FA-94431 / Exam timetabling constraints / Open access

Proximity cost normalised by enrolment rows · case 01

The reported per-student cost shrinks as students take more exams.

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

ROOT CAUSE

The denominator counts enrolment rows rather than distinct students.

VERIFIED REPAIR

Divide by the number of distinct students.

Unsuccessful approach: Dividing by the number of exams is also not per student.

Case contract

enrol [student, exam] rows (may repeat) and exam periods. For each student, each pair of distinct exams d = 1..5 periods apart costs 2^(5-d). Return [total, number of students, total/students as a reduced fraction string].

Why this case matters

The Carter proximity cost is the standard exam-timetabling quality measure; each piece has a known implementation pitfall.

1 / The failure

Exit 1

"""Failure Map reference implementation. Python standard library only."""
import json
from fractions import Fraction
N = 1
observations = []
def solve(enrol, period):
    by = {}
    for st, ex in enrol:
        by.setdefault(st, set()).add(ex)
    total = 0
    for st, exs in by.items():
        ps = sorted(period[e] for e in exs)
        for i in range(len(ps)):
            for j in range(i + 1, len(ps)):
                d = ps[j] - ps[i]
                if 1 <= d <= 5:
                    total += 2 ** (5 - d)
    n = len(enrol)
    return [total, n, str(Fraction(total, n)) if n else '0']
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('regression: normaliser 1', [[['s1', 'MATH101'], ['s1', 'PHYS110']], {'MATH101': 0, 'PHYS110': 1}],
   [16, 1, '16']),
  ('regression variant: normaliser 2',
   [[['s2', 'CHEM120'], ['s5', 'BIO130'], ['s2', 'MATH101'], ['s5', 'CHEM120'], ['s1', 'MATH101H'],
     ['s1', 'HIST140'], ['s1', 'ECON150'], ['s1', 'PHYS110'], ['s4', 'MATH101'], ['s5', 'HIST140'],
     ['s4', 'MATH101H']],
    {'MATH101': 6, 'MATH101H': 0, 'PHYS110': 7, 'CHEM120': 5, 'BIO130': 1, 'HIST140': 3, 'ECON150': 4}],
   [62, 4, '31/2']),
  ('partial repair guard 3',
   [[['s3', 'CHEM120'], ['s1', 'MATH101'], ['s2', 'CHEM120'], ['s5', 'HIST140'], ['s5', 'BIO130'],
     ['s1', 'HIST140'], ['s1', 'CHEM120'], ['s1', 'BIO130'], ['s3', 'BIO130'], ['s2', 'MATH101H'],
     ['s2', 'MATH101'], ['s2', 'HIST140']],
    {'MATH101': 2, 'MATH101H': 0, 'PHYS110': 3, 'CHEM120': 5, 'BIO130': 4, 'HIST140': 0, 'ECON150': 0}],
   [79, 4, '79/4']),
  ('boundary control 4', [[['s1', 'MATH101'], ['s1', 'PHYS110']], {'MATH101': 3, 'PHYS110': 3}], [0, 1, '0']),
  ('boundary control 5', [[['s1', 'MATH101'], ['s1', 'PHYS110']], {'MATH101': 0, 'PHYS110': 6}], [0, 1, '0']),
  ('normal control 6',
   [[['s5', 'ECON150'], ['s5', 'MATH101'], ['s4', 'PHYS110'], ['s5', 'BIO130'], ['s5', 'MATH101H']],
    {'MATH101': 6, 'MATH101H': 2, 'PHYS110': 2, 'CHEM120': 4, 'BIO130': 6, 'HIST140': 1, 'ECON150': 3}],
   [28, 2, '14']),
  ('normal control 7',
   [[['s4', 'ECON150'], ['s3', 'PHYS110'], ['s1', 'ECON150'], ['s4', 'CHEM120'], ['s1', 'MATH101'],
     ['s1', 'BIO130'], ['s4', 'HIST140'], ['s4', 'PHYS110']],
    {'MATH101': 0, 'MATH101H': 5, 'PHYS110': 3, 'CHEM120': 3, 'BIO130': 7, 'HIST140': 7, 'ECON150': 5}],
   [37, 3, '37/3']),
  ('normal control 8',
   [[['s2', 'PHYS110'], ['s5', 'CHEM120'], ['s3', 'PHYS110'], ['s3', 'MATH101H'], ['s1', 'MATH101H'],
     ['s5', 'MATH101H'], ['s5', 'ECON150'], ['s3', 'MATH101'], ['s4', 'PHYS110'], ['s2', 'MATH101'],
     ['s3', 'CHEM120']],
    {'MATH101': 0, 'MATH101H': 5, 'PHYS110': 7, 'CHEM120': 6, 'BIO130': 7, 'HIST140': 7, 'ECON150': 2}],
   [63, 5, '63/5'])],
 [('regression: normaliser 1', [[['s1', 'MATH101'], ['s1', 'PHYS110']], {'MATH101': 0, 'PHYS110': 5}],
   [1, 1, '1']),
  ('regression variant: normaliser 2',
   [[['s4', 'BIO130'], ['s4', 'CHEM120'], ['s4', 'MATH101'], ['s4', 'MATH101H']],
    {'MATH101': 1, 'MATH101H': 0, 'PHYS110': 1, 'CHEM120': 1, 'BIO130': 2, 'HIST140': 4, 'ECON150': 4}],
   [72, 1, '72']),
  ('partial repair guard 3',
   [[['s3', 'MATH101'], ['s3', 'MATH101H'], ['s3', 'CHEM120'], ['s3', 'MATH101'], ['s1', 'PHYS110']],
    {'MATH101': 5, 'MATH101H': 6, 'PHYS110': 5, 'CHEM120': 4, 'BIO130': 0, 'HIST140': 1, 'ECON150': 5}],
   [40, 2, '20']),
  ('boundary control 4', [[['s1', 'MATH101'], ['s1', 'PHYS110']], {'MATH101': 0, 'PHYS110': 1}],
   [16, 1, '16']),
  ('boundary control 5',
   [[['s1', 'MATH101'], ['s1', 'PHYS110'], ['s1', 'CHEM120'], ['s2', 'BIO130']],
    {'MATH101': 0, 'PHYS110': 0, 'CHEM120': 1, 'BIO130': 1}],
   [32, 2, '16']),
  ('normal control 6',
   [[['s1', 'ECON150'], ['s1', 'CHEM120'], ['s1', 'HIST140']],
    {'MATH101': 0, 'MATH101H': 6, 'PHYS110': 4, 'CHEM120': 3, 'BIO130': 0, 'HIST140': 1, 'ECON150': 7}],
   [10, 1, '10']),
  ('normal control 7',
   [[['s4', 'CHEM120'], ['s5', 'CHEM120'], ['s2', 'BIO130'], ['s5', 'ECON150'], ['s4', 'MATH101'],
     ['s4', 'MATH101H'], ['s2', 'MATH101H'], ['s5', 'MATH101H'], ['s4', 'HIST140'], ['s2', 'CHEM120'],
     ['s2', 'HIST140'], ['s5', 'MATH101']],
    {'MATH101': 2, 'MATH101H': 0, 'PHYS110': 3, 'CHEM120': 5, 'BIO130': 7, 'HIST140': 6, 'ECON150': 1}],
   [119, 3, '119/3']),
  ('normal control 8',
   [[['s4', 'CHEM120'], ['s1', 'HIST140'], ['s1', 'MATH101']],
    {'MATH101': 3, 'MATH101H': 4, 'PHYS110': 4, 'CHEM120': 5, 'BIO130': 7, 'HIST140': 5, 'ECON150': 2}],
   [8, 2, '4'])],
 [('regression: normaliser 1', [[['s1', 'MATH101'], ['s1', 'PHYS110']], {'MATH101': 0, 'PHYS110': 6}],
   [0, 1, '0']),
  ('regression variant: normaliser 2',
   [[['s4', 'MATH101H'], ['s4', 'MATH101'], ['s1', 'PHYS110'], ['s4', 'BIO130']],
    {'MATH101': 0, 'MATH101H': 1, 'PHYS110': 4, 'CHEM120': 2, 'BIO130': 1, 'HIST140': 2, 'ECON150': 4}],
   [32, 2, '16']),
  ('partial repair guard 3',
   [[['s1', 'CHEM120'], ['s1', 'BIO130'], ['s1', 'PHYS110'], ['s1', 'HIST140']],
    {'MATH101': 0, 'MATH101H': 2, 'PHYS110': 5, 'CHEM120': 2, 'BIO130': 7, 'HIST140': 3, 'ECON150': 3}],
   [39, 1, '39']),
  ('boundary control 4', [[['s1', 'MATH101'], ['s1', 'PHYS110']], {'MATH101': 3, 'PHYS110': 3}], [0, 1, '0']),
  ('normal control 5',
   [[['s2', 'BIO130'], ['s5', 'BIO130'], ['s4', 'MATH101H'], ['s2', 'MATH101H'], ['s2', 'CHEM120'],
     ['s3', 'MATH101'], ['s4', 'MATH101'], ['s1', 'MATH101H'], ['s1', 'BIO130'], ['s5', 'MATH101'],
     ['s4', 'CHEM120'], ['s5', 'MATH101H'], ['s4', 'BIO130'], ['s3', 'BIO130'], ['s3', 'MATH101H'],
     ['s5', 'PHYS110'], ['s2', 'MATH101']],
    {'MATH101': 5, 'MATH101H': 6, 'PHYS110': 5, 'CHEM120': 7, 'BIO130': 1, 'HIST140': 3, 'ECON150': 5}],
   [143, 5, '143/5']),
  ('normal control 6',
   [[['s5', 'MATH101'], ['s4', 'BIO130'], ['s4', 'MATH101'], ['s4', 'PHYS110'], ['s2', 'MATH101'],
     ['s5', 'ECON150'], ['s5', 'CHEM120']],
    {'MATH101': 1, 'MATH101H': 1, 'PHYS110': 1, 'CHEM120': 2, 'BIO130': 6, 'HIST140': 7, 'ECON150': 5}],
   [24, 3, '8']),
  ('normal control 7',
   [[['s5', 'PHYS110'], ['s1', 'HIST140'], ['s1', 'MATH101'], ['s5', 'MATH101H'], ['s2', 'MATH101'],
     ['s2', 'MATH101']],
    {'MATH101': 2, 'MATH101H': 6, 'PHYS110': 1, 'CHEM120': 2, 'BIO130': 0, 'HIST140': 2, 'ECON150': 3}],
   [1, 3, '1/3']),
  ('normal control 8',
   [[['s5', 'PHYS110'], ['s5', 'MATH101'], ['s5', 'PHYS110']],
    {'MATH101': 1, 'MATH101H': 1, 'PHYS110': 7, 'CHEM120': 1, 'BIO130': 4, 'HIST140': 4, 'ECON150': 5}],
   [0, 1, '0'])],
 [('regression: normaliser 1', [[['s1', 'MATH101'], ['s1', 'PHYS110']], {'MATH101': 3, 'PHYS110': 3}],
   [0, 1, '0']),
  ('regression variant: normaliser 2',
   [[['s4', 'CHEM120'], ['s4', 'PHYS110'], ['s4', 'PHYS110'], ['s4', 'HIST140']],
    {'MATH101': 0, 'MATH101H': 7, 'PHYS110': 5, 'CHEM120': 6, 'BIO130': 0, 'HIST140': 0, 'ECON150': 4}],
   [17, 1, '17']),
  ('partial repair guard 3',
   [[['s2', 'HIST140'], ['s2', 'BIO130'], ['s3', 'ECON150'], ['s3', 'MATH101H'], ['s3', 'CHEM120'],
     ['s4', 'HIST140'], ['s2', 'PHYS110'], ['s3', 'BIO130']],
    {'MATH101': 3, 'MATH101H': 6, 'PHYS110': 7, 'CHEM120': 1, 'BIO130': 5, 'HIST140': 6, 'ECON150': 6}],
   [76, 3, '76/3']),
  ('boundary control 4', [[['s1', 'MATH101'], ['s1', 'PHYS110']], {'MATH101': 0, 'PHYS110': 1}],
   [16, 1, '16']),
  ('boundary control 5',
   [[['s1', 'MATH101'], ['s1', 'PHYS110'], ['s1', 'CHEM120'], ['s2', 'BIO130']],
    {'MATH101': 0, 'PHYS110': 0, 'CHEM120': 1, 'BIO130': 1}],
   [32, 2, '16']),
  ('normal control 6',
   [[['s3', 'MATH101'], ['s3', 'MATH101H'], ['s3', 'CHEM120'], ['s3', 'MATH101'], ['s1', 'PHYS110']],
    {'MATH101': 5, 'MATH101H': 6, 'PHYS110': 5, 'CHEM120': 4, 'BIO130': 0, 'HIST140': 1, 'ECON150': 5}],
   [40, 2, '20']),
  ('normal control 7',
   [[['s3', 'BIO130'], ['s5', 'BIO130'], ['s1', 'ECON150'], ['s3', 'MATH101'], ['s1', 'MATH101'],
     ['s5', 'HIST140'], ['s3', 'CHEM120'], ['s1', 'CHEM120'], ['s5', 'PHYS110'], ['s1', 'BIO130'],
     ['s3', 'MATH101H'], ['s3', 'MATH101'], ['s5', 'MATH101']],
    {'MATH101': 4, 'MATH101H': 6, 'PHYS110': 3, 'CHEM120': 6, 'BIO130': 0, 'HIST140': 6, 'ECON150': 2}],
   [80, 3, '80/3']),
  ('normal control 8',
   [[['s4', 'HIST140'], ['s4', 'ECON150'], ['s2', 'BIO130'], ['s4', 'BIO130'], ['s2', 'CHEM120'],
     ['s2', 'MATH101H'], ['s2', 'MATH101']],
    {'MATH101': 4, 'MATH101H': 5, 'PHYS110': 4, 'CHEM120': 6, 'BIO130': 6, 'HIST140': 6, 'ECON150': 2}],
   [68, 2, '34'])],
 [('regression: normaliser 1',
   [[['s1', 'MATH101'], ['s1', 'MATH101'], ['s1', 'PHYS110']], {'MATH101': 0, 'PHYS110': 2}], [8, 1, '8']),
  ('regression variant: normaliser 2',
   [[['s4', 'MATH101H'], ['s5', 'MATH101'], ['s5', 'HIST140'], ['s1', 'MATH101H'], ['s1', 'ECON150'],
     ['s1', 'PHYS110'], ['s5', 'CHEM120'], ['s2', 'ECON150'], ['s5', 'PHYS110'], ['s1', 'HIST140'],
     ['s3', 'PHYS110'], ['s5', 'MATH101'], ['s2', 'HIST140'], ['s2', 'BIO130'], ['s4', 'MATH101']],
    {'MATH101': 0, 'MATH101H': 0, 'PHYS110': 5, 'CHEM120': 2, 'BIO130': 3, 'HIST140': 6, 'ECON150': 7}],
   [94, 5, '94/5']),
  ('partial repair guard 3',
   [[['s3', 'MATH101H'], ['s3', 'CHEM120'], ['s3', 'MATH101'], ['s3', 'BIO130']],
    {'MATH101': 7, 'MATH101H': 2, 'PHYS110': 6, 'CHEM120': 7, 'BIO130': 7, 'HIST140': 3, 'ECON150': 0}],
   [3, 1, '3']),
  ('boundary control 4', [[['s1', 'MATH101'], ['s1', 'PHYS110']], {'MATH101': 3, 'PHYS110': 3}], [0, 1, '0']),
  ('boundary control 5', [[['s1', 'MATH101'], ['s1', 'PHYS110']], {'MATH101': 0, 'PHYS110': 6}], [0, 1, '0']),
  ('normal control 6',
   [[['s1', 'MATH101H'], ['s2', 'BIO130'], ['s1', 'ECON150'], ['s1', 'ECON150'], ['s2', 'ECON150'],
     ['s3', 'MATH101'], ['s4', 'MATH101H'], ['s2', 'MATH101H'], ['s4', 'ECON150'], ['s2', 'PHYS110']],
    {'MATH101': 6, 'MATH101H': 7, 'PHYS110': 4, 'CHEM120': 2, 'BIO130': 4, 'HIST140': 3, 'ECON150': 4}],
   [20, 4, '5']),
  ('normal control 7',
   [[['s5', 'PHYS110'], ['s5', 'MATH101H'], ['s5', 'PHYS110'], ['s5', 'ECON150']],
    {'MATH101': 2, 'MATH101H': 5, 'PHYS110': 3, 'CHEM120': 3, 'BIO130': 7, 'HIST140': 4, 'ECON150': 3}],
   [16, 1, '16']),
  ('normal control 8',
   [[['s2', 'MATH101'], ['s2', 'MATH101H'], ['s2', 'HIST140'], ['s2', 'HIST140']],
    {'MATH101': 5, 'MATH101H': 3, 'PHYS110': 0, 'CHEM120': 2, 'BIO130': 3, 'HIST140': 1, 'ECON150': 6}],
   [18, 1, '18'])]]
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: normaliser 1	`[16, 2, '8']`	`[16, 1, '16']`	Failed
regression variant: normaliser 2	`[62, 11, '62/11']`	`[62, 4, '31/2']`	Failed
partial repair guard 3	`[79, 12, '79/12']`	`[79, 4, '79/4']`	Failed
boundary control 4	`[0, 2, '0']`	`[0, 1, '0']`	Failed
boundary control 5	`[0, 2, '0']`	`[0, 1, '0']`	Failed
normal control 6	`[28, 5, '28/5']`	`[28, 2, '14']`	Failed
normal control 7	`[37, 8, '37/8']`	`[37, 3, '37/3']`	Failed
normal control 8	`[63, 11, '63/11']`	`[63, 5, '63/5']`	Failed

SHA-256 / 22e465b43aa1091b52a2047d21f5f12ca6ba0eb0af37fb6ff8586c9a5705f4ad

2 / The unsuccessful fix

Exit 1

"""Failure Map reference implementation. Python standard library only."""
import json
from fractions import Fraction
N = 1
observations = []
def solve(enrol, period):
    by = {}
    for st, ex in enrol:
        by.setdefault(st, set()).add(ex)
    total = 0
    for st, exs in by.items():
        ps = sorted(period[e] for e in exs)
        for i in range(len(ps)):
            for j in range(i + 1, len(ps)):
                d = ps[j] - ps[i]
                if 1 <= d <= 5:
                    total += 2 ** (5 - d)
    n = len(period)
    return [total, n, str(Fraction(total, n)) if n else '0']
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('regression: normaliser 1', [[['s1', 'MATH101'], ['s1', 'PHYS110']], {'MATH101': 0, 'PHYS110': 1}],
   [16, 1, '16']),
  ('regression variant: normaliser 2',
   [[['s2', 'CHEM120'], ['s5', 'BIO130'], ['s2', 'MATH101'], ['s5', 'CHEM120'], ['s1', 'MATH101H'],
     ['s1', 'HIST140'], ['s1', 'ECON150'], ['s1', 'PHYS110'], ['s4', 'MATH101'], ['s5', 'HIST140'],
     ['s4', 'MATH101H']],
    {'MATH101': 6, 'MATH101H': 0, 'PHYS110': 7, 'CHEM120': 5, 'BIO130': 1, 'HIST140': 3, 'ECON150': 4}],
   [62, 4, '31/2']),
  ('partial repair guard 3',
   [[['s3', 'CHEM120'], ['s1', 'MATH101'], ['s2', 'CHEM120'], ['s5', 'HIST140'], ['s5', 'BIO130'],
     ['s1', 'HIST140'], ['s1', 'CHEM120'], ['s1', 'BIO130'], ['s3', 'BIO130'], ['s2', 'MATH101H'],
     ['s2', 'MATH101'], ['s2', 'HIST140']],
    {'MATH101': 2, 'MATH101H': 0, 'PHYS110': 3, 'CHEM120': 5, 'BIO130': 4, 'HIST140': 0, 'ECON150': 0}],
   [79, 4, '79/4']),
  ('boundary control 4', [[['s1', 'MATH101'], ['s1', 'PHYS110']], {'MATH101': 3, 'PHYS110': 3}], [0, 1, '0']),
  ('boundary control 5', [[['s1', 'MATH101'], ['s1', 'PHYS110']], {'MATH101': 0, 'PHYS110': 6}], [0, 1, '0']),
  ('normal control 6',
   [[['s5', 'ECON150'], ['s5', 'MATH101'], ['s4', 'PHYS110'], ['s5', 'BIO130'], ['s5', 'MATH101H']],
    {'MATH101': 6, 'MATH101H': 2, 'PHYS110': 2, 'CHEM120': 4, 'BIO130': 6, 'HIST140': 1, 'ECON150': 3}],
   [28, 2, '14']),
  ('normal control 7',
   [[['s4', 'ECON150'], ['s3', 'PHYS110'], ['s1', 'ECON150'], ['s4', 'CHEM120'], ['s1', 'MATH101'],
     ['s1', 'BIO130'], ['s4', 'HIST140'], ['s4', 'PHYS110']],
    {'MATH101': 0, 'MATH101H': 5, 'PHYS110': 3, 'CHEM120': 3, 'BIO130': 7, 'HIST140': 7, 'ECON150': 5}],
   [37, 3, '37/3']),
  ('normal control 8',
   [[['s2', 'PHYS110'], ['s5', 'CHEM120'], ['s3', 'PHYS110'], ['s3', 'MATH101H'], ['s1', 'MATH101H'],
     ['s5', 'MATH101H'], ['s5', 'ECON150'], ['s3', 'MATH101'], ['s4', 'PHYS110'], ['s2', 'MATH101'],
     ['s3', 'CHEM120']],
    {'MATH101': 0, 'MATH101H': 5, 'PHYS110': 7, 'CHEM120': 6, 'BIO130': 7, 'HIST140': 7, 'ECON150': 2}],
   [63, 5, '63/5'])],
 [('regression: normaliser 1', [[['s1', 'MATH101'], ['s1', 'PHYS110']], {'MATH101': 0, 'PHYS110': 5}],
   [1, 1, '1']),
  ('regression variant: normaliser 2',
   [[['s4', 'BIO130'], ['s4', 'CHEM120'], ['s4', 'MATH101'], ['s4', 'MATH101H']],
    {'MATH101': 1, 'MATH101H': 0, 'PHYS110': 1, 'CHEM120': 1, 'BIO130': 2, 'HIST140': 4, 'ECON150': 4}],
   [72, 1, '72']),
  ('partial repair guard 3',
   [[['s3', 'MATH101'], ['s3', 'MATH101H'], ['s3', 'CHEM120'], ['s3', 'MATH101'], ['s1', 'PHYS110']],
    {'MATH101': 5, 'MATH101H': 6, 'PHYS110': 5, 'CHEM120': 4, 'BIO130': 0, 'HIST140': 1, 'ECON150': 5}],
   [40, 2, '20']),
  ('boundary control 4', [[['s1', 'MATH101'], ['s1', 'PHYS110']], {'MATH101': 0, 'PHYS110': 1}],
   [16, 1, '16']),
  ('boundary control 5',
   [[['s1', 'MATH101'], ['s1', 'PHYS110'], ['s1', 'CHEM120'], ['s2', 'BIO130']],
    {'MATH101': 0, 'PHYS110': 0, 'CHEM120': 1, 'BIO130': 1}],
   [32, 2, '16']),
  ('normal control 6',
   [[['s1', 'ECON150'], ['s1', 'CHEM120'], ['s1', 'HIST140']],
    {'MATH101': 0, 'MATH101H': 6, 'PHYS110': 4, 'CHEM120': 3, 'BIO130': 0, 'HIST140': 1, 'ECON150': 7}],
   [10, 1, '10']),
  ('normal control 7',
   [[['s4', 'CHEM120'], ['s5', 'CHEM120'], ['s2', 'BIO130'], ['s5', 'ECON150'], ['s4', 'MATH101'],
     ['s4', 'MATH101H'], ['s2', 'MATH101H'], ['s5', 'MATH101H'], ['s4', 'HIST140'], ['s2', 'CHEM120'],
     ['s2', 'HIST140'], ['s5', 'MATH101']],
    {'MATH101': 2, 'MATH101H': 0, 'PHYS110': 3, 'CHEM120': 5, 'BIO130': 7, 'HIST140': 6, 'ECON150': 1}],
   [119, 3, '119/3']),
  ('normal control 8',
   [[['s4', 'CHEM120'], ['s1', 'HIST140'], ['s1', 'MATH101']],
    {'MATH101': 3, 'MATH101H': 4, 'PHYS110': 4, 'CHEM120': 5, 'BIO130': 7, 'HIST140': 5, 'ECON150': 2}],
   [8, 2, '4'])],
 [('regression: normaliser 1', [[['s1', 'MATH101'], ['s1', 'PHYS110']], {'MATH101': 0, 'PHYS110': 6}],
   [0, 1, '0']),
  ('regression variant: normaliser 2',
   [[['s4', 'MATH101H'], ['s4', 'MATH101'], ['s1', 'PHYS110'], ['s4', 'BIO130']],
    {'MATH101': 0, 'MATH101H': 1, 'PHYS110': 4, 'CHEM120': 2, 'BIO130': 1, 'HIST140': 2, 'ECON150': 4}],
   [32, 2, '16']),
  ('partial repair guard 3',
   [[['s1', 'CHEM120'], ['s1', 'BIO130'], ['s1', 'PHYS110'], ['s1', 'HIST140']],
    {'MATH101': 0, 'MATH101H': 2, 'PHYS110': 5, 'CHEM120': 2, 'BIO130': 7, 'HIST140': 3, 'ECON150': 3}],
   [39, 1, '39']),
  ('boundary control 4', [[['s1', 'MATH101'], ['s1', 'PHYS110']], {'MATH101': 3, 'PHYS110': 3}], [0, 1, '0']),
  ('normal control 5',
   [[['s2', 'BIO130'], ['s5', 'BIO130'], ['s4', 'MATH101H'], ['s2', 'MATH101H'], ['s2', 'CHEM120'],
     ['s3', 'MATH101'], ['s4', 'MATH101'], ['s1', 'MATH101H'], ['s1', 'BIO130'], ['s5', 'MATH101'],
     ['s4', 'CHEM120'], ['s5', 'MATH101H'], ['s4', 'BIO130'], ['s3', 'BIO130'], ['s3', 'MATH101H'],
     ['s5', 'PHYS110'], ['s2', 'MATH101']],
    {'MATH101': 5, 'MATH101H': 6, 'PHYS110': 5, 'CHEM120': 7, 'BIO130': 1, 'HIST140': 3, 'ECON150': 5}],
   [143, 5, '143/5']),
  ('normal control 6',
   [[['s5', 'MATH101'], ['s4', 'BIO130'], ['s4', 'MATH101'], ['s4', 'PHYS110'], ['s2', 'MATH101'],
     ['s5', 'ECON150'], ['s5', 'CHEM120']],
    {'MATH101': 1, 'MATH101H': 1, 'PHYS110': 1, 'CHEM120': 2, 'BIO130': 6, 'HIST140': 7, 'ECON150': 5}],
   [24, 3, '8']),
  ('normal control 7',
   [[['s5', 'PHYS110'], ['s1', 'HIST140'], ['s1', 'MATH101'], ['s5', 'MATH101H'], ['s2', 'MATH101'],
     ['s2', 'MATH101']],
    {'MATH101': 2, 'MATH101H': 6, 'PHYS110': 1, 'CHEM120': 2, 'BIO130': 0, 'HIST140': 2, 'ECON150': 3}],
   [1, 3, '1/3']),
  ('normal control 8',
   [[['s5', 'PHYS110'], ['s5', 'MATH101'], ['s5', 'PHYS110']],
    {'MATH101': 1, 'MATH101H': 1, 'PHYS110': 7, 'CHEM120': 1, 'BIO130': 4, 'HIST140': 4, 'ECON150': 5}],
   [0, 1, '0'])],
 [('regression: normaliser 1', [[['s1', 'MATH101'], ['s1', 'PHYS110']], {'MATH101': 3, 'PHYS110': 3}],
   [0, 1, '0']),
  ('regression variant: normaliser 2',
   [[['s4', 'CHEM120'], ['s4', 'PHYS110'], ['s4', 'PHYS110'], ['s4', 'HIST140']],
    {'MATH101': 0, 'MATH101H': 7, 'PHYS110': 5, 'CHEM120': 6, 'BIO130': 0, 'HIST140': 0, 'ECON150': 4}],
   [17, 1, '17']),
  ('partial repair guard 3',
   [[['s2', 'HIST140'], ['s2', 'BIO130'], ['s3', 'ECON150'], ['s3', 'MATH101H'], ['s3', 'CHEM120'],
     ['s4', 'HIST140'], ['s2', 'PHYS110'], ['s3', 'BIO130']],
    {'MATH101': 3, 'MATH101H': 6, 'PHYS110': 7, 'CHEM120': 1, 'BIO130': 5, 'HIST140': 6, 'ECON150': 6}],
   [76, 3, '76/3']),
  ('boundary control 4', [[['s1', 'MATH101'], ['s1', 'PHYS110']], {'MATH101': 0, 'PHYS110': 1}],
   [16, 1, '16']),
  ('boundary control 5',
   [[['s1', 'MATH101'], ['s1', 'PHYS110'], ['s1', 'CHEM120'], ['s2', 'BIO130']],
    {'MATH101': 0, 'PHYS110': 0, 'CHEM120': 1, 'BIO130': 1}],
   [32, 2, '16']),
  ('normal control 6',
   [[['s3', 'MATH101'], ['s3', 'MATH101H'], ['s3', 'CHEM120'], ['s3', 'MATH101'], ['s1', 'PHYS110']],
    {'MATH101': 5, 'MATH101H': 6, 'PHYS110': 5, 'CHEM120': 4, 'BIO130': 0, 'HIST140': 1, 'ECON150': 5}],
   [40, 2, '20']),
  ('normal control 7',
   [[['s3', 'BIO130'], ['s5', 'BIO130'], ['s1', 'ECON150'], ['s3', 'MATH101'], ['s1', 'MATH101'],
     ['s5', 'HIST140'], ['s3', 'CHEM120'], ['s1', 'CHEM120'], ['s5', 'PHYS110'], ['s1', 'BIO130'],
     ['s3', 'MATH101H'], ['s3', 'MATH101'], ['s5', 'MATH101']],
    {'MATH101': 4, 'MATH101H': 6, 'PHYS110': 3, 'CHEM120': 6, 'BIO130': 0, 'HIST140': 6, 'ECON150': 2}],
   [80, 3, '80/3']),
  ('normal control 8',
   [[['s4', 'HIST140'], ['s4', 'ECON150'], ['s2', 'BIO130'], ['s4', 'BIO130'], ['s2', 'CHEM120'],
     ['s2', 'MATH101H'], ['s2', 'MATH101']],
    {'MATH101': 4, 'MATH101H': 5, 'PHYS110': 4, 'CHEM120': 6, 'BIO130': 6, 'HIST140': 6, 'ECON150': 2}],
   [68, 2, '34'])],
 [('regression: normaliser 1',
   [[['s1', 'MATH101'], ['s1', 'MATH101'], ['s1', 'PHYS110']], {'MATH101': 0, 'PHYS110': 2}], [8, 1, '8']),
  ('regression variant: normaliser 2',
   [[['s4', 'MATH101H'], ['s5', 'MATH101'], ['s5', 'HIST140'], ['s1', 'MATH101H'], ['s1', 'ECON150'],
     ['s1', 'PHYS110'], ['s5', 'CHEM120'], ['s2', 'ECON150'], ['s5', 'PHYS110'], ['s1', 'HIST140'],
     ['s3', 'PHYS110'], ['s5', 'MATH101'], ['s2', 'HIST140'], ['s2', 'BIO130'], ['s4', 'MATH101']],
    {'MATH101': 0, 'MATH101H': 0, 'PHYS110': 5, 'CHEM120': 2, 'BIO130': 3, 'HIST140': 6, 'ECON150': 7}],
   [94, 5, '94/5']),
  ('partial repair guard 3',
   [[['s3', 'MATH101H'], ['s3', 'CHEM120'], ['s3', 'MATH101'], ['s3', 'BIO130']],
    {'MATH101': 7, 'MATH101H': 2, 'PHYS110': 6, 'CHEM120': 7, 'BIO130': 7, 'HIST140': 3, 'ECON150': 0}],
   [3, 1, '3']),
  ('boundary control 4', [[['s1', 'MATH101'], ['s1', 'PHYS110']], {'MATH101': 3, 'PHYS110': 3}], [0, 1, '0']),
  ('boundary control 5', [[['s1', 'MATH101'], ['s1', 'PHYS110']], {'MATH101': 0, 'PHYS110': 6}], [0, 1, '0']),
  ('normal control 6',
   [[['s1', 'MATH101H'], ['s2', 'BIO130'], ['s1', 'ECON150'], ['s1', 'ECON150'], ['s2', 'ECON150'],
     ['s3', 'MATH101'], ['s4', 'MATH101H'], ['s2', 'MATH101H'], ['s4', 'ECON150'], ['s2', 'PHYS110']],
    {'MATH101': 6, 'MATH101H': 7, 'PHYS110': 4, 'CHEM120': 2, 'BIO130': 4, 'HIST140': 3, 'ECON150': 4}],
   [20, 4, '5']),
  ('normal control 7',
   [[['s5', 'PHYS110'], ['s5', 'MATH101H'], ['s5', 'PHYS110'], ['s5', 'ECON150']],
    {'MATH101': 2, 'MATH101H': 5, 'PHYS110': 3, 'CHEM120': 3, 'BIO130': 7, 'HIST140': 4, 'ECON150': 3}],
   [16, 1, '16']),
  ('normal control 8',
   [[['s2', 'MATH101'], ['s2', 'MATH101H'], ['s2', 'HIST140'], ['s2', 'HIST140']],
    {'MATH101': 5, 'MATH101H': 3, 'PHYS110': 0, 'CHEM120': 2, 'BIO130': 3, 'HIST140': 1, 'ECON150': 6}],
   [18, 1, '18'])]]
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: normaliser 1	`[16, 2, '8']`	`[16, 1, '16']`	Failed
regression variant: normaliser 2	`[62, 7, '62/7']`	`[62, 4, '31/2']`	Failed
partial repair guard 3	`[79, 7, '79/7']`	`[79, 4, '79/4']`	Failed
boundary control 4	`[0, 2, '0']`	`[0, 1, '0']`	Failed
boundary control 5	`[0, 2, '0']`	`[0, 1, '0']`	Failed
normal control 6	`[28, 7, '4']`	`[28, 2, '14']`	Failed
normal control 7	`[37, 7, '37/7']`	`[37, 3, '37/3']`	Failed
normal control 8	`[63, 7, '9']`	`[63, 5, '63/5']`	Failed

SHA-256 / 477ff9bc860246b1d1e1c5a19832d6cb72b2a69d0a2cc9fdf008741ded3dfe42

3 / The verified repair

Exit 0

"""Failure Map reference implementation. Python standard library only."""
import json
from fractions import Fraction
N = 1
observations = []
def solve(enrol, period):
    by = {}
    for st, ex in enrol:
        by.setdefault(st, set()).add(ex)
    total = 0
    for st, exs in by.items():
        ps = sorted(period[e] for e in exs)
        for i in range(len(ps)):
            for j in range(i + 1, len(ps)):
                d = ps[j] - ps[i]
                if 1 <= d <= 5:
                    total += 2 ** (5 - d)
    n = len(by)
    return [total, n, str(Fraction(total, n)) if n else '0']
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('regression: normaliser 1', [[['s1', 'MATH101'], ['s1', 'PHYS110']], {'MATH101': 0, 'PHYS110': 1}],
   [16, 1, '16']),
  ('regression variant: normaliser 2',
   [[['s2', 'CHEM120'], ['s5', 'BIO130'], ['s2', 'MATH101'], ['s5', 'CHEM120'], ['s1', 'MATH101H'],
     ['s1', 'HIST140'], ['s1', 'ECON150'], ['s1', 'PHYS110'], ['s4', 'MATH101'], ['s5', 'HIST140'],
     ['s4', 'MATH101H']],
    {'MATH101': 6, 'MATH101H': 0, 'PHYS110': 7, 'CHEM120': 5, 'BIO130': 1, 'HIST140': 3, 'ECON150': 4}],
   [62, 4, '31/2']),
  ('partial repair guard 3',
   [[['s3', 'CHEM120'], ['s1', 'MATH101'], ['s2', 'CHEM120'], ['s5', 'HIST140'], ['s5', 'BIO130'],
     ['s1', 'HIST140'], ['s1', 'CHEM120'], ['s1', 'BIO130'], ['s3', 'BIO130'], ['s2', 'MATH101H'],
     ['s2', 'MATH101'], ['s2', 'HIST140']],
    {'MATH101': 2, 'MATH101H': 0, 'PHYS110': 3, 'CHEM120': 5, 'BIO130': 4, 'HIST140': 0, 'ECON150': 0}],
   [79, 4, '79/4']),
  ('boundary control 4', [[['s1', 'MATH101'], ['s1', 'PHYS110']], {'MATH101': 3, 'PHYS110': 3}], [0, 1, '0']),
  ('boundary control 5', [[['s1', 'MATH101'], ['s1', 'PHYS110']], {'MATH101': 0, 'PHYS110': 6}], [0, 1, '0']),
  ('normal control 6',
   [[['s5', 'ECON150'], ['s5', 'MATH101'], ['s4', 'PHYS110'], ['s5', 'BIO130'], ['s5', 'MATH101H']],
    {'MATH101': 6, 'MATH101H': 2, 'PHYS110': 2, 'CHEM120': 4, 'BIO130': 6, 'HIST140': 1, 'ECON150': 3}],
   [28, 2, '14']),
  ('normal control 7',
   [[['s4', 'ECON150'], ['s3', 'PHYS110'], ['s1', 'ECON150'], ['s4', 'CHEM120'], ['s1', 'MATH101'],
     ['s1', 'BIO130'], ['s4', 'HIST140'], ['s4', 'PHYS110']],
    {'MATH101': 0, 'MATH101H': 5, 'PHYS110': 3, 'CHEM120': 3, 'BIO130': 7, 'HIST140': 7, 'ECON150': 5}],
   [37, 3, '37/3']),
  ('normal control 8',
   [[['s2', 'PHYS110'], ['s5', 'CHEM120'], ['s3', 'PHYS110'], ['s3', 'MATH101H'], ['s1', 'MATH101H'],
     ['s5', 'MATH101H'], ['s5', 'ECON150'], ['s3', 'MATH101'], ['s4', 'PHYS110'], ['s2', 'MATH101'],
     ['s3', 'CHEM120']],
    {'MATH101': 0, 'MATH101H': 5, 'PHYS110': 7, 'CHEM120': 6, 'BIO130': 7, 'HIST140': 7, 'ECON150': 2}],
   [63, 5, '63/5'])],
 [('regression: normaliser 1', [[['s1', 'MATH101'], ['s1', 'PHYS110']], {'MATH101': 0, 'PHYS110': 5}],
   [1, 1, '1']),
  ('regression variant: normaliser 2',
   [[['s4', 'BIO130'], ['s4', 'CHEM120'], ['s4', 'MATH101'], ['s4', 'MATH101H']],
    {'MATH101': 1, 'MATH101H': 0, 'PHYS110': 1, 'CHEM120': 1, 'BIO130': 2, 'HIST140': 4, 'ECON150': 4}],
   [72, 1, '72']),
  ('partial repair guard 3',
   [[['s3', 'MATH101'], ['s3', 'MATH101H'], ['s3', 'CHEM120'], ['s3', 'MATH101'], ['s1', 'PHYS110']],
    {'MATH101': 5, 'MATH101H': 6, 'PHYS110': 5, 'CHEM120': 4, 'BIO130': 0, 'HIST140': 1, 'ECON150': 5}],
   [40, 2, '20']),
  ('boundary control 4', [[['s1', 'MATH101'], ['s1', 'PHYS110']], {'MATH101': 0, 'PHYS110': 1}],
   [16, 1, '16']),
  ('boundary control 5',
   [[['s1', 'MATH101'], ['s1', 'PHYS110'], ['s1', 'CHEM120'], ['s2', 'BIO130']],
    {'MATH101': 0, 'PHYS110': 0, 'CHEM120': 1, 'BIO130': 1}],
   [32, 2, '16']),
  ('normal control 6',
   [[['s1', 'ECON150'], ['s1', 'CHEM120'], ['s1', 'HIST140']],
    {'MATH101': 0, 'MATH101H': 6, 'PHYS110': 4, 'CHEM120': 3, 'BIO130': 0, 'HIST140': 1, 'ECON150': 7}],
   [10, 1, '10']),
  ('normal control 7',
   [[['s4', 'CHEM120'], ['s5', 'CHEM120'], ['s2', 'BIO130'], ['s5', 'ECON150'], ['s4', 'MATH101'],
     ['s4', 'MATH101H'], ['s2', 'MATH101H'], ['s5', 'MATH101H'], ['s4', 'HIST140'], ['s2', 'CHEM120'],
     ['s2', 'HIST140'], ['s5', 'MATH101']],
    {'MATH101': 2, 'MATH101H': 0, 'PHYS110': 3, 'CHEM120': 5, 'BIO130': 7, 'HIST140': 6, 'ECON150': 1}],
   [119, 3, '119/3']),
  ('normal control 8',
   [[['s4', 'CHEM120'], ['s1', 'HIST140'], ['s1', 'MATH101']],
    {'MATH101': 3, 'MATH101H': 4, 'PHYS110': 4, 'CHEM120': 5, 'BIO130': 7, 'HIST140': 5, 'ECON150': 2}],
   [8, 2, '4'])],
 [('regression: normaliser 1', [[['s1', 'MATH101'], ['s1', 'PHYS110']], {'MATH101': 0, 'PHYS110': 6}],
   [0, 1, '0']),
  ('regression variant: normaliser 2',
   [[['s4', 'MATH101H'], ['s4', 'MATH101'], ['s1', 'PHYS110'], ['s4', 'BIO130']],
    {'MATH101': 0, 'MATH101H': 1, 'PHYS110': 4, 'CHEM120': 2, 'BIO130': 1, 'HIST140': 2, 'ECON150': 4}],
   [32, 2, '16']),
  ('partial repair guard 3',
   [[['s1', 'CHEM120'], ['s1', 'BIO130'], ['s1', 'PHYS110'], ['s1', 'HIST140']],
    {'MATH101': 0, 'MATH101H': 2, 'PHYS110': 5, 'CHEM120': 2, 'BIO130': 7, 'HIST140': 3, 'ECON150': 3}],
   [39, 1, '39']),
  ('boundary control 4', [[['s1', 'MATH101'], ['s1', 'PHYS110']], {'MATH101': 3, 'PHYS110': 3}], [0, 1, '0']),
  ('normal control 5',
   [[['s2', 'BIO130'], ['s5', 'BIO130'], ['s4', 'MATH101H'], ['s2', 'MATH101H'], ['s2', 'CHEM120'],
     ['s3', 'MATH101'], ['s4', 'MATH101'], ['s1', 'MATH101H'], ['s1', 'BIO130'], ['s5', 'MATH101'],
     ['s4', 'CHEM120'], ['s5', 'MATH101H'], ['s4', 'BIO130'], ['s3', 'BIO130'], ['s3', 'MATH101H'],
     ['s5', 'PHYS110'], ['s2', 'MATH101']],
    {'MATH101': 5, 'MATH101H': 6, 'PHYS110': 5, 'CHEM120': 7, 'BIO130': 1, 'HIST140': 3, 'ECON150': 5}],
   [143, 5, '143/5']),
  ('normal control 6',
   [[['s5', 'MATH101'], ['s4', 'BIO130'], ['s4', 'MATH101'], ['s4', 'PHYS110'], ['s2', 'MATH101'],
     ['s5', 'ECON150'], ['s5', 'CHEM120']],
    {'MATH101': 1, 'MATH101H': 1, 'PHYS110': 1, 'CHEM120': 2, 'BIO130': 6, 'HIST140': 7, 'ECON150': 5}],
   [24, 3, '8']),
  ('normal control 7',
   [[['s5', 'PHYS110'], ['s1', 'HIST140'], ['s1', 'MATH101'], ['s5', 'MATH101H'], ['s2', 'MATH101'],
     ['s2', 'MATH101']],
    {'MATH101': 2, 'MATH101H': 6, 'PHYS110': 1, 'CHEM120': 2, 'BIO130': 0, 'HIST140': 2, 'ECON150': 3}],
   [1, 3, '1/3']),
  ('normal control 8',
   [[['s5', 'PHYS110'], ['s5', 'MATH101'], ['s5', 'PHYS110']],
    {'MATH101': 1, 'MATH101H': 1, 'PHYS110': 7, 'CHEM120': 1, 'BIO130': 4, 'HIST140': 4, 'ECON150': 5}],
   [0, 1, '0'])],
 [('regression: normaliser 1', [[['s1', 'MATH101'], ['s1', 'PHYS110']], {'MATH101': 3, 'PHYS110': 3}],
   [0, 1, '0']),
  ('regression variant: normaliser 2',
   [[['s4', 'CHEM120'], ['s4', 'PHYS110'], ['s4', 'PHYS110'], ['s4', 'HIST140']],
    {'MATH101': 0, 'MATH101H': 7, 'PHYS110': 5, 'CHEM120': 6, 'BIO130': 0, 'HIST140': 0, 'ECON150': 4}],
   [17, 1, '17']),
  ('partial repair guard 3',
   [[['s2', 'HIST140'], ['s2', 'BIO130'], ['s3', 'ECON150'], ['s3', 'MATH101H'], ['s3', 'CHEM120'],
     ['s4', 'HIST140'], ['s2', 'PHYS110'], ['s3', 'BIO130']],
    {'MATH101': 3, 'MATH101H': 6, 'PHYS110': 7, 'CHEM120': 1, 'BIO130': 5, 'HIST140': 6, 'ECON150': 6}],
   [76, 3, '76/3']),
  ('boundary control 4', [[['s1', 'MATH101'], ['s1', 'PHYS110']], {'MATH101': 0, 'PHYS110': 1}],
   [16, 1, '16']),
  ('boundary control 5',
   [[['s1', 'MATH101'], ['s1', 'PHYS110'], ['s1', 'CHEM120'], ['s2', 'BIO130']],
    {'MATH101': 0, 'PHYS110': 0, 'CHEM120': 1, 'BIO130': 1}],
   [32, 2, '16']),
  ('normal control 6',
   [[['s3', 'MATH101'], ['s3', 'MATH101H'], ['s3', 'CHEM120'], ['s3', 'MATH101'], ['s1', 'PHYS110']],
    {'MATH101': 5, 'MATH101H': 6, 'PHYS110': 5, 'CHEM120': 4, 'BIO130': 0, 'HIST140': 1, 'ECON150': 5}],
   [40, 2, '20']),
  ('normal control 7',
   [[['s3', 'BIO130'], ['s5', 'BIO130'], ['s1', 'ECON150'], ['s3', 'MATH101'], ['s1', 'MATH101'],
     ['s5', 'HIST140'], ['s3', 'CHEM120'], ['s1', 'CHEM120'], ['s5', 'PHYS110'], ['s1', 'BIO130'],
     ['s3', 'MATH101H'], ['s3', 'MATH101'], ['s5', 'MATH101']],
    {'MATH101': 4, 'MATH101H': 6, 'PHYS110': 3, 'CHEM120': 6, 'BIO130': 0, 'HIST140': 6, 'ECON150': 2}],
   [80, 3, '80/3']),
  ('normal control 8',
   [[['s4', 'HIST140'], ['s4', 'ECON150'], ['s2', 'BIO130'], ['s4', 'BIO130'], ['s2', 'CHEM120'],
     ['s2', 'MATH101H'], ['s2', 'MATH101']],
    {'MATH101': 4, 'MATH101H': 5, 'PHYS110': 4, 'CHEM120': 6, 'BIO130': 6, 'HIST140': 6, 'ECON150': 2}],
   [68, 2, '34'])],
 [('regression: normaliser 1',
   [[['s1', 'MATH101'], ['s1', 'MATH101'], ['s1', 'PHYS110']], {'MATH101': 0, 'PHYS110': 2}], [8, 1, '8']),
  ('regression variant: normaliser 2',
   [[['s4', 'MATH101H'], ['s5', 'MATH101'], ['s5', 'HIST140'], ['s1', 'MATH101H'], ['s1', 'ECON150'],
     ['s1', 'PHYS110'], ['s5', 'CHEM120'], ['s2', 'ECON150'], ['s5', 'PHYS110'], ['s1', 'HIST140'],
     ['s3', 'PHYS110'], ['s5', 'MATH101'], ['s2', 'HIST140'], ['s2', 'BIO130'], ['s4', 'MATH101']],
    {'MATH101': 0, 'MATH101H': 0, 'PHYS110': 5, 'CHEM120': 2, 'BIO130': 3, 'HIST140': 6, 'ECON150': 7}],
   [94, 5, '94/5']),
  ('partial repair guard 3',
   [[['s3', 'MATH101H'], ['s3', 'CHEM120'], ['s3', 'MATH101'], ['s3', 'BIO130']],
    {'MATH101': 7, 'MATH101H': 2, 'PHYS110': 6, 'CHEM120': 7, 'BIO130': 7, 'HIST140': 3, 'ECON150': 0}],
   [3, 1, '3']),
  ('boundary control 4', [[['s1', 'MATH101'], ['s1', 'PHYS110']], {'MATH101': 3, 'PHYS110': 3}], [0, 1, '0']),
  ('boundary control 5', [[['s1', 'MATH101'], ['s1', 'PHYS110']], {'MATH101': 0, 'PHYS110': 6}], [0, 1, '0']),
  ('normal control 6',
   [[['s1', 'MATH101H'], ['s2', 'BIO130'], ['s1', 'ECON150'], ['s1', 'ECON150'], ['s2', 'ECON150'],
     ['s3', 'MATH101'], ['s4', 'MATH101H'], ['s2', 'MATH101H'], ['s4', 'ECON150'], ['s2', 'PHYS110']],
    {'MATH101': 6, 'MATH101H': 7, 'PHYS110': 4, 'CHEM120': 2, 'BIO130': 4, 'HIST140': 3, 'ECON150': 4}],
   [20, 4, '5']),
  ('normal control 7',
   [[['s5', 'PHYS110'], ['s5', 'MATH101H'], ['s5', 'PHYS110'], ['s5', 'ECON150']],
    {'MATH101': 2, 'MATH101H': 5, 'PHYS110': 3, 'CHEM120': 3, 'BIO130': 7, 'HIST140': 4, 'ECON150': 3}],
   [16, 1, '16']),
  ('normal control 8',
   [[['s2', 'MATH101'], ['s2', 'MATH101H'], ['s2', 'HIST140'], ['s2', 'HIST140']],
    {'MATH101': 5, 'MATH101H': 3, 'PHYS110': 0, 'CHEM120': 2, 'BIO130': 3, 'HIST140': 1, 'ECON150': 6}],
   [18, 1, '18'])]]
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: normaliser 1	`[16, 1, '16']`	`[16, 1, '16']`	Passed
regression variant: normaliser 2	`[62, 4, '31/2']`	`[62, 4, '31/2']`	Passed
partial repair guard 3	`[79, 4, '79/4']`	`[79, 4, '79/4']`	Passed
boundary control 4	`[0, 1, '0']`	`[0, 1, '0']`	Passed
boundary control 5	`[0, 1, '0']`	`[0, 1, '0']`	Passed
normal control 6	`[28, 2, '14']`	`[28, 2, '14']`	Passed
normal control 7	`[37, 3, '37/3']`	`[37, 3, '37/3']`	Passed
normal control 8	`[63, 5, '63/5']`	`[63, 5, '63/5']`	Passed

SHA-256 / ca933683e948e1c24ce90256fd5a4561f6d3426939f02c4e341047c432310bf6

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 2026-09-29T14:52:04.311305+00:00.

Case digest / 7e08bfffff809ab1e19bf76a117de6997ba0fcd635cd38d1b12fca8adb49f5c8