FA-94421 / Exam timetabling constraints / Open access

Same-period clashes included in proximity cost · case 01

Clashing pairs add 32 to the soft cost.

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

ROOT CAUSE

The proximity window includes distance zero.

VERIFIED REPAIR

Only distances 1 through 5 carry a proximity cost.

Unsuccessful approach: An exclusive upper bound drops pairs five periods apart.

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 0 <= 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: proximity window 1', [[['s1', 'MATH101'], ['s1', 'PHYS110']], {'MATH101': 3, 'PHYS110': 3}],
   [0, 1, '0']),
  ('regression variant: proximity window 2',
   [[['s4', 'CHEM120'], ['s2', 'BIO130'], ['s3', 'MATH101H'], ['s5', 'MATH101H'], ['s1', 'ECON150'],
     ['s5', 'CHEM120'], ['s1', 'MATH101'], ['s1', 'HIST140'], ['s4', 'MATH101H'], ['s3', 'CHEM120'],
     ['s1', 'PHYS110'], ['s2', 'PHYS110'], ['s4', 'HIST140']],
    {'MATH101': 0, 'MATH101H': 2, 'PHYS110': 7, 'CHEM120': 2, 'BIO130': 4, 'HIST140': 7, 'ECON150': 3}],
   [14, 5, '14/5']),
  ('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': 6}], [0, 1, '0']),
  ('normal control 5',
   [[['s1', 'ECON150'], ['s5', 'BIO130'], ['s5', 'PHYS110'], ['s5', 'HIST140'], ['s3', 'HIST140'],
     ['s2', 'PHYS110'], ['s2', 'HIST140'], ['s5', 'MATH101H'], ['s1', 'MATH101'], ['s1', 'HIST140'],
     ['s2', 'BIO130'], ['s2', 'CHEM120']],
    {'MATH101': 7, 'MATH101H': 5, 'PHYS110': 2, 'CHEM120': 2, 'BIO130': 7, 'HIST140': 0, 'ECON150': 2}],
   [49, 4, '49/4']),
  ('normal control 6',
   [[['s5', 'ECON150'], ['s2', 'HIST140'], ['s3', 'MATH101'], ['s3', 'PHYS110'], ['s3', 'MATH101'],
     ['s1', 'HIST140'], ['s3', 'MATH101H'], ['s4', 'CHEM120'], ['s4', 'MATH101'], ['s5', 'PHYS110'],
     ['s5', 'CHEM120'], ['s5', 'MATH101'], ['s2', 'MATH101'], ['s4', 'BIO130'], ['s4', 'PHYS110']],
    {'MATH101': 5, 'MATH101H': 1, 'PHYS110': 3, 'CHEM120': 4, 'BIO130': 4, 'HIST140': 4, 'ECON150': 0}],
   [153, 5, '153/5']),
  ('normal control 7',
   [[['s3', 'CHEM120'], ['s4', 'CHEM120'], ['s4', 'PHYS110'], ['s5', 'BIO130'], ['s5', 'PHYS110'],
     ['s3', 'CHEM120']],
    {'MATH101': 1, 'MATH101H': 6, 'PHYS110': 4, 'CHEM120': 7, 'BIO130': 1, 'HIST140': 7, 'ECON150': 5}],
   [8, 3, '8/3']),
  ('normal control 8',
   [[['s4', 'BIO130'], ['s4', 'MATH101H'], ['s2', 'MATH101H'], ['s1', 'CHEM120'], ['s2', 'MATH101'],
     ['s1', 'MATH101'], ['s5', 'CHEM120'], ['s4', 'CHEM120'], ['s4', 'HIST140'], ['s1', 'MATH101']],
    {'MATH101': 4, 'MATH101H': 2, 'PHYS110': 5, 'CHEM120': 1, 'BIO130': 4, 'HIST140': 0, 'ECON150': 3}],
   [66, 4, '33/2'])],
 [('regression: proximity window 1',
   [[['s1', 'MATH101'], ['s1', 'PHYS110'], ['s1', 'CHEM120'], ['s2', 'BIO130']],
    {'MATH101': 0, 'PHYS110': 0, 'CHEM120': 1, 'BIO130': 1}],
   [32, 2, '16']),
  ('regression variant: proximity window 2',
   [[['s2', 'CHEM120'], ['s2', 'ECON150'], ['s2', 'PHYS110'], ['s1', 'MATH101H'], ['s1', 'HIST140']],
    {'MATH101': 6, 'MATH101H': 5, 'PHYS110': 0, 'CHEM120': 5, 'BIO130': 6, 'HIST140': 5, 'ECON150': 1}],
   [19, 2, '19/2']),
  ('partial repair guard 3',
   [[['s4', 'MATH101'], ['s3', 'PHYS110'], ['s1', 'CHEM120'], ['s3', 'MATH101'], ['s5', 'CHEM120'],
     ['s1', 'MATH101H'], ['s4', 'MATH101H'], ['s4', 'ECON150']],
    {'MATH101': 3, 'MATH101H': 7, 'PHYS110': 7, 'CHEM120': 3, 'BIO130': 4, 'HIST140': 2, 'ECON150': 2}],
   [23, 4, '23/4']),
  ('boundary control 4', [[['s1', 'MATH101'], ['s1', 'PHYS110']], {'MATH101': 0, 'PHYS110': 1}],
   [16, 1, '16']),
  ('normal control 5',
   [[['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 6',
   [[['s4', 'BIO130'], ['s4', 'HIST140'], ['s3', 'MATH101H'], ['s5', 'HIST140'], ['s4', 'PHYS110']],
    {'MATH101': 4, 'MATH101H': 5, 'PHYS110': 0, 'CHEM120': 3, 'BIO130': 6, 'HIST140': 5, 'ECON150': 4}],
   [17, 3, '17/3']),
  ('normal control 7',
   [[['s4', 'MATH101H'], ['s4', 'BIO130'], ['s2', 'MATH101H'], ['s4', 'PHYS110'], ['s5', 'BIO130'],
     ['s4', 'MATH101'], ['s2', 'HIST140'], ['s2', 'BIO130']],
    {'MATH101': 4, 'MATH101H': 5, 'PHYS110': 0, 'CHEM120': 5, 'BIO130': 0, 'HIST140': 6, 'ECON150': 5}],
   [39, 3, '13']),
  ('normal control 8',
   [[['s4', 'MATH101'], ['s4', 'PHYS110']],
    {'MATH101': 5, 'MATH101H': 4, 'PHYS110': 5, 'CHEM120': 2, 'BIO130': 1, 'HIST140': 4, 'ECON150': 2}],
   [0, 1, '0'])],
 [('regression: proximity window 1',
   [[['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']),
  ('regression variant: proximity window 2',
   [[['s3', 'MATH101H'], ['s3', 'ECON150'], ['s5', 'BIO130'], ['s2', 'HIST140'], ['s1', 'MATH101'],
     ['s5', 'MATH101'], ['s2', 'CHEM120'], ['s3', 'CHEM120'], ['s1', 'PHYS110'], ['s5', 'MATH101H'],
     ['s5', 'ECON150'], ['s3', 'PHYS110']],
    {'MATH101': 6, 'MATH101H': 3, 'PHYS110': 6, 'CHEM120': 4, 'BIO130': 3, 'HIST140': 5, 'ECON150': 7}],
   [94, 4, '47/2']),
  ('partial repair guard 3',
   [[['s3', 'MATH101H'], ['s1', 'PHYS110'], ['s3', 'BIO130'], ['s3', 'HIST140'], ['s4', 'BIO130'],
     ['s2', 'ECON150'], ['s5', 'PHYS110'], ['s1', 'CHEM120'], ['s1', 'HIST140'], ['s2', 'PHYS110'],
     ['s5', 'MATH101H'], ['s3', 'PHYS110'], ['s1', 'ECON150']],
    {'MATH101': 7, 'MATH101H': 3, 'PHYS110': 1, 'CHEM120': 4, 'BIO130': 7, 'HIST140': 6, 'ECON150': 2}],
   [94, 5, '94/5']),
  ('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',
   [[['s3', 'MATH101H'], ['s2', 'MATH101'], ['s1', 'MATH101'], ['s4', 'CHEM120'], ['s4', 'PHYS110'],
     ['s4', 'HIST140'], ['s2', 'HIST140'], ['s4', 'HIST140'], ['s1', 'HIST140'], ['s3', 'MATH101'],
     ['s4', 'ECON150']],
    {'MATH101': 4, 'MATH101H': 5, 'PHYS110': 4, 'CHEM120': 3, 'BIO130': 0, 'HIST140': 2, 'ECON150': 0}],
   [86, 4, '43/2']),
  ('normal control 7',
   [[['s5', 'CHEM120'], ['s2', 'ECON150'], ['s5', 'BIO130'], ['s5', 'ECON150'], ['s1', 'MATH101H'],
     ['s4', 'ECON150'], ['s5', 'MATH101'], ['s1', 'HIST140'], ['s1', 'MATH101'], ['s4', 'BIO130'],
     ['s4', 'MATH101H'], ['s2', 'MATH101'], ['s4', 'MATH101'], ['s1', 'CHEM120'], ['s2', 'CHEM120'],
     ['s2', 'PHYS110']],
    {'MATH101': 4, 'MATH101H': 1, 'PHYS110': 1, 'CHEM120': 5, 'BIO130': 0, 'HIST140': 6, 'ECON150': 2}],
   [190, 4, '95/2']),
  ('normal control 8',
   [[['s5', 'ECON150'], ['s5', 'MATH101H'], ['s2', 'MATH101H'], ['s2', 'MATH101'], ['s4', 'BIO130'],
     ['s3', 'CHEM120'], ['s2', 'MATH101'], ['s4', 'PHYS110'], ['s2', 'ECON150'], ['s3', 'ECON150']],
    {'MATH101': 1, 'MATH101H': 3, 'PHYS110': 4, 'CHEM120': 2, 'BIO130': 6, 'HIST140': 4, 'ECON150': 5}],
   [38, 4, '19/2'])],
 [('regression: proximity window 1',
   [[['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']),
  ('regression variant: proximity window 2',
   [[['s4', 'MATH101H'], ['s3', 'MATH101'], ['s5', 'MATH101'], ['s3', 'BIO130'], ['s5', 'MATH101H'],
     ['s2', 'HIST140'], ['s5', 'HIST140'], ['s2', 'CHEM120'], ['s4', 'PHYS110'], ['s4', 'ECON150'],
     ['s1', 'MATH101'], ['s1', 'MATH101H']],
    {'MATH101': 2, 'MATH101H': 7, 'PHYS110': 5, 'CHEM120': 7, 'BIO130': 2, 'HIST140': 2, 'ECON150': 6}],
   [44, 5, '44/5']),
  ('partial repair guard 3',
   [[['s5', 'BIO130'], ['s5', 'MATH101H'], ['s3', 'MATH101H'], ['s1', 'MATH101'], ['s1', 'PHYS110'],
     ['s2', 'CHEM120'], ['s2', 'ECON150'], ['s5', 'PHYS110'], ['s3', 'CHEM120'], ['s1', 'HIST140'],
     ['s2', 'BIO130'], ['s4', 'ECON150'], ['s2', 'PHYS110']],
    {'MATH101': 6, 'MATH101H': 0, 'PHYS110': 2, 'CHEM120': 0, 'BIO130': 3, 'HIST140': 3, 'ECON150': 5}],
   [91, 5, '91/5']),
  ('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', 'CHEM120'], ['s2', 'HIST140'], ['s1', 'HIST140'], ['s2', 'ECON150'], ['s4', 'PHYS110'],
     ['s4', 'MATH101H'], ['s3', 'PHYS110'], ['s3', 'CHEM120'], ['s5', 'ECON150'], ['s3', 'CHEM120'],
     ['s3', 'HIST140'], ['s3', 'MATH101'], ['s4', 'MATH101'], ['s4', 'HIST140']],
    {'MATH101': 7, 'MATH101H': 3, 'PHYS110': 0, 'CHEM120': 4, 'BIO130': 3, 'HIST140': 4, 'ECON150': 4}],
   [40, 5, '8']),
  ('normal control 7',
   [[['s4', 'MATH101'], ['s4', 'PHYS110'], ['s5', 'PHYS110'], ['s3', 'PHYS110'], ['s2', 'CHEM120'],
     ['s3', 'CHEM120'], ['s5', 'CHEM120']],
    {'MATH101': 1, 'MATH101H': 3, 'PHYS110': 3, 'CHEM120': 0, 'BIO130': 3, 'HIST140': 0, 'ECON150': 1}],
   [16, 4, '4']),
  ('normal control 8',
   [[['s5', 'MATH101H'], ['s5', 'PHYS110'], ['s3', 'ECON150'], ['s3', 'PHYS110']],
    {'MATH101': 5, 'MATH101H': 2, 'PHYS110': 3, 'CHEM120': 6, 'BIO130': 1, 'HIST140': 6, 'ECON150': 7}],
   [18, 2, '9'])],
 [('regression: proximity window 1',
   [[['s5', 'PHYS110'], ['s4', 'ECON150'], ['s3', 'MATH101'], ['s3', 'PHYS110'], ['s2', 'CHEM120'],
     ['s2', 'ECON150'], ['s4', 'MATH101H'], ['s5', 'BIO130'], ['s4', 'HIST140'], ['s3', 'BIO130'],
     ['s4', 'PHYS110'], ['s3', 'ECON150'], ['s2', 'HIST140'], ['s5', 'MATH101'], ['s1', 'HIST140']],
    {'MATH101': 3, 'MATH101H': 0, 'PHYS110': 0, 'CHEM120': 6, 'BIO130': 0, 'HIST140': 0, 'ECON150': 2}],
   [82, 5, '82/5']),
  ('regression variant: proximity window 2',
   [[['s2', 'CHEM120'], ['s4', 'ECON150'], ['s4', 'CHEM120'], ['s4', 'HIST140'], ['s5', 'MATH101H'],
     ['s2', 'MATH101'], ['s5', 'ECON150'], ['s2', 'PHYS110'], ['s2', 'ECON150']],
    {'MATH101': 3, 'MATH101H': 3, 'PHYS110': 5, 'CHEM120': 6, 'BIO130': 2, 'HIST140': 4, 'ECON150': 5}],
   [100, 3, '100/3']),
  ('partial repair guard 3',
   [[['s1', 'MATH101H'], ['s5', 'HIST140'], ['s5', 'BIO130'], ['s1', 'MATH101'], ['s5', 'BIO130'],
     ['s5', 'MATH101']],
    {'MATH101': 7, 'MATH101H': 2, 'PHYS110': 7, 'CHEM120': 5, 'BIO130': 7, 'HIST140': 0, 'ECON150': 7}],
   [1, 2, '1/2']),
  ('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', 'ECON150'], ['s5', 'CHEM120'], ['s4', 'ECON150'], ['s1', 'HIST140'], ['s4', 'MATH101'],
     ['s4', 'MATH101'], ['s1', 'PHYS110']],
    {'MATH101': 1, 'MATH101H': 4, 'PHYS110': 6, 'CHEM120': 4, 'BIO130': 5, 'HIST140': 2, 'ECON150': 3}],
   [30, 3, '10']),
  ('normal control 7',
   [[['s4', 'BIO130'], ['s4', 'CHEM120'], ['s4', 'ECON150']],
    {'MATH101': 4, 'MATH101H': 4, 'PHYS110': 5, 'CHEM120': 4, 'BIO130': 4, 'HIST140': 1, 'ECON150': 5}],
   [32, 1, '32']),
  ('normal control 8',
   [[['s3', 'HIST140'], ['s3', 'MATH101'], ['s4', 'BIO130'], ['s4', 'MATH101'], ['s4', 'CHEM120'],
     ['s4', 'MATH101'], ['s1', 'HIST140'], ['s1', 'ECON150'], ['s1', 'MATH101'], ['s3', 'MATH101H'],
     ['s3', 'CHEM120']],
    {'MATH101': 6, 'MATH101H': 3, 'PHYS110': 7, 'CHEM120': 6, 'BIO130': 0, 'HIST140': 5, 'ECON150': 3}],
   [76, 3, '76/3'])]]
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: proximity window 1	`[32, 1, '32']`	`[0, 1, '0']`	Failed
regression variant: proximity window 2	`[142, 5, '142/5']`	`[14, 5, '14/5']`	Failed
partial repair guard 3	`[108, 3, '36']`	`[76, 3, '76/3']`	Failed
boundary control 4	`[0, 1, '0']`	`[0, 1, '0']`	Passed
normal control 5	`[81, 4, '81/4']`	`[49, 4, '49/4']`	Failed
normal control 6	`[185, 5, '37']`	`[153, 5, '153/5']`	Failed
normal control 7	`[8, 3, '8/3']`	`[8, 3, '8/3']`	Passed
normal control 8	`[66, 4, '33/2']`	`[66, 4, '33/2']`	Passed

SHA-256 / f900e8dfa4b2081f2037a1388dbca60f61f51c99938de4f11bc325bf5468f327

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(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: proximity window 1', [[['s1', 'MATH101'], ['s1', 'PHYS110']], {'MATH101': 3, 'PHYS110': 3}],
   [0, 1, '0']),
  ('regression variant: proximity window 2',
   [[['s4', 'CHEM120'], ['s2', 'BIO130'], ['s3', 'MATH101H'], ['s5', 'MATH101H'], ['s1', 'ECON150'],
     ['s5', 'CHEM120'], ['s1', 'MATH101'], ['s1', 'HIST140'], ['s4', 'MATH101H'], ['s3', 'CHEM120'],
     ['s1', 'PHYS110'], ['s2', 'PHYS110'], ['s4', 'HIST140']],
    {'MATH101': 0, 'MATH101H': 2, 'PHYS110': 7, 'CHEM120': 2, 'BIO130': 4, 'HIST140': 7, 'ECON150': 3}],
   [14, 5, '14/5']),
  ('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': 6}], [0, 1, '0']),
  ('normal control 5',
   [[['s1', 'ECON150'], ['s5', 'BIO130'], ['s5', 'PHYS110'], ['s5', 'HIST140'], ['s3', 'HIST140'],
     ['s2', 'PHYS110'], ['s2', 'HIST140'], ['s5', 'MATH101H'], ['s1', 'MATH101'], ['s1', 'HIST140'],
     ['s2', 'BIO130'], ['s2', 'CHEM120']],
    {'MATH101': 7, 'MATH101H': 5, 'PHYS110': 2, 'CHEM120': 2, 'BIO130': 7, 'HIST140': 0, 'ECON150': 2}],
   [49, 4, '49/4']),
  ('normal control 6',
   [[['s5', 'ECON150'], ['s2', 'HIST140'], ['s3', 'MATH101'], ['s3', 'PHYS110'], ['s3', 'MATH101'],
     ['s1', 'HIST140'], ['s3', 'MATH101H'], ['s4', 'CHEM120'], ['s4', 'MATH101'], ['s5', 'PHYS110'],
     ['s5', 'CHEM120'], ['s5', 'MATH101'], ['s2', 'MATH101'], ['s4', 'BIO130'], ['s4', 'PHYS110']],
    {'MATH101': 5, 'MATH101H': 1, 'PHYS110': 3, 'CHEM120': 4, 'BIO130': 4, 'HIST140': 4, 'ECON150': 0}],
   [153, 5, '153/5']),
  ('normal control 7',
   [[['s3', 'CHEM120'], ['s4', 'CHEM120'], ['s4', 'PHYS110'], ['s5', 'BIO130'], ['s5', 'PHYS110'],
     ['s3', 'CHEM120']],
    {'MATH101': 1, 'MATH101H': 6, 'PHYS110': 4, 'CHEM120': 7, 'BIO130': 1, 'HIST140': 7, 'ECON150': 5}],
   [8, 3, '8/3']),
  ('normal control 8',
   [[['s4', 'BIO130'], ['s4', 'MATH101H'], ['s2', 'MATH101H'], ['s1', 'CHEM120'], ['s2', 'MATH101'],
     ['s1', 'MATH101'], ['s5', 'CHEM120'], ['s4', 'CHEM120'], ['s4', 'HIST140'], ['s1', 'MATH101']],
    {'MATH101': 4, 'MATH101H': 2, 'PHYS110': 5, 'CHEM120': 1, 'BIO130': 4, 'HIST140': 0, 'ECON150': 3}],
   [66, 4, '33/2'])],
 [('regression: proximity window 1',
   [[['s1', 'MATH101'], ['s1', 'PHYS110'], ['s1', 'CHEM120'], ['s2', 'BIO130']],
    {'MATH101': 0, 'PHYS110': 0, 'CHEM120': 1, 'BIO130': 1}],
   [32, 2, '16']),
  ('regression variant: proximity window 2',
   [[['s2', 'CHEM120'], ['s2', 'ECON150'], ['s2', 'PHYS110'], ['s1', 'MATH101H'], ['s1', 'HIST140']],
    {'MATH101': 6, 'MATH101H': 5, 'PHYS110': 0, 'CHEM120': 5, 'BIO130': 6, 'HIST140': 5, 'ECON150': 1}],
   [19, 2, '19/2']),
  ('partial repair guard 3',
   [[['s4', 'MATH101'], ['s3', 'PHYS110'], ['s1', 'CHEM120'], ['s3', 'MATH101'], ['s5', 'CHEM120'],
     ['s1', 'MATH101H'], ['s4', 'MATH101H'], ['s4', 'ECON150']],
    {'MATH101': 3, 'MATH101H': 7, 'PHYS110': 7, 'CHEM120': 3, 'BIO130': 4, 'HIST140': 2, 'ECON150': 2}],
   [23, 4, '23/4']),
  ('boundary control 4', [[['s1', 'MATH101'], ['s1', 'PHYS110']], {'MATH101': 0, 'PHYS110': 1}],
   [16, 1, '16']),
  ('normal control 5',
   [[['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 6',
   [[['s4', 'BIO130'], ['s4', 'HIST140'], ['s3', 'MATH101H'], ['s5', 'HIST140'], ['s4', 'PHYS110']],
    {'MATH101': 4, 'MATH101H': 5, 'PHYS110': 0, 'CHEM120': 3, 'BIO130': 6, 'HIST140': 5, 'ECON150': 4}],
   [17, 3, '17/3']),
  ('normal control 7',
   [[['s4', 'MATH101H'], ['s4', 'BIO130'], ['s2', 'MATH101H'], ['s4', 'PHYS110'], ['s5', 'BIO130'],
     ['s4', 'MATH101'], ['s2', 'HIST140'], ['s2', 'BIO130']],
    {'MATH101': 4, 'MATH101H': 5, 'PHYS110': 0, 'CHEM120': 5, 'BIO130': 0, 'HIST140': 6, 'ECON150': 5}],
   [39, 3, '13']),
  ('normal control 8',
   [[['s4', 'MATH101'], ['s4', 'PHYS110']],
    {'MATH101': 5, 'MATH101H': 4, 'PHYS110': 5, 'CHEM120': 2, 'BIO130': 1, 'HIST140': 4, 'ECON150': 2}],
   [0, 1, '0'])],
 [('regression: proximity window 1',
   [[['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']),
  ('regression variant: proximity window 2',
   [[['s3', 'MATH101H'], ['s3', 'ECON150'], ['s5', 'BIO130'], ['s2', 'HIST140'], ['s1', 'MATH101'],
     ['s5', 'MATH101'], ['s2', 'CHEM120'], ['s3', 'CHEM120'], ['s1', 'PHYS110'], ['s5', 'MATH101H'],
     ['s5', 'ECON150'], ['s3', 'PHYS110']],
    {'MATH101': 6, 'MATH101H': 3, 'PHYS110': 6, 'CHEM120': 4, 'BIO130': 3, 'HIST140': 5, 'ECON150': 7}],
   [94, 4, '47/2']),
  ('partial repair guard 3',
   [[['s3', 'MATH101H'], ['s1', 'PHYS110'], ['s3', 'BIO130'], ['s3', 'HIST140'], ['s4', 'BIO130'],
     ['s2', 'ECON150'], ['s5', 'PHYS110'], ['s1', 'CHEM120'], ['s1', 'HIST140'], ['s2', 'PHYS110'],
     ['s5', 'MATH101H'], ['s3', 'PHYS110'], ['s1', 'ECON150']],
    {'MATH101': 7, 'MATH101H': 3, 'PHYS110': 1, 'CHEM120': 4, 'BIO130': 7, 'HIST140': 6, 'ECON150': 2}],
   [94, 5, '94/5']),
  ('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',
   [[['s3', 'MATH101H'], ['s2', 'MATH101'], ['s1', 'MATH101'], ['s4', 'CHEM120'], ['s4', 'PHYS110'],
     ['s4', 'HIST140'], ['s2', 'HIST140'], ['s4', 'HIST140'], ['s1', 'HIST140'], ['s3', 'MATH101'],
     ['s4', 'ECON150']],
    {'MATH101': 4, 'MATH101H': 5, 'PHYS110': 4, 'CHEM120': 3, 'BIO130': 0, 'HIST140': 2, 'ECON150': 0}],
   [86, 4, '43/2']),
  ('normal control 7',
   [[['s5', 'CHEM120'], ['s2', 'ECON150'], ['s5', 'BIO130'], ['s5', 'ECON150'], ['s1', 'MATH101H'],
     ['s4', 'ECON150'], ['s5', 'MATH101'], ['s1', 'HIST140'], ['s1', 'MATH101'], ['s4', 'BIO130'],
     ['s4', 'MATH101H'], ['s2', 'MATH101'], ['s4', 'MATH101'], ['s1', 'CHEM120'], ['s2', 'CHEM120'],
     ['s2', 'PHYS110']],
    {'MATH101': 4, 'MATH101H': 1, 'PHYS110': 1, 'CHEM120': 5, 'BIO130': 0, 'HIST140': 6, 'ECON150': 2}],
   [190, 4, '95/2']),
  ('normal control 8',
   [[['s5', 'ECON150'], ['s5', 'MATH101H'], ['s2', 'MATH101H'], ['s2', 'MATH101'], ['s4', 'BIO130'],
     ['s3', 'CHEM120'], ['s2', 'MATH101'], ['s4', 'PHYS110'], ['s2', 'ECON150'], ['s3', 'ECON150']],
    {'MATH101': 1, 'MATH101H': 3, 'PHYS110': 4, 'CHEM120': 2, 'BIO130': 6, 'HIST140': 4, 'ECON150': 5}],
   [38, 4, '19/2'])],
 [('regression: proximity window 1',
   [[['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']),
  ('regression variant: proximity window 2',
   [[['s4', 'MATH101H'], ['s3', 'MATH101'], ['s5', 'MATH101'], ['s3', 'BIO130'], ['s5', 'MATH101H'],
     ['s2', 'HIST140'], ['s5', 'HIST140'], ['s2', 'CHEM120'], ['s4', 'PHYS110'], ['s4', 'ECON150'],
     ['s1', 'MATH101'], ['s1', 'MATH101H']],
    {'MATH101': 2, 'MATH101H': 7, 'PHYS110': 5, 'CHEM120': 7, 'BIO130': 2, 'HIST140': 2, 'ECON150': 6}],
   [44, 5, '44/5']),
  ('partial repair guard 3',
   [[['s5', 'BIO130'], ['s5', 'MATH101H'], ['s3', 'MATH101H'], ['s1', 'MATH101'], ['s1', 'PHYS110'],
     ['s2', 'CHEM120'], ['s2', 'ECON150'], ['s5', 'PHYS110'], ['s3', 'CHEM120'], ['s1', 'HIST140'],
     ['s2', 'BIO130'], ['s4', 'ECON150'], ['s2', 'PHYS110']],
    {'MATH101': 6, 'MATH101H': 0, 'PHYS110': 2, 'CHEM120': 0, 'BIO130': 3, 'HIST140': 3, 'ECON150': 5}],
   [91, 5, '91/5']),
  ('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', 'CHEM120'], ['s2', 'HIST140'], ['s1', 'HIST140'], ['s2', 'ECON150'], ['s4', 'PHYS110'],
     ['s4', 'MATH101H'], ['s3', 'PHYS110'], ['s3', 'CHEM120'], ['s5', 'ECON150'], ['s3', 'CHEM120'],
     ['s3', 'HIST140'], ['s3', 'MATH101'], ['s4', 'MATH101'], ['s4', 'HIST140']],
    {'MATH101': 7, 'MATH101H': 3, 'PHYS110': 0, 'CHEM120': 4, 'BIO130': 3, 'HIST140': 4, 'ECON150': 4}],
   [40, 5, '8']),
  ('normal control 7',
   [[['s4', 'MATH101'], ['s4', 'PHYS110'], ['s5', 'PHYS110'], ['s3', 'PHYS110'], ['s2', 'CHEM120'],
     ['s3', 'CHEM120'], ['s5', 'CHEM120']],
    {'MATH101': 1, 'MATH101H': 3, 'PHYS110': 3, 'CHEM120': 0, 'BIO130': 3, 'HIST140': 0, 'ECON150': 1}],
   [16, 4, '4']),
  ('normal control 8',
   [[['s5', 'MATH101H'], ['s5', 'PHYS110'], ['s3', 'ECON150'], ['s3', 'PHYS110']],
    {'MATH101': 5, 'MATH101H': 2, 'PHYS110': 3, 'CHEM120': 6, 'BIO130': 1, 'HIST140': 6, 'ECON150': 7}],
   [18, 2, '9'])],
 [('regression: proximity window 1',
   [[['s5', 'PHYS110'], ['s4', 'ECON150'], ['s3', 'MATH101'], ['s3', 'PHYS110'], ['s2', 'CHEM120'],
     ['s2', 'ECON150'], ['s4', 'MATH101H'], ['s5', 'BIO130'], ['s4', 'HIST140'], ['s3', 'BIO130'],
     ['s4', 'PHYS110'], ['s3', 'ECON150'], ['s2', 'HIST140'], ['s5', 'MATH101'], ['s1', 'HIST140']],
    {'MATH101': 3, 'MATH101H': 0, 'PHYS110': 0, 'CHEM120': 6, 'BIO130': 0, 'HIST140': 0, 'ECON150': 2}],
   [82, 5, '82/5']),
  ('regression variant: proximity window 2',
   [[['s2', 'CHEM120'], ['s4', 'ECON150'], ['s4', 'CHEM120'], ['s4', 'HIST140'], ['s5', 'MATH101H'],
     ['s2', 'MATH101'], ['s5', 'ECON150'], ['s2', 'PHYS110'], ['s2', 'ECON150']],
    {'MATH101': 3, 'MATH101H': 3, 'PHYS110': 5, 'CHEM120': 6, 'BIO130': 2, 'HIST140': 4, 'ECON150': 5}],
   [100, 3, '100/3']),
  ('partial repair guard 3',
   [[['s1', 'MATH101H'], ['s5', 'HIST140'], ['s5', 'BIO130'], ['s1', 'MATH101'], ['s5', 'BIO130'],
     ['s5', 'MATH101']],
    {'MATH101': 7, 'MATH101H': 2, 'PHYS110': 7, 'CHEM120': 5, 'BIO130': 7, 'HIST140': 0, 'ECON150': 7}],
   [1, 2, '1/2']),
  ('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', 'ECON150'], ['s5', 'CHEM120'], ['s4', 'ECON150'], ['s1', 'HIST140'], ['s4', 'MATH101'],
     ['s4', 'MATH101'], ['s1', 'PHYS110']],
    {'MATH101': 1, 'MATH101H': 4, 'PHYS110': 6, 'CHEM120': 4, 'BIO130': 5, 'HIST140': 2, 'ECON150': 3}],
   [30, 3, '10']),
  ('normal control 7',
   [[['s4', 'BIO130'], ['s4', 'CHEM120'], ['s4', 'ECON150']],
    {'MATH101': 4, 'MATH101H': 4, 'PHYS110': 5, 'CHEM120': 4, 'BIO130': 4, 'HIST140': 1, 'ECON150': 5}],
   [32, 1, '32']),
  ('normal control 8',
   [[['s3', 'HIST140'], ['s3', 'MATH101'], ['s4', 'BIO130'], ['s4', 'MATH101'], ['s4', 'CHEM120'],
     ['s4', 'MATH101'], ['s1', 'HIST140'], ['s1', 'ECON150'], ['s1', 'MATH101'], ['s3', 'MATH101H'],
     ['s3', 'CHEM120']],
    {'MATH101': 6, 'MATH101H': 3, 'PHYS110': 7, 'CHEM120': 6, 'BIO130': 0, 'HIST140': 5, 'ECON150': 3}],
   [76, 3, '76/3'])]]
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: proximity window 1	`[0, 1, '0']`	`[0, 1, '0']`	Passed
regression variant: proximity window 2	`[12, 5, '12/5']`	`[14, 5, '14/5']`	Failed
partial repair guard 3	`[74, 3, '74/3']`	`[76, 3, '76/3']`	Failed
boundary control 4	`[0, 1, '0']`	`[0, 1, '0']`	Passed
normal control 5	`[44, 4, '11']`	`[49, 4, '49/4']`	Failed
normal control 6	`[152, 5, '152/5']`	`[153, 5, '153/5']`	Failed
normal control 7	`[8, 3, '8/3']`	`[8, 3, '8/3']`	Passed
normal control 8	`[66, 4, '33/2']`	`[66, 4, '33/2']`	Passed

SHA-256 / 7e1a22d5eaa4589fad65ddfd1c8283e4427c164fd90bdcdd7b3032556fb72df8

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: proximity window 1', [[['s1', 'MATH101'], ['s1', 'PHYS110']], {'MATH101': 3, 'PHYS110': 3}],
   [0, 1, '0']),
  ('regression variant: proximity window 2',
   [[['s4', 'CHEM120'], ['s2', 'BIO130'], ['s3', 'MATH101H'], ['s5', 'MATH101H'], ['s1', 'ECON150'],
     ['s5', 'CHEM120'], ['s1', 'MATH101'], ['s1', 'HIST140'], ['s4', 'MATH101H'], ['s3', 'CHEM120'],
     ['s1', 'PHYS110'], ['s2', 'PHYS110'], ['s4', 'HIST140']],
    {'MATH101': 0, 'MATH101H': 2, 'PHYS110': 7, 'CHEM120': 2, 'BIO130': 4, 'HIST140': 7, 'ECON150': 3}],
   [14, 5, '14/5']),
  ('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': 6}], [0, 1, '0']),
  ('normal control 5',
   [[['s1', 'ECON150'], ['s5', 'BIO130'], ['s5', 'PHYS110'], ['s5', 'HIST140'], ['s3', 'HIST140'],
     ['s2', 'PHYS110'], ['s2', 'HIST140'], ['s5', 'MATH101H'], ['s1', 'MATH101'], ['s1', 'HIST140'],
     ['s2', 'BIO130'], ['s2', 'CHEM120']],
    {'MATH101': 7, 'MATH101H': 5, 'PHYS110': 2, 'CHEM120': 2, 'BIO130': 7, 'HIST140': 0, 'ECON150': 2}],
   [49, 4, '49/4']),
  ('normal control 6',
   [[['s5', 'ECON150'], ['s2', 'HIST140'], ['s3', 'MATH101'], ['s3', 'PHYS110'], ['s3', 'MATH101'],
     ['s1', 'HIST140'], ['s3', 'MATH101H'], ['s4', 'CHEM120'], ['s4', 'MATH101'], ['s5', 'PHYS110'],
     ['s5', 'CHEM120'], ['s5', 'MATH101'], ['s2', 'MATH101'], ['s4', 'BIO130'], ['s4', 'PHYS110']],
    {'MATH101': 5, 'MATH101H': 1, 'PHYS110': 3, 'CHEM120': 4, 'BIO130': 4, 'HIST140': 4, 'ECON150': 0}],
   [153, 5, '153/5']),
  ('normal control 7',
   [[['s3', 'CHEM120'], ['s4', 'CHEM120'], ['s4', 'PHYS110'], ['s5', 'BIO130'], ['s5', 'PHYS110'],
     ['s3', 'CHEM120']],
    {'MATH101': 1, 'MATH101H': 6, 'PHYS110': 4, 'CHEM120': 7, 'BIO130': 1, 'HIST140': 7, 'ECON150': 5}],
   [8, 3, '8/3']),
  ('normal control 8',
   [[['s4', 'BIO130'], ['s4', 'MATH101H'], ['s2', 'MATH101H'], ['s1', 'CHEM120'], ['s2', 'MATH101'],
     ['s1', 'MATH101'], ['s5', 'CHEM120'], ['s4', 'CHEM120'], ['s4', 'HIST140'], ['s1', 'MATH101']],
    {'MATH101': 4, 'MATH101H': 2, 'PHYS110': 5, 'CHEM120': 1, 'BIO130': 4, 'HIST140': 0, 'ECON150': 3}],
   [66, 4, '33/2'])],
 [('regression: proximity window 1',
   [[['s1', 'MATH101'], ['s1', 'PHYS110'], ['s1', 'CHEM120'], ['s2', 'BIO130']],
    {'MATH101': 0, 'PHYS110': 0, 'CHEM120': 1, 'BIO130': 1}],
   [32, 2, '16']),
  ('regression variant: proximity window 2',
   [[['s2', 'CHEM120'], ['s2', 'ECON150'], ['s2', 'PHYS110'], ['s1', 'MATH101H'], ['s1', 'HIST140']],
    {'MATH101': 6, 'MATH101H': 5, 'PHYS110': 0, 'CHEM120': 5, 'BIO130': 6, 'HIST140': 5, 'ECON150': 1}],
   [19, 2, '19/2']),
  ('partial repair guard 3',
   [[['s4', 'MATH101'], ['s3', 'PHYS110'], ['s1', 'CHEM120'], ['s3', 'MATH101'], ['s5', 'CHEM120'],
     ['s1', 'MATH101H'], ['s4', 'MATH101H'], ['s4', 'ECON150']],
    {'MATH101': 3, 'MATH101H': 7, 'PHYS110': 7, 'CHEM120': 3, 'BIO130': 4, 'HIST140': 2, 'ECON150': 2}],
   [23, 4, '23/4']),
  ('boundary control 4', [[['s1', 'MATH101'], ['s1', 'PHYS110']], {'MATH101': 0, 'PHYS110': 1}],
   [16, 1, '16']),
  ('normal control 5',
   [[['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 6',
   [[['s4', 'BIO130'], ['s4', 'HIST140'], ['s3', 'MATH101H'], ['s5', 'HIST140'], ['s4', 'PHYS110']],
    {'MATH101': 4, 'MATH101H': 5, 'PHYS110': 0, 'CHEM120': 3, 'BIO130': 6, 'HIST140': 5, 'ECON150': 4}],
   [17, 3, '17/3']),
  ('normal control 7',
   [[['s4', 'MATH101H'], ['s4', 'BIO130'], ['s2', 'MATH101H'], ['s4', 'PHYS110'], ['s5', 'BIO130'],
     ['s4', 'MATH101'], ['s2', 'HIST140'], ['s2', 'BIO130']],
    {'MATH101': 4, 'MATH101H': 5, 'PHYS110': 0, 'CHEM120': 5, 'BIO130': 0, 'HIST140': 6, 'ECON150': 5}],
   [39, 3, '13']),
  ('normal control 8',
   [[['s4', 'MATH101'], ['s4', 'PHYS110']],
    {'MATH101': 5, 'MATH101H': 4, 'PHYS110': 5, 'CHEM120': 2, 'BIO130': 1, 'HIST140': 4, 'ECON150': 2}],
   [0, 1, '0'])],
 [('regression: proximity window 1',
   [[['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']),
  ('regression variant: proximity window 2',
   [[['s3', 'MATH101H'], ['s3', 'ECON150'], ['s5', 'BIO130'], ['s2', 'HIST140'], ['s1', 'MATH101'],
     ['s5', 'MATH101'], ['s2', 'CHEM120'], ['s3', 'CHEM120'], ['s1', 'PHYS110'], ['s5', 'MATH101H'],
     ['s5', 'ECON150'], ['s3', 'PHYS110']],
    {'MATH101': 6, 'MATH101H': 3, 'PHYS110': 6, 'CHEM120': 4, 'BIO130': 3, 'HIST140': 5, 'ECON150': 7}],
   [94, 4, '47/2']),
  ('partial repair guard 3',
   [[['s3', 'MATH101H'], ['s1', 'PHYS110'], ['s3', 'BIO130'], ['s3', 'HIST140'], ['s4', 'BIO130'],
     ['s2', 'ECON150'], ['s5', 'PHYS110'], ['s1', 'CHEM120'], ['s1', 'HIST140'], ['s2', 'PHYS110'],
     ['s5', 'MATH101H'], ['s3', 'PHYS110'], ['s1', 'ECON150']],
    {'MATH101': 7, 'MATH101H': 3, 'PHYS110': 1, 'CHEM120': 4, 'BIO130': 7, 'HIST140': 6, 'ECON150': 2}],
   [94, 5, '94/5']),
  ('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',
   [[['s3', 'MATH101H'], ['s2', 'MATH101'], ['s1', 'MATH101'], ['s4', 'CHEM120'], ['s4', 'PHYS110'],
     ['s4', 'HIST140'], ['s2', 'HIST140'], ['s4', 'HIST140'], ['s1', 'HIST140'], ['s3', 'MATH101'],
     ['s4', 'ECON150']],
    {'MATH101': 4, 'MATH101H': 5, 'PHYS110': 4, 'CHEM120': 3, 'BIO130': 0, 'HIST140': 2, 'ECON150': 0}],
   [86, 4, '43/2']),
  ('normal control 7',
   [[['s5', 'CHEM120'], ['s2', 'ECON150'], ['s5', 'BIO130'], ['s5', 'ECON150'], ['s1', 'MATH101H'],
     ['s4', 'ECON150'], ['s5', 'MATH101'], ['s1', 'HIST140'], ['s1', 'MATH101'], ['s4', 'BIO130'],
     ['s4', 'MATH101H'], ['s2', 'MATH101'], ['s4', 'MATH101'], ['s1', 'CHEM120'], ['s2', 'CHEM120'],
     ['s2', 'PHYS110']],
    {'MATH101': 4, 'MATH101H': 1, 'PHYS110': 1, 'CHEM120': 5, 'BIO130': 0, 'HIST140': 6, 'ECON150': 2}],
   [190, 4, '95/2']),
  ('normal control 8',
   [[['s5', 'ECON150'], ['s5', 'MATH101H'], ['s2', 'MATH101H'], ['s2', 'MATH101'], ['s4', 'BIO130'],
     ['s3', 'CHEM120'], ['s2', 'MATH101'], ['s4', 'PHYS110'], ['s2', 'ECON150'], ['s3', 'ECON150']],
    {'MATH101': 1, 'MATH101H': 3, 'PHYS110': 4, 'CHEM120': 2, 'BIO130': 6, 'HIST140': 4, 'ECON150': 5}],
   [38, 4, '19/2'])],
 [('regression: proximity window 1',
   [[['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']),
  ('regression variant: proximity window 2',
   [[['s4', 'MATH101H'], ['s3', 'MATH101'], ['s5', 'MATH101'], ['s3', 'BIO130'], ['s5', 'MATH101H'],
     ['s2', 'HIST140'], ['s5', 'HIST140'], ['s2', 'CHEM120'], ['s4', 'PHYS110'], ['s4', 'ECON150'],
     ['s1', 'MATH101'], ['s1', 'MATH101H']],
    {'MATH101': 2, 'MATH101H': 7, 'PHYS110': 5, 'CHEM120': 7, 'BIO130': 2, 'HIST140': 2, 'ECON150': 6}],
   [44, 5, '44/5']),
  ('partial repair guard 3',
   [[['s5', 'BIO130'], ['s5', 'MATH101H'], ['s3', 'MATH101H'], ['s1', 'MATH101'], ['s1', 'PHYS110'],
     ['s2', 'CHEM120'], ['s2', 'ECON150'], ['s5', 'PHYS110'], ['s3', 'CHEM120'], ['s1', 'HIST140'],
     ['s2', 'BIO130'], ['s4', 'ECON150'], ['s2', 'PHYS110']],
    {'MATH101': 6, 'MATH101H': 0, 'PHYS110': 2, 'CHEM120': 0, 'BIO130': 3, 'HIST140': 3, 'ECON150': 5}],
   [91, 5, '91/5']),
  ('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', 'CHEM120'], ['s2', 'HIST140'], ['s1', 'HIST140'], ['s2', 'ECON150'], ['s4', 'PHYS110'],
     ['s4', 'MATH101H'], ['s3', 'PHYS110'], ['s3', 'CHEM120'], ['s5', 'ECON150'], ['s3', 'CHEM120'],
     ['s3', 'HIST140'], ['s3', 'MATH101'], ['s4', 'MATH101'], ['s4', 'HIST140']],
    {'MATH101': 7, 'MATH101H': 3, 'PHYS110': 0, 'CHEM120': 4, 'BIO130': 3, 'HIST140': 4, 'ECON150': 4}],
   [40, 5, '8']),
  ('normal control 7',
   [[['s4', 'MATH101'], ['s4', 'PHYS110'], ['s5', 'PHYS110'], ['s3', 'PHYS110'], ['s2', 'CHEM120'],
     ['s3', 'CHEM120'], ['s5', 'CHEM120']],
    {'MATH101': 1, 'MATH101H': 3, 'PHYS110': 3, 'CHEM120': 0, 'BIO130': 3, 'HIST140': 0, 'ECON150': 1}],
   [16, 4, '4']),
  ('normal control 8',
   [[['s5', 'MATH101H'], ['s5', 'PHYS110'], ['s3', 'ECON150'], ['s3', 'PHYS110']],
    {'MATH101': 5, 'MATH101H': 2, 'PHYS110': 3, 'CHEM120': 6, 'BIO130': 1, 'HIST140': 6, 'ECON150': 7}],
   [18, 2, '9'])],
 [('regression: proximity window 1',
   [[['s5', 'PHYS110'], ['s4', 'ECON150'], ['s3', 'MATH101'], ['s3', 'PHYS110'], ['s2', 'CHEM120'],
     ['s2', 'ECON150'], ['s4', 'MATH101H'], ['s5', 'BIO130'], ['s4', 'HIST140'], ['s3', 'BIO130'],
     ['s4', 'PHYS110'], ['s3', 'ECON150'], ['s2', 'HIST140'], ['s5', 'MATH101'], ['s1', 'HIST140']],
    {'MATH101': 3, 'MATH101H': 0, 'PHYS110': 0, 'CHEM120': 6, 'BIO130': 0, 'HIST140': 0, 'ECON150': 2}],
   [82, 5, '82/5']),
  ('regression variant: proximity window 2',
   [[['s2', 'CHEM120'], ['s4', 'ECON150'], ['s4', 'CHEM120'], ['s4', 'HIST140'], ['s5', 'MATH101H'],
     ['s2', 'MATH101'], ['s5', 'ECON150'], ['s2', 'PHYS110'], ['s2', 'ECON150']],
    {'MATH101': 3, 'MATH101H': 3, 'PHYS110': 5, 'CHEM120': 6, 'BIO130': 2, 'HIST140': 4, 'ECON150': 5}],
   [100, 3, '100/3']),
  ('partial repair guard 3',
   [[['s1', 'MATH101H'], ['s5', 'HIST140'], ['s5', 'BIO130'], ['s1', 'MATH101'], ['s5', 'BIO130'],
     ['s5', 'MATH101']],
    {'MATH101': 7, 'MATH101H': 2, 'PHYS110': 7, 'CHEM120': 5, 'BIO130': 7, 'HIST140': 0, 'ECON150': 7}],
   [1, 2, '1/2']),
  ('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', 'ECON150'], ['s5', 'CHEM120'], ['s4', 'ECON150'], ['s1', 'HIST140'], ['s4', 'MATH101'],
     ['s4', 'MATH101'], ['s1', 'PHYS110']],
    {'MATH101': 1, 'MATH101H': 4, 'PHYS110': 6, 'CHEM120': 4, 'BIO130': 5, 'HIST140': 2, 'ECON150': 3}],
   [30, 3, '10']),
  ('normal control 7',
   [[['s4', 'BIO130'], ['s4', 'CHEM120'], ['s4', 'ECON150']],
    {'MATH101': 4, 'MATH101H': 4, 'PHYS110': 5, 'CHEM120': 4, 'BIO130': 4, 'HIST140': 1, 'ECON150': 5}],
   [32, 1, '32']),
  ('normal control 8',
   [[['s3', 'HIST140'], ['s3', 'MATH101'], ['s4', 'BIO130'], ['s4', 'MATH101'], ['s4', 'CHEM120'],
     ['s4', 'MATH101'], ['s1', 'HIST140'], ['s1', 'ECON150'], ['s1', 'MATH101'], ['s3', 'MATH101H'],
     ['s3', 'CHEM120']],
    {'MATH101': 6, 'MATH101H': 3, 'PHYS110': 7, 'CHEM120': 6, 'BIO130': 0, 'HIST140': 5, 'ECON150': 3}],
   [76, 3, '76/3'])]]
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: proximity window 1	`[0, 1, '0']`	`[0, 1, '0']`	Passed
regression variant: proximity window 2	`[14, 5, '14/5']`	`[14, 5, '14/5']`	Passed
partial repair guard 3	`[76, 3, '76/3']`	`[76, 3, '76/3']`	Passed
boundary control 4	`[0, 1, '0']`	`[0, 1, '0']`	Passed
normal control 5	`[49, 4, '49/4']`	`[49, 4, '49/4']`	Passed
normal control 6	`[153, 5, '153/5']`	`[153, 5, '153/5']`	Passed
normal control 7	`[8, 3, '8/3']`	`[8, 3, '8/3']`	Passed
normal control 8	`[66, 4, '33/2']`	`[66, 4, '33/2']`	Passed

SHA-256 / bafd980547c6a681cc49a582cc003405dbc5edef3c4c0f012d163913a983a73a

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 2026-09-29T14:52:04.172215+00:00.

Case digest / 6801cf80044279c4dd410873d8d8ae224e161e66f87a867a11c5040aef1fcb9a