 1, True], ['s1', 'BIO130', 1, False],
     ['s5', 'MATH101H', 2, False], ['s2', 'PHYS110', 0, False], ['s5', 'CHEM120', 1, True],
     ['s1', 'MATH101', 1, False]],
    {0: 2, 1: 2, 2: 2},
    {'MATH101': 'online', 'MATH101H': 'online', 'PHYS110': 'paper', 'CHEM120': 'paper', 'BIO130': 'paper'}],
   [[1, 3, 2]])]]
for label, args, expected in fixtures[N-1]:
    check(label, solve(*args), expected)
print(json.dumps({"observations": observations, "passed": all(x["passed"] for x in observations)}, ensure_ascii=False))
raise SystemExit(0 if all(x["passed"] for x in observations) else 1)

Boundary fixture	Actual	Expected	Outcome
regression: online seats 1	`[]`	`[]`	Passed
regression variant: online seats 2	`[]`	`[]`	Passed
partial repair guard 3	`[]`	`[[0, 2, 1]]`	Failed
boundary control 4	`[]`	`[[0, 2, 1]]`	Failed
boundary control 5	`[]`	`[]`	Passed
normal control 6	`[[1, 2, 1]]`	`[[1, 2, 1]]`	Passed
normal control 7	`[]`	`[]`	Passed
normal control 8	`[]`	`[[1, 5, 4]]`	Failed

SHA-256 / adbd9abfc0f62b962555261f5169c3ce49c8a45abaeb8cb2dff6babddb9c51d7

3 / The verified repair

Exit 0

"""Failure Map reference implementation. Python standard library only."""
import json

N = 1
observations = []
def solve(sits, cap, mode):
    seen = set()
    used = {}
    for st, ex, p, acc in sits:
        if (st, ex) in seen:
            continue
        seen.add((st, ex))
        if mode.get(ex) == 'online':
            continue
        used[p] = used.get(p, 0) + (2 if acc else 1)
    return [[p, used[p], cap.get(p, 0)] for p in sorted(used) if used[p] > cap.get(p, 0)]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('regression: online seats 1', [[['s1', 'A', 0, False], ['s2', 'A', 0, False]], {0: 1}, {'A': 'online'}],
   []),
  ('regression variant: online seats 2',
   [[['s1', 'MATH101', 1, True], ['s1', 'CHEM120', 0, False], ['s5', 'PHYS110', 0, False],
     ['s5', 'CHEM120', 0, False], ['s3', 'PHYS110', 1, False], ['s3', 'MATH101H', 0, False],
     ['s1', 'CHEM120', 1, False], ['s1', 'CHEM120', 0, False], ['s3', 'CHEM120', 2, False],
     ['s3', 'PHYS110', 2, False], ['s3', 'PHYS110', 1, False]],
    {0: 3, 1: 2, 2: 4}, {'MATH101': 'online', 'MATH101H': 'online', 'CHEM120': 'online', 'BIO130': 'paper'}],
   []),
  ('partial repair guard 3',
   [[['s3', 'MATH101', 0, False], ['s3', 'BIO130', 2, False], ['s2', 'MATH101H', 0, False],
     ['s2', 'MATH101H', 2, False], ['s3', 'BIO130', 2, False]],
    {0: 1, 1: 2, 2: 3}, {'MATH101': 'paper', 'PHYS110': 'paper', 'BIO130': 'online'}],
   [[0, 2, 1]]),
  ('boundary control 4', [[['s1', 'A', 0, False], ['s1', 'B', 0, False]], {0: 1}, {}], [[0, 2, 1]]),
  ('boundary control 5', [[['s1', 'A', 0, False], ['s1', 'A', 0, False]], {0: 1}, {'A': 'paper'}], []),
  ('normal control 6',
   [[['s1', 'BIO130', 1, False], ['s2', 'PHYS110', 1, False]], {0: 1, 1: 1, 2: 2},
    {'MATH101H': 'paper', 'PHYS110': 'paper', 'CHEM120': 'online', 'BIO130': 'paper'}],
   [[1, 2, 1]]),
  ('normal control 7',
   [[['s2', 'PHYS110', 0, False], ['s5', 'PHYS110', 2, False], ['s5', 'BIO130', 2, True],
     ['s1', 'MATH101H', 1, False], ['s5', 'BIO130', 2, True]],
    {0: 4, 1: 3, 2: 3},
    {'MATH101': 'paper', 'MATH101H': 'online', 'PHYS110': 'paper', 'CHEM120': 'paper', 'BIO130': 'paper'}],
   []),
  ('normal control 8',
   [[['s3', 'BIO130', 1, False], ['s5', 'PHYS110', 2, False], ['s3', 'MATH101H', 1, False],
     ['s3', 'MATH101H', 0, False], ['s4', 'MATH101H', 1, True], ['s1', 'CHEM120', 2, False],
     ['s3', 'MATH101H', 1, False], ['s1', 'BIO130', 1, False]],
    {0: 3, 1: 4, 2: 1}, {'MATH101': 'paper', 'MATH101H': 'paper', 'PHYS110': 'online', 'CHEM120': 'online'}],
   [[1, 5, 4]])],
 [('regression: online seats 1',
   [[['s4', 'MATH101H', 0, False], ['s5', 'CHEM120', 1, False], ['s5', 'MATH101H', 1, False],
     ['s5', 'MATH101H', 2, False], ['s4', 'MATH101H', 2, False], ['s2', 'CHEM120', 1, False],
     ['s3', 'MATH101', 0, False], ['s2', 'MATH101', 2, False], ['s2', 'BIO130', 1, False],
     ['s2', 'MATH101H', 0, False]],
    {0: 3, 1: 1, 2: 3},
    {'MATH101': 'online', 'MATH101H': 'online', 'PHYS110': 'online', 'CHEM120': 'paper'}],
   [[1, 3, 1]]),
  ('regression variant: online seats 2',
   [[['s1', 'PHYS110', 2, False], ['s4', 'MATH101H', 0, False], ['s1', 'MATH101H', 2, False],
     ['s5', 'MATH101', 1, True], ['s5', 'PHYS110', 2, False], ['s3', 'BIO130', 2, True],
     ['s4', 'MATH101H', 2, False]],
    {1: 2, 2: 1}, {'MATH101': 'paper', 'MATH101H': 'online'}],
   [[2, 4, 1]]),
  ('partial repair guard 3',
   [[['s2', 'MATH101H', 2, True], ['s4', 'MATH101', 0, False], ['s3', 'CHEM120', 0, True],
     ['s1', 'MATH101', 2, False], ['s2', 'PHYS110', 1, True], ['s4', 'BIO130', 0, True],
     ['s3', 'CHEM120', 2, False], ['s4', 'BIO130', 0, True]],
    {0: 2, 1: 3}, {'MATH101': 'paper', 'MATH101H': 'online', 'CHEM120': 'paper'}],
   [[0, 5, 2], [2, 1, 0]]),
  ('boundary control 4', [[['s1', 'A', 0, False], ['s2', 'A', 0, False]], {0: 2}, {'A': 'paper'}], []),
  ('boundary control 5', [[['s1', 'A', 0, False], ['s2', 'A', 0, False]], {0: 1}, {'A': 'online'}], []),
  ('normal control 6',
   [[['s1', 'PHYS110', 2, False], ['s4', 'MATH101', 1, False], ['s4', 'MATH101', 1, False]], {1: 1, 2: 3},
    {'MATH101': 'online', 'MATH101H': 'paper', 'PHYS110': 'paper', 'CHEM120': 'paper', 'BIO130': 'paper'}],
   []),
  ('normal control 7',
   [[['s5', 'BIO130', 0, False], ['s5', 'PHYS110', 1, False], ['s1', 'PHYS110', 0, False],
     ['s5', 'MATH101', 1, False], ['s3', 'MATH101', 2, False]],
    {0: 4, 1: 4, 2: 3}, {'MATH101': 'paper', 'MATH101H': 'online', 'PHYS110': 'paper', 'CHEM120': 'online'}],
   []),
  ('normal control 8',
   [[['s2', 'PHYS110', 1, False], ['s4', 'MATH101', 2, False], ['s5', 'MATH101', 0, True],
     ['s4', 'MATH101', 0, True], ['s1', 'MATH101', 2, True], ['s2', 'MATH101', 0, False],
     ['s2', 'BIO130', 2, True], ['s4', 'BIO130', 2, False], ['s2', 'MATH101H', 2, False],
     ['s3', 'BIO130', 1, False]],
    {0: 1, 1: 2, 2: 1}, {'PHYS110': 'paper', 'CHEM120': 'paper', 'BIO130': 'paper'}],
   [[0, 3, 1], [2, 7, 1]])],
 [('regression: online seats 1',
   [[['s3', 'MATH101H', 2, False], ['s3', 'MATH101H', 0, False], ['s5', 'PHYS110', 0, False],
     ['s2', 'MATH101H', 0, False], ['s4', 'MATH101H', 0, False], ['s3', 'PHYS110', 1, False],
     ['s2', 'MATH101', 1, False], ['s5', 'PHYS110', 0, False], ['s4', 'CHEM120', 0, False],
     ['s3', 'MATH101H', 1, True]],
    {0: 1, 2: 1},
    {'MATH101': 'online', 'MATH101H': 'online', 'PHYS110': 'paper', 'CHEM120': 'paper', 'BIO130': 'online'}],
   [[0, 2, 1], [1, 1, 0]]),
  ('regression variant: online seats 2',
   [[['s4', 'PHYS110', 1, False], ['s1', 'MATH101H', 1, True], ['s3', 'BIO130', 1, False],
     ['s1', 'MATH101H', 1, False], ['s4', 'MATH101H', 1, False], ['s1', 'MATH101H', 1, True]],
    {0: 2, 1: 2, 2: 4},
    {'MATH101': 'online', 'MATH101H': 'online', 'PHYS110': 'online', 'CHEM120': 'paper'}],
   []),
  ('partial repair guard 3',
   [[['s1', 'PHYS110', 2, False], ['s4', 'MATH101H', 0, False], ['s1', 'MATH101H', 2, False],
     ['s5', 'MATH101', 1, True], ['s5', 'PHYS110', 2, False], ['s3', 'BIO130', 2, True],
     ['s4', 'MATH101H', 2, False]],
    {1: 2, 2: 1}, {'MATH101': 'paper', 'MATH101H': 'online'}],
   [[2, 4, 1]]),
  ('boundary control 4', [[['s1', 'A', 0, False], ['s1', 'B', 0, False]], {0: 1}, {}], [[0, 2, 1]]),
  ('boundary control 5', [[['s1', 'A', 0, False], ['s1', 'A', 0, False]], {0: 1}, {'A': 'paper'}], []),
  ('normal control 6',
   [[['s4', 'CHEM120', 1, True], ['s5', 'CHEM120', 0, False], ['s3', 'MATH101', 0, False],
     ['s4', 'BIO130', 0, False], ['s4', 'MATH101', 1, False], ['s3', 'MATH101H', 1, False],
     ['s4', 'MATH101', 1, False], ['s1', 'MATH101', 0, True]],
    {0: 4, 1: 4, 2: 1},
    {'MATH101': 'paper', 'MATH101H': 'paper', 'PHYS110': 'online', 'CHEM120': 'online', 'BIO130': 'paper'}],
   []),
  ('normal control 7',
   [[['s5', 'PHYS110', 0, True], ['s2', 'MATH101', 0, False], ['s3', 'PHYS110', 0, False],
     ['s4', 'BIO130', 2, False], ['s2', 'MATH101', 0, False]],
    {1: 4, 2: 3},
    {'MATH101': 'online', 'MATH101H': 'paper', 'PHYS110': 'paper', 'CHEM120': 'paper', 'BIO130': 'paper'}],
   [[0, 3, 0]]),
  ('normal control 8',
   [[['s3', 'PHYS110', 2, True], ['s5', 'MATH101', 1, True], ['s5', 'CHEM120', 0, True],
     ['s4', 'CHEM120', 2, False], ['s4', 'PHYS110', 0, False], ['s2', 'MATH101H', 0, True],
     ['s3', 'PHYS110', 1, True], ['s5', 'MATH101', 1, True]],
    {0: 3, 1: 3, 2: 3},
    {'MATH101': 'paper', 'MATH101H': 'paper', 'PHYS110': 'paper', 'CHEM120': 'online', 'BIO130': 'online'}],
   [])],
 [('regression: online seats 1',
   [[['s5', 'CHEM120', 0, False], ['s2', 'MATH101H', 2, True], ['s5', 'PHYS110', 2, False],
     ['s3', 'PHYS110', 0, False], ['s3', 'MATH101', 1, False], ['s1', 'MATH101H', 1, True],
     ['s2', 'MATH101H', 0, True], ['s3', 'MATH101', 2, False], ['s4', 'PHYS110', 2, False],
     ['s3', 'MATH101', 2, False]],
    {0: 3, 1: 2, 2: 1}, {'MATH101': 'online', 'PHYS110': 'paper', 'CHEM120': 'paper', 'BIO130': 'paper'}],
   [[2, 4, 1]]),
  ('regression variant: online seats 2',
   [[['s4', 'PHYS110', 1, False], ['s1', 'CHEM120', 2, False], ['s1', 'CHEM120', 0, True],
     ['s2', 'MATH101H', 1, False], ['s3', 'CHEM120', 0, False], ['s5', 'PHYS110', 0, True],
     ['s1', 'PHYS110', 1, True], ['s1', 'MATH101H', 0, True], ['s1', 'BIO130', 0, True],
     ['s4', 'MATH101', 1, False]],
    {0: 3, 1: 2, 2: 1}, {'MATH101': 'online', 'MATH101H': 'paper', 'CHEM120': 'paper', 'BIO130': 'online'}],
   [[0, 5, 3], [1, 4, 2]]),
  ('partial repair guard 3',
   [[['s2', 'BIO130', 1, False], ['s2', 'BIO130', 0, False], ['s2', 'MATH101', 2, False],
     ['s4', 'MATH101H', 2, False], ['s2', 'MATH101', 2, False], ['s3', 'CHEM120', 0, False],
     ['s3', 'MATH101H', 1, False], ['s2', 'MATH101H', 1, False], ['s5', 'BIO130', 2, False],
     ['s4', 'MATH101', 1, True]],
    {0: 1, 1: 4, 2: 1}, {'MATH101': 'paper', 'MATH101H': 'online', 'CHEM120': 'paper'}],
   [[2, 2, 1]]),
  ('boundary control 4', [[['s1', 'A', 0, False], ['s2', 'A', 0, False]], {0: 2}, {'A': 'paper'}], []),
  ('boundary control 5', [[['s1', 'A', 0, False], ['s2', 'A', 0, False]], {0: 1}, {'A': 'online'}], []),
  ('normal control 6',
   [[['s1', 'CHEM120', 2, False], ['s3', 'BIO130', 0, True], ['s1', 'MATH101', 1, True],
     ['s5', 'BIO130', 1, False], ['s3', 'BIO130', 0, True]],
    {0: 1, 1: 2}, {'MATH101': 'online', 'CHEM120': 'online', 'BIO130': 'online'}],
   []),
  ('normal control 7',
   [[['s3', 'BIO130', 1, False], ['s2', 'PHYS110', 0, False], ['s2', 'MATH101H', 2, False],
     ['s5', 'CHEM120', 0, False], ['s4', 'MATH101', 1, False], ['s3', 'CHEM120', 0, True],
     ['s1', 'PHYS110', 1, False]],
    {0: 2, 2: 4},
    {'MATH101': 'paper', 'MATH101H': 'online', 'PHYS110': 'paper', 'CHEM120': 'paper', 'BIO130': 'online'}],
   [[0, 4, 2], [1, 2, 0]]),
  ('normal control 8',
   [[['s1', 'PHYS110', 1, False], ['s3', 'CHEM120', 2, False], ['s4', 'MATH101H', 1, False],
     ['s3', 'MATH101H', 0, False]],
    {0: 2, 1: 2, 2: 4},
    {'MATH101': 'paper', 'MATH101H': 'paper', 'PHYS110': 'online', 'CHEM120': 'online', 'BIO130': 'paper'}],
   [])],
 [('regression: online seats 1',
   [[['s5', 'BIO130', 1, False], ['s2', 'MATH101H', 2, False], ['s5', 'BIO130', 1, False],
     ['s3', 'MATH101H', 2, False], ['s2', 'MATH101', 2, False], ['s2', 'PHYS110', 0, False],
     ['s3', 'PHYS110', 1, False], ['s1', 'BIO130', 1, False], ['s2', 'CHEM120', 1, True],
     ['s1', 'PHYS110', 2, False], ['s1', 'PHYS110', 2, False]],
    {0: 2, 1: 2},
    {'MATH101': 'paper', 'MATH101H': 'online', 'PHYS110': 'paper', 'CHEM120': 'online', 'BIO130': 'paper'}],
   [[1, 3, 2], [2, 2, 0]]),
  ('regression variant: online seats 2',
   [[['s1', 'PHYS110', 0, False], ['s2', 'CHEM120', 1, False], ['s1', 'PHYS110', 2, False],
     ['s1', 'CHEM120', 2, False], ['s1', 'CHEM120', 1, False], ['s2', 'PHYS110', 0, False],
     ['s4', 'MATH101H', 0, False]],
    {0: 1, 1: 3, 2: 2},
    {'MATH101': 'online', 'MATH101H': 'online', 'PHYS110': 'online', 'CHEM120': 'paper', 'BIO130': 'paper'}],
   []),
  ('partial repair guard 3',
   [[['s1', 'PHYS110', 0, True], ['s1', 'PHYS110', 1, False], ['s3', 'MATH101H', 0, True],
     ['s4', 'MATH101', 1, True], ['s4', 'BIO130', 2, False], ['s3', 'MATH101', 2, False],
     ['s1', 'PHYS110', 1, False]],
    {0: 1, 1: 2}, {'MATH101': 'paper', 'MATH101H': 'online', 'PHYS110': 'paper', 'CHEM120': 'online'}],
   [[0, 2, 1], [2, 2, 0]]),
  ('boundary control 4', [[['s1', 'A', 0, False], ['s1', 'B', 0, False]], {0: 1}, {}], [[0, 2, 1]]),
  ('boundary control 5', [[['s1', 'A', 0, False], ['s1', 'A', 0, False]], {0: 1}, {'A': 'paper'}], []),
  ('normal control 6',
   [[['s2', 'PHYS110', 0, False], ['s1', 'MATH101H', 1, False], ['s2', 'MATH101', 1, False],
     ['s4', 'CHEM120', 0, False]],
    {0: 1, 1: 3, 2: 2}, {'MATH101': 'online', 'MATH101H': 'paper', 'PHYS110': 'paper', 'CHEM120': 'paper'}],
   [[0, 2, 1]]),
  ('normal control 7',
   [[['s3', 'PHYS110', 2, False], ['s2', 'MATH101', 2, False]], {0: 1, 1: 4},
    {'MATH101': 'paper', 'MATH101H': 'online', 'PHYS110': 'paper', 'BIO130': 'online'}],
   [[2, 2, 0]]),
  ('normal control 8',
   [[['s1', 'MATH101H', 2, False], ['s3', 'MATH101H', 1, True], ['s1', 'BIO130', 1, False],
     ['s5', 'MATH101H', 2, False], ['s2', 'PHYS110', 0, False], ['s5', 'CHEM120', 1, True],
     ['s1', 'MATH101', 1, False]],
    {0: 2, 1: 2, 2: 2},
    {'MATH101': 'online', 'MATH101H': 'online', 'PHYS110': 'paper', 'CHEM120': 'paper', 'BIO130': 'paper'}],
   [[1, 3, 2]])]]
for label, args, expected in fixtures[N-1]:
    check(label, solve(*args), expected)
print(json.dumps({"observations": observations, "passed": all(x["passed"] for x in observations)}, ensure_ascii=False))
raise SystemExit(0 if all(x["passed"] for x in observations) else 1)

Boundary fixture	Actual	Expected	Outcome
regression: online seats 1	`[]`	`[]`	Passed
regression variant: online seats 2	`[]`	`[]`	Passed
partial repair guard 3	`[[0, 2, 1]]`	`[[0, 2, 1]]`	Passed
boundary control 4	`[[0, 2, 1]]`	`[[0, 2, 1]]`	Passed
boundary control 5	`[]`	`[]`	Passed
normal control 6	`[[1, 2, 1]]`	`[[1, 2, 1]]`	Passed
normal control 7	`[]`	`[]`	Passed
normal control 8	`[[1, 5, 4]]`	`[[1, 5, 4]]`	Passed

SHA-256 / 1d9103e9c9209152622134ec29be12e294175ccaed8c9d20e5b0c7fa40befe55

Verification & scope

Stipulated toy exam-timetabling rule set for a bounded model; it does not claim conformance with any institution's regulations or a benchmark specification, and it performs no search or optimisation. This reproducer isolates one failure mechanism. Results cover the supplied fixtures. Variants within a family share a test contract and should remain grouped when constructing evaluation splits. Related mechanisms with a shared evaluation_group must also remain together; these controlled models are not independent production incidents.

Observations recorded using Python 3.12.14 at 2026-09-29T14:52:06.732124+00:00.

Case digest / e06e044683f6beffe02af53ccdce7f9c079d401c5c6ab7988428dc57545e982f