FAILURE MAP
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FA-94371 / Exam timetabling constraints / Open access

Same-period clash counted as period spread · case 01

Clashing exams add a spread penalty on top of the clash.

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

ROOT CAUSE

The spread test includes a distance of zero.

THE FAILURE

The spread test includes a distance of zero.

Unsuccessful approach: An exclusive upper bound misses pairs exactly spread periods apart.

Case contract

Periods are numbered consecutively with spd slots per day (day = p // spd). For each student and each pair of their distinct exams: same day and adjacent periods counts two-in-a-row; same day and further apart counts two-in-a-day (same-period clashes count neither); periods 1..spread apart count period spread regardless of day. w = [row weight, day weight, spread]. Return [row, day, spread count, weighted total].

Why this case matters

Proximity soft constraints are what exam timetabling quality is judged on; each counter has its own boundary.

1 / The failure

Exit 1
"""Failure Map reference implementation. Python standard library only."""
import json

N = 1
observations = []
def solve(enrol, period, spd, w):
    wr, wd, spread = w
    by = {}
    for st, ex in enrol:
        by.setdefault(st, set()).add(ex)
    row = day = spr = 0
    for st in by:
        ps = sorted(period[e] for e in by[st])
        for i in range(len(ps)):
            for j in range(i + 1, len(ps)):
                a, b = ps[i], ps[j]
                if a // spd == b // spd:
                    if b - a == 1:
                        row += 1
                    elif b - a > 1:
                        day += 1
                if b - a <= spread:
                    spr += 1
    return [row, day, spr, row * wr + day * wd + spr]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('regression: clash not two in day 1',
   [[['s1', 'MATH101'], ['s1', 'PHYS110']], {'MATH101': 1, 'PHYS110': 1}, 3, [10, 2, 2]], [0, 0, 0, 0]),
  ('regression variant: clash not two in day 2',
   [[['s2', 'MATH101H'], ['s5', 'MATH101H'], ['s5', 'HIST140'], ['s3', 'MATH101H'], ['s3', 'ECON150'],
     ['s4', 'ECON150'], ['s4', 'HIST140'], ['s3', 'MATH101'], ['s1', 'BIO130']],
    {'MATH101': 4, 'MATH101H': 5, 'PHYS110': 4, 'CHEM120': 2, 'BIO130': 5, 'HIST140': 5, 'ECON150': 2}, 2,
    [10, 1, 2]],
   [1, 0, 2, 12]),
  ('partial repair guard 3',
   [[['s5', 'CHEM120'], ['s1', 'ECON150'], ['s5', 'BIO130'], ['s5', 'HIST140'], ['s1', 'PHYS110'],
     ['s4', 'PHYS110'], ['s5', 'MATH101H'], ['s2', 'MATH101H'], ['s3', 'CHEM120'], ['s5', 'BIO130'],
     ['s3', 'BIO130'], ['s3', 'MATH101H'], ['s4', 'HIST140'], ['s2', 'BIO130'], ['s4', 'MATH101'],
     ['s3', 'MATH101'], ['s2', 'PHYS110']],
    {'MATH101': 0, 'MATH101H': 2, 'PHYS110': 0, 'CHEM120': 5, 'BIO130': 1, 'HIST140': 3, 'ECON150': 5}, 2,
    [10, 3, 4]],
   [3, 0, 16, 46]),
  ('boundary control 4',
   [[['s1', 'MATH101'], ['s1', 'PHYS110']], {'MATH101': 0, 'PHYS110': 2}, 3, [10, 2, 2]], [0, 1, 1, 3]),
  ('normal control 5',
   [[['s2', 'ECON150'], ['s2', 'CHEM120'], ['s5', 'ECON150'], ['s3', 'MATH101H'], ['s5', 'MATH101'],
     ['s2', 'MATH101H'], ['s4', 'HIST140'], ['s1', 'MATH101'], ['s4', 'MATH101'], ['s5', 'BIO130'],
     ['s4', 'ECON150'], ['s2', 'HIST140']],
    {'MATH101': 0, 'MATH101H': 1, 'PHYS110': 4, 'CHEM120': 0, 'BIO130': 8, 'HIST140': 8, 'ECON150': 8}, 3,
    [10, 1, 2]],
   [1, 0, 1, 11]),
  ('normal control 6',
   [[['s3', 'BIO130'], ['s4', 'MATH101'], ['s5', 'ECON150'], ['s1', 'MATH101H'], ['s1', 'BIO130'],
     ['s5', 'PHYS110'], ['s5', 'BIO130']],
    {'MATH101': 1, 'MATH101H': 5, 'PHYS110': 4, 'CHEM120': 4, 'BIO130': 4, 'HIST140': 3, 'ECON150': 4}, 2,
    [10, 3, 2]],
   [1, 0, 1, 11]),
  ('normal control 7',
   [[['s4', 'MATH101H'], ['s2', 'MATH101'], ['s2', 'PHYS110'], ['s3', 'HIST140'], ['s4', 'BIO130'],
     ['s1', 'HIST140'], ['s5', 'HIST140'], ['s5', 'MATH101H'], ['s4', 'PHYS110'], ['s2', 'ECON150'],
     ['s3', 'MATH101H'], ['s4', 'ECON150']],
    {'MATH101': 1, 'MATH101H': 5, 'PHYS110': 5, 'CHEM120': 3, 'BIO130': 4, 'HIST140': 4, 'ECON150': 3}, 2,
    [5, 2, 1]],
   [4, 0, 5, 25]),
  ('normal control 8',
   [[['s1', 'ECON150'], ['s5', 'ECON150'], ['s3', 'ECON150'], ['s4', 'HIST140'], ['s1', 'CHEM120'],
     ['s4', 'ECON150'], ['s2', 'ECON150'], ['s2', 'PHYS110'], ['s2', 'HIST140'], ['s4', 'BIO130'],
     ['s2', 'MATH101H'], ['s5', 'MATH101H']],
    {'MATH101': 3, 'MATH101H': 5, 'PHYS110': 1, 'CHEM120': 1, 'BIO130': 4, 'HIST140': 3, 'ECON150': 4}, 3,
    [10, 1, 1]],
   [5, 1, 5, 56])],
 [('regression: clash not two in day 1',
   [[['s1', 'ECON150'], ['s2', 'MATH101'], ['s2', 'PHYS110'], ['s3', 'CHEM120'], ['s2', 'HIST140'],
     ['s1', 'ECON150'], ['s2', 'BIO130']],
    {'MATH101': 4, 'MATH101H': 0, 'PHYS110': 3, 'CHEM120': 4, 'BIO130': 3, 'HIST140': 1, 'ECON150': 2}, 2,
    [10, 3, 2]],
   [0, 0, 4, 4]),
  ('regression variant: clash not two in day 2',
   [[['s4', 'MATH101'], ['s2', 'HIST140'], ['s1', 'PHYS110'], ['s3', 'PHYS110'], ['s4', 'CHEM120'],
     ['s3', 'ECON150'], ['s3', 'BIO130'], ['s1', 'MATH101H'], ['s2', 'PHYS110'], ['s3', 'PHYS110'],
     ['s5', 'HIST140'], ['s1', 'CHEM120'], ['s1', 'ECON150'], ['s4', 'MATH101H'], ['s3', 'MATH101'],
     ['s4', 'PHYS110']],
    {'MATH101': 9, 'MATH101H': 7, 'PHYS110': 11, 'CHEM120': 8, 'BIO130': 0, 'HIST140': 7, 'ECON150': 0}, 4,
    [10, 1, 2]],
   [1, 4, 6, 20]),
  ('partial repair guard 3',
   [[['s1', 'CHEM120'], ['s1', 'MATH101']],
    {'MATH101': 6, 'MATH101H': 1, 'PHYS110': 5, 'CHEM120': 7, 'BIO130': 5, 'HIST140': 7, 'ECON150': 8}, 3,
    [10, 1, 1]],
   [1, 0, 1, 11]),
  ('boundary control 4',
   [[['s1', 'MATH101'], ['s1', 'PHYS110']], {'MATH101': 2, 'PHYS110': 3}, 4, [10, 2, 2]], [1, 0, 1, 11]),
  ('normal control 5',
   [[['s3', 'MATH101H'], ['s4', 'CHEM120'], ['s3', 'CHEM120'], ['s3', 'BIO130'], ['s5', 'MATH101H'],
     ['s5', 'MATH101'], ['s4', 'CHEM120'], ['s5', 'BIO130'], ['s2', 'MATH101']],
    {'MATH101': 11, 'MATH101H': 11, 'PHYS110': 5, 'CHEM120': 11, 'BIO130': 3, 'HIST140': 1, 'ECON150': 1}, 4,
    [5, 1, 1]],
   [0, 0, 0, 0]),
  ('normal control 6',
   [[['s1', 'HIST140'], ['s1', 'MATH101']],
    {'MATH101': 0, 'MATH101H': 1, 'PHYS110': 7, 'CHEM120': 1, 'BIO130': 1, 'HIST140': 3, 'ECON150': 8}, 3,
    [10, 2, 1]],
   [0, 0, 0, 0]),
  ('normal control 7',
   [[['s4', 'PHYS110'], ['s1', 'MATH101'], ['s1', 'MATH101H'], ['s1', 'BIO130']],
    {'MATH101': 1, 'MATH101H': 2, 'PHYS110': 3, 'CHEM120': 6, 'BIO130': 8, 'HIST140': 1, 'ECON150': 0}, 4,
    [10, 1, 4]],
   [1, 0, 1, 11]),
  ('normal control 8',
   [[['s3', 'MATH101'], ['s3', 'CHEM120'], ['s3', 'PHYS110'], ['s5', 'MATH101'], ['s3', 'HIST140'],
     ['s1', 'PHYS110'], ['s1', 'CHEM120'], ['s5', 'ECON150']],
    {'MATH101': 0, 'MATH101H': 5, 'PHYS110': 1, 'CHEM120': 7, 'BIO130': 6, 'HIST140': 3, 'ECON150': 6}, 3,
    [5, 3, 4]],
   [1, 0, 4, 9])],
 [('regression: clash not two in day 1',
   [[['s2', 'HIST140'], ['s1', 'PHYS110'], ['s1', 'BIO130'], ['s2', 'BIO130'], ['s1', 'HIST140'],
     ['s2', 'MATH101H'], ['s2', 'MATH101'], ['s2', 'BIO130']],
    {'MATH101': 2, 'MATH101H': 7, 'PHYS110': 6, 'CHEM120': 4, 'BIO130': 1, 'HIST140': 7, 'ECON150': 8}, 3,
    [5, 2, 4]],
   [2, 0, 2, 12]),
  ('regression variant: clash not two in day 2',
   [[['s3', 'ECON150'], ['s1', 'MATH101'], ['s1', 'ECON150'], ['s3', 'HIST140'], ['s3', 'BIO130'],
     ['s4', 'ECON150'], ['s4', 'ECON150'], ['s4', 'MATH101H'], ['s3', 'CHEM120'], ['s2', 'ECON150'],
     ['s1', 'HIST140'], ['s1', 'BIO130']],
    {'MATH101': 5, 'MATH101H': 0, 'PHYS110': 1, 'CHEM120': 3, 'BIO130': 4, 'HIST140': 0, 'ECON150': 4}, 2,
    [5, 1, 2]],
   [2, 0, 4, 14]),
  ('partial repair guard 3',
   [[['s4', 'MATH101'], ['s2', 'HIST140'], ['s1', 'PHYS110'], ['s3', 'PHYS110'], ['s4', 'CHEM120'],
     ['s3', 'ECON150'], ['s3', 'BIO130'], ['s1', 'MATH101H'], ['s2', 'PHYS110'], ['s3', 'PHYS110'],
     ['s5', 'HIST140'], ['s1', 'CHEM120'], ['s1', 'ECON150'], ['s4', 'MATH101H'], ['s3', 'MATH101'],
     ['s4', 'PHYS110']],
    {'MATH101': 9, 'MATH101H': 7, 'PHYS110': 11, 'CHEM120': 8, 'BIO130': 0, 'HIST140': 7, 'ECON150': 0}, 4,
    [10, 1, 2]],
   [1, 4, 6, 20]),
  ('boundary control 4',
   [[['s1', 'MATH101'], ['s1', 'PHYS110']], {'MATH101': 0, 'PHYS110': 4}, 3, [10, 2, 4]], [0, 0, 1, 1]),
  ('normal control 5',
   [[['s1', 'HIST140'], ['s1', 'HIST140']],
    {'MATH101': 3, 'MATH101H': 5, 'PHYS110': 2, 'CHEM120': 3, 'BIO130': 3, 'HIST140': 3, 'ECON150': 2}, 2,
    [10, 2, 2]],
   [0, 0, 0, 0]),
  ('normal control 6',
   [[['s2', 'HIST140'], ['s5', 'BIO130'], ['s1', 'PHYS110'], ['s5', 'HIST140'], ['s5', 'MATH101'],
     ['s5', 'CHEM120'], ['s4', 'HIST140'], ['s2', 'ECON150'], ['s2', 'PHYS110'], ['s1', 'ECON150'],
     ['s4', 'BIO130'], ['s4', 'ECON150'], ['s4', 'PHYS110']],
    {'MATH101': 1, 'MATH101H': 0, 'PHYS110': 1, 'CHEM120': 10, 'BIO130': 6, 'HIST140': 10, 'ECON150': 8}, 4,
    [5, 3, 1]],
   [0, 2, 0, 6]),
  ('normal control 7',
   [[['s2', 'HIST140'], ['s5', 'CHEM120'], ['s5', 'ECON150'], ['s4', 'MATH101'], ['s1', 'BIO130'],
     ['s2', 'BIO130'], ['s5', 'MATH101H'], ['s4', 'PHYS110'], ['s1', 'ECON150'], ['s5', 'HIST140'],
     ['s1', 'MATH101'], ['s1', 'PHYS110']],
    {'MATH101': 2, 'MATH101H': 3, 'PHYS110': 4, 'CHEM120': 2, 'BIO130': 0, 'HIST140': 5, 'ECON150': 1}, 2,
    [5, 1, 1]],
   [2, 0, 4, 14]),
  ('normal control 8',
   [[['s2', 'PHYS110'], ['s2', 'CHEM120'], ['s2', 'PHYS110']],
    {'MATH101': 4, 'MATH101H': 10, 'PHYS110': 8, 'CHEM120': 10, 'BIO130': 6, 'HIST140': 5, 'ECON150': 3}, 4,
    [10, 3, 4]],
   [0, 1, 1, 4])],
 [('regression: clash not two in day 1',
   [[['s5', 'BIO130'], ['s1', 'HIST140'], ['s5', 'PHYS110'], ['s1', 'BIO130'], ['s1', 'HIST140'],
     ['s5', 'ECON150']],
    {'MATH101': 5, 'MATH101H': 3, 'PHYS110': 4, 'CHEM120': 2, 'BIO130': 0, 'HIST140': 0, 'ECON150': 3}, 2,
    [10, 3, 1]],
   [0, 0, 1, 1]),
  ('regression variant: clash not two in day 2',
   [[['s4', 'MATH101H'], ['s2', 'MATH101H'], ['s5', 'BIO130'], ['s1', 'BIO130'], ['s3', 'MATH101H'],
     ['s5', 'MATH101'], ['s2', 'CHEM120'], ['s3', 'MATH101'], ['s1', 'CHEM120'], ['s1', 'ECON150'],
     ['s1', 'HIST140'], ['s4', 'HIST140'], ['s4', 'CHEM120']],
    {'MATH101': 2, 'MATH101H': 1, 'PHYS110': 0, 'CHEM120': 5, 'BIO130': 5, 'HIST140': 4, 'ECON150': 4}, 2,
    [10, 2, 2]],
   [5, 0, 6, 56]),
  ('partial repair guard 3',
   [[['s1', 'MATH101H'], ['s1', 'HIST140'], ['s1', 'MATH101'], ['s1', 'PHYS110']],
    {'MATH101': 0, 'MATH101H': 2, 'PHYS110': 3, 'CHEM120': 5, 'BIO130': 5, 'HIST140': 2, 'ECON150': 1}, 2,
    [5, 2, 1]],
   [2, 0, 2, 12]),
  ('boundary control 4',
   [[['s1', 'MATH101'], ['s1', 'PHYS110']], {'MATH101': 1, 'PHYS110': 1}, 3, [10, 2, 2]], [0, 0, 0, 0]),
  ('normal control 5',
   [[['s5', 'BIO130'], ['s5', 'PHYS110'], ['s5', 'BIO130']],
    {'MATH101': 3, 'MATH101H': 4, 'PHYS110': 1, 'CHEM120': 1, 'BIO130': 0, 'HIST140': 4, 'ECON150': 4}, 2,
    [5, 3, 4]],
   [1, 0, 1, 6]),
  ('normal control 6',
   [[['s3', 'PHYS110'], ['s3', 'MATH101H'], ['s3', 'MATH101']],
    {'MATH101': 3, 'MATH101H': 5, 'PHYS110': 6, 'CHEM120': 3, 'BIO130': 5, 'HIST140': 2, 'ECON150': 6}, 3,
    [5, 1, 2]],
   [0, 1, 2, 3]),
  ('normal control 7',
   [[['s2', 'CHEM120'], ['s2', 'MATH101']],
    {'MATH101': 3, 'MATH101H': 5, 'PHYS110': 3, 'CHEM120': 4, 'BIO130': 2, 'HIST140': 4, 'ECON150': 7}, 3,
    [5, 3, 2]],
   [1, 0, 1, 6]),
  ('normal control 8',
   [[['s3', 'PHYS110'], ['s3', 'MATH101'], ['s3', 'HIST140'], ['s3', 'MATH101H'], ['s2', 'MATH101'],
     ['s2', 'BIO130']],
    {'MATH101': 9, 'MATH101H': 0, 'PHYS110': 10, 'CHEM120': 4, 'BIO130': 1, 'HIST140': 9, 'ECON150': 2}, 4,
    [10, 1, 2]],
   [2, 0, 2, 22])],
 [('regression: clash not two in day 1',
   [[['s5', 'MATH101'], ['s5', 'HIST140'], ['s5', 'MATH101H'], ['s2', 'MATH101H'], ['s2', 'PHYS110'],
     ['s3', 'MATH101'], ['s1', 'CHEM120'], ['s1', 'MATH101'], ['s4', 'CHEM120'], ['s3', 'PHYS110'],
     ['s5', 'PHYS110'], ['s3', 'HIST140'], ['s3', 'PHYS110']],
    {'MATH101': 9, 'MATH101H': 5, 'PHYS110': 1, 'CHEM120': 7, 'BIO130': 10, 'HIST140': 9, 'ECON150': 1}, 4,
    [5, 1, 1]],
   [0, 0, 0, 0]),
  ('regression variant: clash not two in day 2',
   [[['s2', 'ECON150'], ['s1', 'PHYS110'], ['s1', 'MATH101H'], ['s1', 'HIST140'], ['s2', 'MATH101H'],
     ['s1', 'MATH101H'], ['s2', 'PHYS110']],
    {'MATH101': 6, 'MATH101H': 8, 'PHYS110': 7, 'CHEM120': 4, 'BIO130': 6, 'HIST140': 8, 'ECON150': 2}, 3,
    [5, 3, 2]],
   [3, 0, 3, 18]),
  ('partial repair guard 3',
   [[['s2', 'CHEM120'], ['s5', 'BIO130'], ['s2', 'PHYS110'], ['s2', 'MATH101H'], ['s5', 'MATH101'],
     ['s2', 'HIST140'], ['s3', 'MATH101'], ['s1', 'MATH101H'], ['s5', 'HIST140'], ['s3', 'ECON150']],
    {'MATH101': 3, 'MATH101H': 1, 'PHYS110': 5, 'CHEM120': 5, 'BIO130': 11, 'HIST140': 7, 'ECON150': 2}, 4,
    [10, 3, 1]],
   [1, 2, 1, 17]),
  ('boundary control 4',
   [[['s1', 'MATH101'], ['s1', 'PHYS110']], {'MATH101': 2, 'PHYS110': 3}, 3, [10, 2, 2]], [0, 0, 1, 1]),
  ('normal control 5',
   [[['s5', 'MATH101'], ['s3', 'CHEM120'], ['s5', 'BIO130'], ['s2', 'ECON150'], ['s2', 'HIST140'],
     ['s4', 'PHYS110'], ['s5', 'MATH101H'], ['s4', 'MATH101'], ['s5', 'MATH101'], ['s5', 'HIST140'],
     ['s3', 'HIST140']],
    {'MATH101': 3, 'MATH101H': 7, 'PHYS110': 5, 'CHEM120': 7, 'BIO130': 4, 'HIST140': 8, 'ECON150': 1}, 3,
    [10, 1, 1]],
   [3, 1, 3, 34]),
  ('normal control 6',
   [[['s4', 'MATH101'], ['s1', 'ECON150'], ['s4', 'BIO130'], ['s5', 'PHYS110'], ['s1', 'MATH101H'],
     ['s2', 'CHEM120'], ['s2', 'ECON150'], ['s5', 'HIST140'], ['s1', 'CHEM120'], ['s2', 'ECON150'],
     ['s4', 'PHYS110'], ['s3', 'ECON150'], ['s1', 'PHYS110'], ['s3', 'PHYS110']],
    {'MATH101': 3, 'MATH101H': 3, 'PHYS110': 3, 'CHEM120': 1, 'BIO130': 3, 'HIST140': 4, 'ECON150': 2}, 2,
    [5, 3, 2]],
   [3, 0, 8, 23]),
  ('normal control 7',
   [[['s2', 'ECON150'], ['s5', 'ECON150'], ['s5', 'PHYS110'], ['s4', 'ECON150'], ['s2', 'CHEM120'],
     ['s4', 'MATH101'], ['s5', 'MATH101H'], ['s2', 'MATH101'], ['s4', 'HIST140'], ['s2', 'BIO130'],
     ['s3', 'ECON150'], ['s5', 'BIO130'], ['s3', 'MATH101H'], ['s3', 'MATH101'], ['s4', 'BIO130'],
     ['s1', 'ECON150']],
    {'MATH101': 2, 'MATH101H': 5, 'PHYS110': 4, 'CHEM120': 3, 'BIO130': 4, 'HIST140': 3, 'ECON150': 0}, 2,
    [5, 1, 4]],
   [4, 0, 18, 38]),
  ('normal control 8',
   [[['s5', 'CHEM120'], ['s1', 'ECON150'], ['s5', 'BIO130'], ['s5', 'HIST140'], ['s1', 'PHYS110'],
     ['s4', 'PHYS110'], ['s5', 'MATH101H'], ['s2', 'MATH101H'], ['s3', 'CHEM120'], ['s5', 'BIO130'],
     ['s3', 'BIO130'], ['s3', 'MATH101H'], ['s4', 'HIST140'], ['s2', 'BIO130'], ['s4', 'MATH101'],
     ['s3', 'MATH101'], ['s2', 'PHYS110']],
    {'MATH101': 0, 'MATH101H': 2, 'PHYS110': 0, 'CHEM120': 5, 'BIO130': 1, 'HIST140': 3, 'ECON150': 5}, 2,
    [10, 3, 4]],
   [3, 0, 16, 46])]]
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 fixtureActualExpectedOutcome
regression: clash not two in day 1[0, 0, 1, 1][0, 0, 0, 0]Failed
regression variant: clash not two in day 2[1, 0, 3, 13][1, 0, 2, 12]Failed
partial repair guard 3[3, 0, 17, 47][3, 0, 16, 46]Failed
boundary control 4[0, 1, 1, 3][0, 1, 1, 3]Passed
normal control 5[1, 0, 4, 14][1, 0, 1, 11]Failed
normal control 6[1, 0, 4, 14][1, 0, 1, 11]Failed
normal control 7[4, 0, 6, 26][4, 0, 5, 25]Failed
normal control 8[5, 1, 6, 57][5, 1, 5, 56]Failed

SHA-256 / 59f443517914c8491f77a6cb9c6ddb58004ae42d90cce8bd00c93be52feec686

2 / The unsuccessful fix

Exit 1
"""Failure Map reference implementation. Python standard library only."""
import json

N = 1
observations = []
def solve(enrol, period, spd, w):
    wr, wd, spread = w
    by = {}
    for st, ex in enrol:
        by.setdefault(st, set()).add(ex)
    row = day = spr = 0
    for st in by:
        ps = sorted(period[e] for e in by[st])
        for i in range(len(ps)):
            for j in range(i + 1, len(ps)):
                a, b = ps[i], ps[j]
                if a // spd == b // spd:
                    if b - a == 1:
                        row += 1
                    elif b - a > 1:
                        day += 1
                if 0 < b - a < spread:
                    spr += 1
    return [row, day, spr, row * wr + day * wd + spr]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('regression: clash not two in day 1',
   [[['s1', 'MATH101'], ['s1', 'PHYS110']], {'MATH101': 1, 'PHYS110': 1}, 3, [10, 2, 2]], [0, 0, 0, 0]),
  ('regression variant: clash not two in day 2',
   [[['s2', 'MATH101H'], ['s5', 'MATH101H'], ['s5', 'HIST140'], ['s3', 'MATH101H'], ['s3', 'ECON150'],
     ['s4', 'ECON150'], ['s4', 'HIST140'], ['s3', 'MATH101'], ['s1', 'BIO130']],
    {'MATH101': 4, 'MATH101H': 5, 'PHYS110': 4, 'CHEM120': 2, 'BIO130': 5, 'HIST140': 5, 'ECON150': 2}, 2,
    [10, 1, 2]],
   [1, 0, 2, 12]),
  ('partial repair guard 3',
   [[['s5', 'CHEM120'], ['s1', 'ECON150'], ['s5', 'BIO130'], ['s5', 'HIST140'], ['s1', 'PHYS110'],
     ['s4', 'PHYS110'], ['s5', 'MATH101H'], ['s2', 'MATH101H'], ['s3', 'CHEM120'], ['s5', 'BIO130'],
     ['s3', 'BIO130'], ['s3', 'MATH101H'], ['s4', 'HIST140'], ['s2', 'BIO130'], ['s4', 'MATH101'],
     ['s3', 'MATH101'], ['s2', 'PHYS110']],
    {'MATH101': 0, 'MATH101H': 2, 'PHYS110': 0, 'CHEM120': 5, 'BIO130': 1, 'HIST140': 3, 'ECON150': 5}, 2,
    [10, 3, 4]],
   [3, 0, 16, 46]),
  ('boundary control 4',
   [[['s1', 'MATH101'], ['s1', 'PHYS110']], {'MATH101': 0, 'PHYS110': 2}, 3, [10, 2, 2]], [0, 1, 1, 3]),
  ('normal control 5',
   [[['s2', 'ECON150'], ['s2', 'CHEM120'], ['s5', 'ECON150'], ['s3', 'MATH101H'], ['s5', 'MATH101'],
     ['s2', 'MATH101H'], ['s4', 'HIST140'], ['s1', 'MATH101'], ['s4', 'MATH101'], ['s5', 'BIO130'],
     ['s4', 'ECON150'], ['s2', 'HIST140']],
    {'MATH101': 0, 'MATH101H': 1, 'PHYS110': 4, 'CHEM120': 0, 'BIO130': 8, 'HIST140': 8, 'ECON150': 8}, 3,
    [10, 1, 2]],
   [1, 0, 1, 11]),
  ('normal control 6',
   [[['s3', 'BIO130'], ['s4', 'MATH101'], ['s5', 'ECON150'], ['s1', 'MATH101H'], ['s1', 'BIO130'],
     ['s5', 'PHYS110'], ['s5', 'BIO130']],
    {'MATH101': 1, 'MATH101H': 5, 'PHYS110': 4, 'CHEM120': 4, 'BIO130': 4, 'HIST140': 3, 'ECON150': 4}, 2,
    [10, 3, 2]],
   [1, 0, 1, 11]),
  ('normal control 7',
   [[['s4', 'MATH101H'], ['s2', 'MATH101'], ['s2', 'PHYS110'], ['s3', 'HIST140'], ['s4', 'BIO130'],
     ['s1', 'HIST140'], ['s5', 'HIST140'], ['s5', 'MATH101H'], ['s4', 'PHYS110'], ['s2', 'ECON150'],
     ['s3', 'MATH101H'], ['s4', 'ECON150']],
    {'MATH101': 1, 'MATH101H': 5, 'PHYS110': 5, 'CHEM120': 3, 'BIO130': 4, 'HIST140': 4, 'ECON150': 3}, 2,
    [5, 2, 1]],
   [4, 0, 5, 25]),
  ('normal control 8',
   [[['s1', 'ECON150'], ['s5', 'ECON150'], ['s3', 'ECON150'], ['s4', 'HIST140'], ['s1', 'CHEM120'],
     ['s4', 'ECON150'], ['s2', 'ECON150'], ['s2', 'PHYS110'], ['s2', 'HIST140'], ['s4', 'BIO130'],
     ['s2', 'MATH101H'], ['s5', 'MATH101H']],
    {'MATH101': 3, 'MATH101H': 5, 'PHYS110': 1, 'CHEM120': 1, 'BIO130': 4, 'HIST140': 3, 'ECON150': 4}, 3,
    [10, 1, 1]],
   [5, 1, 5, 56])],
 [('regression: clash not two in day 1',
   [[['s1', 'ECON150'], ['s2', 'MATH101'], ['s2', 'PHYS110'], ['s3', 'CHEM120'], ['s2', 'HIST140'],
     ['s1', 'ECON150'], ['s2', 'BIO130']],
    {'MATH101': 4, 'MATH101H': 0, 'PHYS110': 3, 'CHEM120': 4, 'BIO130': 3, 'HIST140': 1, 'ECON150': 2}, 2,
    [10, 3, 2]],
   [0, 0, 4, 4]),
  ('regression variant: clash not two in day 2',
   [[['s4', 'MATH101'], ['s2', 'HIST140'], ['s1', 'PHYS110'], ['s3', 'PHYS110'], ['s4', 'CHEM120'],
     ['s3', 'ECON150'], ['s3', 'BIO130'], ['s1', 'MATH101H'], ['s2', 'PHYS110'], ['s3', 'PHYS110'],
     ['s5', 'HIST140'], ['s1', 'CHEM120'], ['s1', 'ECON150'], ['s4', 'MATH101H'], ['s3', 'MATH101'],
     ['s4', 'PHYS110']],
    {'MATH101': 9, 'MATH101H': 7, 'PHYS110': 11, 'CHEM120': 8, 'BIO130': 0, 'HIST140': 7, 'ECON150': 0}, 4,
    [10, 1, 2]],
   [1, 4, 6, 20]),
  ('partial repair guard 3',
   [[['s1', 'CHEM120'], ['s1', 'MATH101']],
    {'MATH101': 6, 'MATH101H': 1, 'PHYS110': 5, 'CHEM120': 7, 'BIO130': 5, 'HIST140': 7, 'ECON150': 8}, 3,
    [10, 1, 1]],
   [1, 0, 1, 11]),
  ('boundary control 4',
   [[['s1', 'MATH101'], ['s1', 'PHYS110']], {'MATH101': 2, 'PHYS110': 3}, 4, [10, 2, 2]], [1, 0, 1, 11]),
  ('normal control 5',
   [[['s3', 'MATH101H'], ['s4', 'CHEM120'], ['s3', 'CHEM120'], ['s3', 'BIO130'], ['s5', 'MATH101H'],
     ['s5', 'MATH101'], ['s4', 'CHEM120'], ['s5', 'BIO130'], ['s2', 'MATH101']],
    {'MATH101': 11, 'MATH101H': 11, 'PHYS110': 5, 'CHEM120': 11, 'BIO130': 3, 'HIST140': 1, 'ECON150': 1}, 4,
    [5, 1, 1]],
   [0, 0, 0, 0]),
  ('normal control 6',
   [[['s1', 'HIST140'], ['s1', 'MATH101']],
    {'MATH101': 0, 'MATH101H': 1, 'PHYS110': 7, 'CHEM120': 1, 'BIO130': 1, 'HIST140': 3, 'ECON150': 8}, 3,
    [10, 2, 1]],
   [0, 0, 0, 0]),
  ('normal control 7',
   [[['s4', 'PHYS110'], ['s1', 'MATH101'], ['s1', 'MATH101H'], ['s1', 'BIO130']],
    {'MATH101': 1, 'MATH101H': 2, 'PHYS110': 3, 'CHEM120': 6, 'BIO130': 8, 'HIST140': 1, 'ECON150': 0}, 4,
    [10, 1, 4]],
   [1, 0, 1, 11]),
  ('normal control 8',
   [[['s3', 'MATH101'], ['s3', 'CHEM120'], ['s3', 'PHYS110'], ['s5', 'MATH101'], ['s3', 'HIST140'],
     ['s1', 'PHYS110'], ['s1', 'CHEM120'], ['s5', 'ECON150']],
    {'MATH101': 0, 'MATH101H': 5, 'PHYS110': 1, 'CHEM120': 7, 'BIO130': 6, 'HIST140': 3, 'ECON150': 6}, 3,
    [5, 3, 4]],
   [1, 0, 4, 9])],
 [('regression: clash not two in day 1',
   [[['s2', 'HIST140'], ['s1', 'PHYS110'], ['s1', 'BIO130'], ['s2', 'BIO130'], ['s1', 'HIST140'],
     ['s2', 'MATH101H'], ['s2', 'MATH101'], ['s2', 'BIO130']],
    {'MATH101': 2, 'MATH101H': 7, 'PHYS110': 6, 'CHEM120': 4, 'BIO130': 1, 'HIST140': 7, 'ECON150': 8}, 3,
    [5, 2, 4]],
   [2, 0, 2, 12]),
  ('regression variant: clash not two in day 2',
   [[['s3', 'ECON150'], ['s1', 'MATH101'], ['s1', 'ECON150'], ['s3', 'HIST140'], ['s3', 'BIO130'],
     ['s4', 'ECON150'], ['s4', 'ECON150'], ['s4', 'MATH101H'], ['s3', 'CHEM120'], ['s2', 'ECON150'],
     ['s1', 'HIST140'], ['s1', 'BIO130']],
    {'MATH101': 5, 'MATH101H': 0, 'PHYS110': 1, 'CHEM120': 3, 'BIO130': 4, 'HIST140': 0, 'ECON150': 4}, 2,
    [5, 1, 2]],
   [2, 0, 4, 14]),
  ('partial repair guard 3',
   [[['s4', 'MATH101'], ['s2', 'HIST140'], ['s1', 'PHYS110'], ['s3', 'PHYS110'], ['s4', 'CHEM120'],
     ['s3', 'ECON150'], ['s3', 'BIO130'], ['s1', 'MATH101H'], ['s2', 'PHYS110'], ['s3', 'PHYS110'],
     ['s5', 'HIST140'], ['s1', 'CHEM120'], ['s1', 'ECON150'], ['s4', 'MATH101H'], ['s3', 'MATH101'],
     ['s4', 'PHYS110']],
    {'MATH101': 9, 'MATH101H': 7, 'PHYS110': 11, 'CHEM120': 8, 'BIO130': 0, 'HIST140': 7, 'ECON150': 0}, 4,
    [10, 1, 2]],
   [1, 4, 6, 20]),
  ('boundary control 4',
   [[['s1', 'MATH101'], ['s1', 'PHYS110']], {'MATH101': 0, 'PHYS110': 4}, 3, [10, 2, 4]], [0, 0, 1, 1]),
  ('normal control 5',
   [[['s1', 'HIST140'], ['s1', 'HIST140']],
    {'MATH101': 3, 'MATH101H': 5, 'PHYS110': 2, 'CHEM120': 3, 'BIO130': 3, 'HIST140': 3, 'ECON150': 2}, 2,
    [10, 2, 2]],
   [0, 0, 0, 0]),
  ('normal control 6',
   [[['s2', 'HIST140'], ['s5', 'BIO130'], ['s1', 'PHYS110'], ['s5', 'HIST140'], ['s5', 'MATH101'],
     ['s5', 'CHEM120'], ['s4', 'HIST140'], ['s2', 'ECON150'], ['s2', 'PHYS110'], ['s1', 'ECON150'],
     ['s4', 'BIO130'], ['s4', 'ECON150'], ['s4', 'PHYS110']],
    {'MATH101': 1, 'MATH101H': 0, 'PHYS110': 1, 'CHEM120': 10, 'BIO130': 6, 'HIST140': 10, 'ECON150': 8}, 4,
    [5, 3, 1]],
   [0, 2, 0, 6]),
  ('normal control 7',
   [[['s2', 'HIST140'], ['s5', 'CHEM120'], ['s5', 'ECON150'], ['s4', 'MATH101'], ['s1', 'BIO130'],
     ['s2', 'BIO130'], ['s5', 'MATH101H'], ['s4', 'PHYS110'], ['s1', 'ECON150'], ['s5', 'HIST140'],
     ['s1', 'MATH101'], ['s1', 'PHYS110']],
    {'MATH101': 2, 'MATH101H': 3, 'PHYS110': 4, 'CHEM120': 2, 'BIO130': 0, 'HIST140': 5, 'ECON150': 1}, 2,
    [5, 1, 1]],
   [2, 0, 4, 14]),
  ('normal control 8',
   [[['s2', 'PHYS110'], ['s2', 'CHEM120'], ['s2', 'PHYS110']],
    {'MATH101': 4, 'MATH101H': 10, 'PHYS110': 8, 'CHEM120': 10, 'BIO130': 6, 'HIST140': 5, 'ECON150': 3}, 4,
    [10, 3, 4]],
   [0, 1, 1, 4])],
 [('regression: clash not two in day 1',
   [[['s5', 'BIO130'], ['s1', 'HIST140'], ['s5', 'PHYS110'], ['s1', 'BIO130'], ['s1', 'HIST140'],
     ['s5', 'ECON150']],
    {'MATH101': 5, 'MATH101H': 3, 'PHYS110': 4, 'CHEM120': 2, 'BIO130': 0, 'HIST140': 0, 'ECON150': 3}, 2,
    [10, 3, 1]],
   [0, 0, 1, 1]),
  ('regression variant: clash not two in day 2',
   [[['s4', 'MATH101H'], ['s2', 'MATH101H'], ['s5', 'BIO130'], ['s1', 'BIO130'], ['s3', 'MATH101H'],
     ['s5', 'MATH101'], ['s2', 'CHEM120'], ['s3', 'MATH101'], ['s1', 'CHEM120'], ['s1', 'ECON150'],
     ['s1', 'HIST140'], ['s4', 'HIST140'], ['s4', 'CHEM120']],
    {'MATH101': 2, 'MATH101H': 1, 'PHYS110': 0, 'CHEM120': 5, 'BIO130': 5, 'HIST140': 4, 'ECON150': 4}, 2,
    [10, 2, 2]],
   [5, 0, 6, 56]),
  ('partial repair guard 3',
   [[['s1', 'MATH101H'], ['s1', 'HIST140'], ['s1', 'MATH101'], ['s1', 'PHYS110']],
    {'MATH101': 0, 'MATH101H': 2, 'PHYS110': 3, 'CHEM120': 5, 'BIO130': 5, 'HIST140': 2, 'ECON150': 1}, 2,
    [5, 2, 1]],
   [2, 0, 2, 12]),
  ('boundary control 4',
   [[['s1', 'MATH101'], ['s1', 'PHYS110']], {'MATH101': 1, 'PHYS110': 1}, 3, [10, 2, 2]], [0, 0, 0, 0]),
  ('normal control 5',
   [[['s5', 'BIO130'], ['s5', 'PHYS110'], ['s5', 'BIO130']],
    {'MATH101': 3, 'MATH101H': 4, 'PHYS110': 1, 'CHEM120': 1, 'BIO130': 0, 'HIST140': 4, 'ECON150': 4}, 2,
    [5, 3, 4]],
   [1, 0, 1, 6]),
  ('normal control 6',
   [[['s3', 'PHYS110'], ['s3', 'MATH101H'], ['s3', 'MATH101']],
    {'MATH101': 3, 'MATH101H': 5, 'PHYS110': 6, 'CHEM120': 3, 'BIO130': 5, 'HIST140': 2, 'ECON150': 6}, 3,
    [5, 1, 2]],
   [0, 1, 2, 3]),
  ('normal control 7',
   [[['s2', 'CHEM120'], ['s2', 'MATH101']],
    {'MATH101': 3, 'MATH101H': 5, 'PHYS110': 3, 'CHEM120': 4, 'BIO130': 2, 'HIST140': 4, 'ECON150': 7}, 3,
    [5, 3, 2]],
   [1, 0, 1, 6]),
  ('normal control 8',
   [[['s3', 'PHYS110'], ['s3', 'MATH101'], ['s3', 'HIST140'], ['s3', 'MATH101H'], ['s2', 'MATH101'],
     ['s2', 'BIO130']],
    {'MATH101': 9, 'MATH101H': 0, 'PHYS110': 10, 'CHEM120': 4, 'BIO130': 1, 'HIST140': 9, 'ECON150': 2}, 4,
    [10, 1, 2]],
   [2, 0, 2, 22])],
 [('regression: clash not two in day 1',
   [[['s5', 'MATH101'], ['s5', 'HIST140'], ['s5', 'MATH101H'], ['s2', 'MATH101H'], ['s2', 'PHYS110'],
     ['s3', 'MATH101'], ['s1', 'CHEM120'], ['s1', 'MATH101'], ['s4', 'CHEM120'], ['s3', 'PHYS110'],
     ['s5', 'PHYS110'], ['s3', 'HIST140'], ['s3', 'PHYS110']],
    {'MATH101': 9, 'MATH101H': 5, 'PHYS110': 1, 'CHEM120': 7, 'BIO130': 10, 'HIST140': 9, 'ECON150': 1}, 4,
    [5, 1, 1]],
   [0, 0, 0, 0]),
  ('regression variant: clash not two in day 2',
   [[['s2', 'ECON150'], ['s1', 'PHYS110'], ['s1', 'MATH101H'], ['s1', 'HIST140'], ['s2', 'MATH101H'],
     ['s1', 'MATH101H'], ['s2', 'PHYS110']],
    {'MATH101': 6, 'MATH101H': 8, 'PHYS110': 7, 'CHEM120': 4, 'BIO130': 6, 'HIST140': 8, 'ECON150': 2}, 3,
    [5, 3, 2]],
   [3, 0, 3, 18]),
  ('partial repair guard 3',
   [[['s2', 'CHEM120'], ['s5', 'BIO130'], ['s2', 'PHYS110'], ['s2', 'MATH101H'], ['s5', 'MATH101'],
     ['s2', 'HIST140'], ['s3', 'MATH101'], ['s1', 'MATH101H'], ['s5', 'HIST140'], ['s3', 'ECON150']],
    {'MATH101': 3, 'MATH101H': 1, 'PHYS110': 5, 'CHEM120': 5, 'BIO130': 11, 'HIST140': 7, 'ECON150': 2}, 4,
    [10, 3, 1]],
   [1, 2, 1, 17]),
  ('boundary control 4',
   [[['s1', 'MATH101'], ['s1', 'PHYS110']], {'MATH101': 2, 'PHYS110': 3}, 3, [10, 2, 2]], [0, 0, 1, 1]),
  ('normal control 5',
   [[['s5', 'MATH101'], ['s3', 'CHEM120'], ['s5', 'BIO130'], ['s2', 'ECON150'], ['s2', 'HIST140'],
     ['s4', 'PHYS110'], ['s5', 'MATH101H'], ['s4', 'MATH101'], ['s5', 'MATH101'], ['s5', 'HIST140'],
     ['s3', 'HIST140']],
    {'MATH101': 3, 'MATH101H': 7, 'PHYS110': 5, 'CHEM120': 7, 'BIO130': 4, 'HIST140': 8, 'ECON150': 1}, 3,
    [10, 1, 1]],
   [3, 1, 3, 34]),
  ('normal control 6',
   [[['s4', 'MATH101'], ['s1', 'ECON150'], ['s4', 'BIO130'], ['s5', 'PHYS110'], ['s1', 'MATH101H'],
     ['s2', 'CHEM120'], ['s2', 'ECON150'], ['s5', 'HIST140'], ['s1', 'CHEM120'], ['s2', 'ECON150'],
     ['s4', 'PHYS110'], ['s3', 'ECON150'], ['s1', 'PHYS110'], ['s3', 'PHYS110']],
    {'MATH101': 3, 'MATH101H': 3, 'PHYS110': 3, 'CHEM120': 1, 'BIO130': 3, 'HIST140': 4, 'ECON150': 2}, 2,
    [5, 3, 2]],
   [3, 0, 8, 23]),
  ('normal control 7',
   [[['s2', 'ECON150'], ['s5', 'ECON150'], ['s5', 'PHYS110'], ['s4', 'ECON150'], ['s2', 'CHEM120'],
     ['s4', 'MATH101'], ['s5', 'MATH101H'], ['s2', 'MATH101'], ['s4', 'HIST140'], ['s2', 'BIO130'],
     ['s3', 'ECON150'], ['s5', 'BIO130'], ['s3', 'MATH101H'], ['s3', 'MATH101'], ['s4', 'BIO130'],
     ['s1', 'ECON150']],
    {'MATH101': 2, 'MATH101H': 5, 'PHYS110': 4, 'CHEM120': 3, 'BIO130': 4, 'HIST140': 3, 'ECON150': 0}, 2,
    [5, 1, 4]],
   [4, 0, 18, 38]),
  ('normal control 8',
   [[['s5', 'CHEM120'], ['s1', 'ECON150'], ['s5', 'BIO130'], ['s5', 'HIST140'], ['s1', 'PHYS110'],
     ['s4', 'PHYS110'], ['s5', 'MATH101H'], ['s2', 'MATH101H'], ['s3', 'CHEM120'], ['s5', 'BIO130'],
     ['s3', 'BIO130'], ['s3', 'MATH101H'], ['s4', 'HIST140'], ['s2', 'BIO130'], ['s4', 'MATH101'],
     ['s3', 'MATH101'], ['s2', 'PHYS110']],
    {'MATH101': 0, 'MATH101H': 2, 'PHYS110': 0, 'CHEM120': 5, 'BIO130': 1, 'HIST140': 3, 'ECON150': 5}, 2,
    [10, 3, 4]],
   [3, 0, 16, 46])]]
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 fixtureActualExpectedOutcome
regression: clash not two in day 1[0, 0, 0, 0][0, 0, 0, 0]Passed
regression variant: clash not two in day 2[1, 0, 1, 11][1, 0, 2, 12]Failed
partial repair guard 3[3, 0, 14, 44][3, 0, 16, 46]Failed
boundary control 4[0, 1, 0, 2][0, 1, 1, 3]Failed
normal control 5[1, 0, 1, 11][1, 0, 1, 11]Passed
normal control 6[1, 0, 1, 11][1, 0, 1, 11]Passed
normal control 7[4, 0, 0, 20][4, 0, 5, 25]Failed
normal control 8[5, 1, 0, 51][5, 1, 5, 56]Failed

SHA-256 / 44346d3b601677f7a785fa57362a576d7c4894ad74ba3662146855902ae5a0cf

HELD IN THE MEMBER ARCHIVE

The verified repair and its recorded checks are member-only.

This mechanism has 8 recorded checks per implementation. The open-access tier publishes the failure and the unsuccessful fix; the repaired source that passes every check, and the observations that prove it, are available to members.

Every case sharing this mechanism uses the same contract and the same repair, so this one record is held back for all of them.

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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 2026-09-29T14:52:03.877559+00:00.

Case digest / d3d1dc666ee273ec37d738f11408b7bf1b5faa849fddd23d04e9eb1d9bf19ba5