FA-72941 / Probabilistic sketches / Open access
Counting Bloom filter with 4-bit counters: saturated counter is decremented · case 01
After a saturated counter is decremented, removing the true multiplicity drives it to zero while other items still map there.
ROOT CAUSE
remove decrements counters that have reached the saturation value, although their true count is unknown.
VERIFIED REPAIR
Leave counters at 15 unchanged on remove.
Unsuccessful approach: Clamping at zero does not address saturated counters; it still decrements them.
Case contract
Input {m, k, ops}; items are pre-hashed non-negative integers. Positions are the distinct values of (h1 + i*h2) mod m for i in 0..k-1 with h1 = item mod m and h2 = 1 + (item div m) mod (m-1), in first-seen order. add increments each distinct position once, saturating at 15. A saturated counter is sticky: remove never decrements it. remove is atomic: if any position is zero the result is "absent" and nothing changes; otherwise it decrements every non-saturated position. has requires every position to be positive. Return [results, counters].
Why this case matters
Counting Bloom filters support deletion in caches and routing tables; counter overflow, duplicate positions and non-atomic removals create false negatives that are otherwise impossible.
1 / The failure
Exit 1"""Failure Map reference implementation. Python standard library only."""
import json
N = 1
observations = []
def solve(x):
m = x['m']
k = x['k']
c = [0] * m
def positions(item):
h1 = item % m
h2 = 1 + (item // m) % (m - 1)
out = []
for i in range(k):
p = (h1 + i * h2) % m
if p not in out:
out.append(p)
return out
res = []
for op, item in x['ops']:
pos = positions(item)
if op == 'add':
for p in pos:
if c[p] < 15:
c[p] = c[p] + 1
res.append('added')
elif op == 'remove':
if any(c[p] == 0 for p in pos):
res.append('absent')
continue
for p in pos:
c[p] = c[p] - 1
res.append('removed')
else:
res.append(all(c[p] > 0 for p in pos))
return [res, c]
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
cases = [[['duplicate probe positions',
{'k': 4,
'm': 12,
'ops': [['add', 63], ['add', 1], ['has', 63], ['remove', 63], ['has', 63], ['has', 1]]},
[['added', 'added', True, 'removed', False, True], [0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0]]],
['hot item with repeated positions',
{'k': 4,
'm': 12,
'ops': [['add', 63],
['add', 63],
['add', 63],
['add', 63],
['add', 63],
['add', 63],
['add', 63],
['add', 63],
['remove', 63],
['remove', 63],
['remove', 63],
['remove', 63],
['remove', 63],
['remove', 63],
['remove', 63],
['remove', 63],
['has', 63]]},
[['added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
False],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]],
['wide stride item',
{'k': 3, 'm': 12, 'ops': [['add', 137], ['add', 8], ['has', 137], ['remove', 8]]},
[['added', 'added', True, 'removed'], [0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0]]],
['saturating counter',
{'k': 2,
'm': 12,
'ops': [['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['remove', 4],
['has', 4]]},
[['added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'removed',
True],
[0, 0, 0, 0, 15, 15, 0, 0, 0, 0, 0, 0]]],
['atomic removal of absent item',
{'k': 3, 'm': 12, 'ops': [['add', 6], ['remove', 42], ['has', 6]]},
[['added', 'absent', True], [0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0]]],
['partial overlap membership',
{'k': 3, 'm': 12, 'ops': [['add', 2], ['add', 14], ['has', 26], ['has', 3], ['has', 2]]},
[['added', 'added', False, False, True], [0, 0, 2, 1, 2, 0, 1, 0, 0, 0, 0, 0]]],
['normal add and remove',
{'k': 2, 'm': 12, 'ops': [['add', 31], ['add', 32], ['remove', 31], ['has', 31], ['has', 32]]},
[['added', 'added', 'removed', False, True], [0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1]]],
['remove absent from empty',
{'k': 2, 'm': 12, 'ops': [['remove', 9], ['has', 9]]},
[['absent', False], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]],
['saturated then drained',
{'k': 1,
'm': 12,
'ops': [['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['has', 6]]},
[['added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
True],
[0, 0, 0, 0, 0, 0, 15, 0, 0, 0, 0, 0]]]],
[['duplicate probe positions',
{'k': 4,
'm': 14,
'ops': [['add', 87], ['add', 1], ['has', 87], ['remove', 87], ['has', 87], ['has', 1]]},
[['added', 'added', True, 'removed', False, True], [0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0]]],
['hot item with repeated positions',
{'k': 4,
'm': 14,
'ops': [['add', 87],
['add', 87],
['add', 87],
['add', 87],
['add', 87],
['add', 87],
['add', 87],
['add', 87],
['remove', 87],
['remove', 87],
['remove', 87],
['remove', 87],
['remove', 87],
['remove', 87],
['remove', 87],
['remove', 87],
['has', 87]]},
[['added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
False],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]],
['wide stride item',
{'k': 3, 'm': 14, 'ops': [['add', 187], ['add', 9], ['has', 187], ['remove', 9]]},
[['added', 'added', True, 'removed'], [0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0]]],
['saturating counter',
{'k': 2,
'm': 14,
'ops': [['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['remove', 4],
['has', 4]]},
[['added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'removed',
True],
[0, 0, 0, 0, 15, 15, 0, 0, 0, 0, 0, 0, 0, 0]]],
['atomic removal of absent item',
{'k': 3, 'm': 14, 'ops': [['add', 7], ['remove', 49], ['has', 7]]},
[['added', 'absent', True], [0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0]]],
['partial overlap membership',
{'k': 3, 'm': 14, 'ops': [['add', 2], ['add', 16], ['has', 30], ['has', 3], ['has', 2]]},
[['added', 'added', False, False, True], [0, 0, 2, 1, 2, 0, 1, 0, 0, 0, 0, 0, 0, 0]]],
['normal add and remove',
{'k': 2, 'm': 14, 'ops': [['add', 32], ['add', 33], ['remove', 32], ['has', 32], ['has', 33]]},
[['added', 'added', 'removed', False, True], [0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0]]],
['remove absent from empty',
{'k': 2, 'm': 14, 'ops': [['remove', 9], ['has', 9]]},
[['absent', False], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]],
['saturated then drained',
{'k': 1,
'm': 14,
'ops': [['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['has', 6]]},
[['added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
True],
[0, 0, 0, 0, 0, 0, 15, 0, 0, 0, 0, 0, 0, 0]]]],
[['duplicate probe positions',
{'k': 4,
'm': 15,
'ops': [['add', 63], ['add', 1], ['has', 63], ['remove', 63], ['has', 63], ['has', 1]]},
[['added', 'added', True, 'removed', False, True],
[0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]],
['hot item with repeated positions',
{'k': 4,
'm': 15,
'ops': [['add', 63],
['add', 63],
['add', 63],
['add', 63],
['add', 63],
['add', 63],
['add', 63],
['add', 63],
['remove', 63],
['remove', 63],
['remove', 63],
['remove', 63],
['remove', 63],
['remove', 63],
['remove', 63],
['remove', 63],
['has', 63]]},
[['added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
False],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]],
['wide stride item',
{'k': 3, 'm': 15, 'ops': [['add', 215], ['add', 10], ['has', 215], ['remove', 10]]},
[['added', 'added', True, 'removed'], [0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0]]],
['saturating counter',
{'k': 2,
'm': 15,
'ops': [['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['remove', 4],
['has', 4]]},
[['added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'removed',
True],
[0, 0, 0, 0, 15, 15, 0, 0, 0, 0, 0, 0, 0, 0, 0]]],
['atomic removal of absent item',
{'k': 3, 'm': 15, 'ops': [['add', 8], ['remove', 53], ['has', 8]]},
[['added', 'absent', True], [0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0]]],
['partial overlap membership',
{'k': 3, 'm': 15, 'ops': [['add', 2], ['add', 17], ['has', 32], ['has', 3], ['has', 2]]},
[['added', 'added', False, False, True], [0, 0, 2, 1, 2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0]]],
['normal add and remove',
{'k': 2, 'm': 15, 'ops': [['add', 33], ['add', 34], ['remove', 33], ['has', 33], ['has', 34]]},
[['added', 'added', 'removed', False, True], [0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0]]],
['remove absent from empty',
{'k': 2, 'm': 15, 'ops': [['remove', 9], ['has', 9]]},
[['absent', False], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]],
['saturated then drained',
{'k': 1,
'm': 15,
'ops': [['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['has', 6]]},
[['added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
True],
[0, 0, 0, 0, 0, 0, 15, 0, 0, 0, 0, 0, 0, 0, 0]]]],
[['duplicate probe positions',
{'k': 4,
'm': 16,
'ops': [['add', 115], ['add', 1], ['has', 115], ['remove', 115], ['has', 115], ['has', 1]]},
[['added', 'added', True, 'removed', False, True],
[0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]],
['hot item with repeated positions',
{'k': 4,
'm': 16,
'ops': [['add', 115],
['add', 115],
['add', 115],
['add', 115],
['add', 115],
['add', 115],
['add', 115],
['add', 115],
['remove', 115],
['remove', 115],
['remove', 115],
['remove', 115],
['remove', 115],
['remove', 115],
['remove', 115],
['remove', 115],
['has', 115]]},
[['added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
False],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]],
['wide stride item',
{'k': 3, 'm': 16, 'ops': [['add', 245], ['add', 11], ['has', 245], ['remove', 11]]},
[['added', 'added', True, 'removed'], [0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0]]],
['saturating counter',
{'k': 2,
'm': 16,
'ops': [['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['remove', 4],
['has', 4]]},
[['added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'removed',
True],
[0, 0, 0, 0, 15, 15, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]],
['atomic removal of absent item',
{'k': 3, 'm': 16, 'ops': [['add', 9], ['remove', 57], ['has', 9]]},
[['added', 'absent', True], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0]]],
['partial overlap membership',
{'k': 3, 'm': 16, 'ops': [['add', 2], ['add', 18], ['has', 34], ['has', 3], ['has', 2]]},
[['added', 'added', False, False, True], [0, 0, 2, 1, 2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0]]],
['normal add and remove',
{'k': 2, 'm': 16, 'ops': [['add', 34], ['add', 35], ['remove', 34], ['has', 34], ['has', 35]]},
[['added', 'added', 'removed', False, True], [0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0]]],
['remove absent from empty',
{'k': 2, 'm': 16, 'ops': [['remove', 9], ['has', 9]]},
[['absent', False], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]],
['saturated then drained',
{'k': 1,
'm': 16,
'ops': [['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['has', 6]]},
[['added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
True],
[0, 0, 0, 0, 0, 0, 15, 0, 0, 0, 0, 0, 0, 0, 0, 0]]]],
[['duplicate probe positions',
{'k': 4,
'm': 18,
'ops': [['add', 147], ['add', 1], ['has', 147], ['remove', 147], ['has', 147], ['has', 1]]},
[['added', 'added', True, 'removed', False, True],
[0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]],
['hot item with repeated positions',
{'k': 4,
'm': 18,
'ops': [['add', 147],
['add', 147],
['add', 147],
['add', 147],
['add', 147],
['add', 147],
['add', 147],
['add', 147],
['remove', 147],
['remove', 147],
['remove', 147],
['remove', 147],
['remove', 147],
['remove', 147],
['remove', 147],
['remove', 147],
['has', 147]]},
[['added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
False],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]],
['wide stride item',
{'k': 3, 'm': 18, 'ops': [['add', 311], ['add', 12], ['has', 311], ['remove', 12]]},
[['added', 'added', True, 'removed'], [0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]],
['saturating counter',
{'k': 2,
'm': 18,
'ops': [['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['remove', 4],
['has', 4]]},
[['added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'removed',
True],
[0, 0, 0, 0, 15, 15, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]],
['atomic removal of absent item',
{'k': 3, 'm': 18, 'ops': [['add', 10], ['remove', 64], ['has', 10]]},
[['added', 'absent', True], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0]]],
['partial overlap membership',
{'k': 3, 'm': 18, 'ops': [['add', 2], ['add', 20], ['has', 38], ['has', 3], ['has', 2]]},
[['added', 'added', False, False, True],
[0, 0, 2, 1, 2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]],
['normal add and remove',
{'k': 2, 'm': 18, 'ops': [['add', 35], ['add', 36], ['remove', 35], ['has', 35], ['has', 36]]},
[['added', 'added', 'removed', False, True],
[1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]],
['remove absent from empty',
{'k': 2, 'm': 18, 'ops': [['remove', 9], ['has', 9]]},
[['absent', False], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]],
['saturated then drained',
{'k': 1,
'm': 18,
'ops': [['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['has', 6]]},
[['added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
True],
[0, 0, 0, 0, 0, 0, 15, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]]]]
for label, args, expected in cases[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 |
|---|---|---|---|
| duplicate probe positions | [['added', 'added', True, 'removed', False, True], [0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0]] | [['added', 'added', True, 'removed', False, True], [0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0]] | Passed |
| hot item with repeated positions | [['added', 'added', 'added', 'added', 'added', 'added', 'added', 'added', 'removed', 'removed', 'removed', 'removed', 'removed', 'removed', 'removed', 'removed', False], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]] | [['added', 'added', 'added', 'added', 'added', 'added', 'added', 'added', 'removed', 'removed', 'removed', 'removed', 'removed', 'removed', 'removed', 'removed', False], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]] | Passed |
| wide stride item | [['added', 'added', True, 'removed'], [0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0]] | [['added', 'added', True, 'removed'], [0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0]] | Passed |
| saturating counter | [['added', 'added', 'added', 'added', 'added', 'added', 'added', 'added', 'added', 'added', 'added', 'added', 'added', 'added', 'added', 'added', 'added', 'removed', True], [0, 0, 0, 0, 14, 14, 0, 0, 0, 0, 0, 0]] | [['added', 'added', 'added', 'added', 'added', 'added', 'added', 'added', 'added', 'added', 'added', 'added', 'added', 'added', 'added', 'added', 'added', 'removed', True], [0, 0, 0, 0, 15, 15, 0, 0, 0, 0, 0, 0]] | Failed |
| atomic removal of absent item | [['added', 'absent', True], [0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0]] | [['added', 'absent', True], [0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0]] | Passed |
| partial overlap membership | [['added', 'added', False, False, True], [0, 0, 2, 1, 2, 0, 1, 0, 0, 0, 0, 0]] | [['added', 'added', False, False, True], [0, 0, 2, 1, 2, 0, 1, 0, 0, 0, 0, 0]] | Passed |
| normal add and remove | [['added', 'added', 'removed', False, True], [0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1]] | [['added', 'added', 'removed', False, True], [0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1]] | Passed |
| remove absent from empty | [['absent', False], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]] | [['absent', False], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]] | Passed |
| saturated then drained | [['added', 'added', 'added', 'added', 'added', 'added', 'added', 'added', 'added', 'added', 'added', 'added', 'added', 'added', 'added', 'added', 'removed', 'removed', 'removed', 'removed', 'removed', 'removed', 'removed', 'removed', 'removed', 'removed', 'removed', 'removed', 'removed', 'removed', 'removed', 'absent', False], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]] | [['added', 'added', 'added', 'added', 'added', 'added', 'added', 'added', 'added', 'added', 'added', 'added', 'added', 'added', 'added', 'added', 'removed', 'removed', 'removed', 'removed', 'removed', 'removed', 'removed', 'removed', 'removed', 'removed', 'removed', 'removed', 'removed', 'removed', 'removed', 'removed', True], [0, 0, 0, 0, 0, 0, 15, 0, 0, 0, 0, 0]] | Failed |
SHA-256 / 857c15a21435bd5d6e4e51d4a1361be471de92c98557b8c708e6128288d30b73
2 / The unsuccessful fix
Exit 1"""Failure Map reference implementation. Python standard library only."""
import json
N = 1
observations = []
def solve(x):
m = x['m']
k = x['k']
c = [0] * m
def positions(item):
h1 = item % m
h2 = 1 + (item // m) % (m - 1)
out = []
for i in range(k):
p = (h1 + i * h2) % m
if p not in out:
out.append(p)
return out
res = []
for op, item in x['ops']:
pos = positions(item)
if op == 'add':
for p in pos:
if c[p] < 15:
c[p] = c[p] + 1
res.append('added')
elif op == 'remove':
if any(c[p] == 0 for p in pos):
res.append('absent')
continue
for p in pos:
c[p] = max(c[p] - 1, 0)
res.append('removed')
else:
res.append(all(c[p] > 0 for p in pos))
return [res, c]
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
cases = [[['duplicate probe positions',
{'k': 4,
'm': 12,
'ops': [['add', 63], ['add', 1], ['has', 63], ['remove', 63], ['has', 63], ['has', 1]]},
[['added', 'added', True, 'removed', False, True], [0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0]]],
['hot item with repeated positions',
{'k': 4,
'm': 12,
'ops': [['add', 63],
['add', 63],
['add', 63],
['add', 63],
['add', 63],
['add', 63],
['add', 63],
['add', 63],
['remove', 63],
['remove', 63],
['remove', 63],
['remove', 63],
['remove', 63],
['remove', 63],
['remove', 63],
['remove', 63],
['has', 63]]},
[['added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
False],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]],
['wide stride item',
{'k': 3, 'm': 12, 'ops': [['add', 137], ['add', 8], ['has', 137], ['remove', 8]]},
[['added', 'added', True, 'removed'], [0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0]]],
['saturating counter',
{'k': 2,
'm': 12,
'ops': [['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['remove', 4],
['has', 4]]},
[['added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'removed',
True],
[0, 0, 0, 0, 15, 15, 0, 0, 0, 0, 0, 0]]],
['atomic removal of absent item',
{'k': 3, 'm': 12, 'ops': [['add', 6], ['remove', 42], ['has', 6]]},
[['added', 'absent', True], [0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0]]],
['partial overlap membership',
{'k': 3, 'm': 12, 'ops': [['add', 2], ['add', 14], ['has', 26], ['has', 3], ['has', 2]]},
[['added', 'added', False, False, True], [0, 0, 2, 1, 2, 0, 1, 0, 0, 0, 0, 0]]],
['normal add and remove',
{'k': 2, 'm': 12, 'ops': [['add', 31], ['add', 32], ['remove', 31], ['has', 31], ['has', 32]]},
[['added', 'added', 'removed', False, True], [0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1]]],
['remove absent from empty',
{'k': 2, 'm': 12, 'ops': [['remove', 9], ['has', 9]]},
[['absent', False], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]],
['saturated then drained',
{'k': 1,
'm': 12,
'ops': [['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['has', 6]]},
[['added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
True],
[0, 0, 0, 0, 0, 0, 15, 0, 0, 0, 0, 0]]]],
[['duplicate probe positions',
{'k': 4,
'm': 14,
'ops': [['add', 87], ['add', 1], ['has', 87], ['remove', 87], ['has', 87], ['has', 1]]},
[['added', 'added', True, 'removed', False, True], [0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0]]],
['hot item with repeated positions',
{'k': 4,
'm': 14,
'ops': [['add', 87],
['add', 87],
['add', 87],
['add', 87],
['add', 87],
['add', 87],
['add', 87],
['add', 87],
['remove', 87],
['remove', 87],
['remove', 87],
['remove', 87],
['remove', 87],
['remove', 87],
['remove', 87],
['remove', 87],
['has', 87]]},
[['added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
False],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]],
['wide stride item',
{'k': 3, 'm': 14, 'ops': [['add', 187], ['add', 9], ['has', 187], ['remove', 9]]},
[['added', 'added', True, 'removed'], [0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0]]],
['saturating counter',
{'k': 2,
'm': 14,
'ops': [['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['remove', 4],
['has', 4]]},
[['added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'removed',
True],
[0, 0, 0, 0, 15, 15, 0, 0, 0, 0, 0, 0, 0, 0]]],
['atomic removal of absent item',
{'k': 3, 'm': 14, 'ops': [['add', 7], ['remove', 49], ['has', 7]]},
[['added', 'absent', True], [0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0]]],
['partial overlap membership',
{'k': 3, 'm': 14, 'ops': [['add', 2], ['add', 16], ['has', 30], ['has', 3], ['has', 2]]},
[['added', 'added', False, False, True], [0, 0, 2, 1, 2, 0, 1, 0, 0, 0, 0, 0, 0, 0]]],
['normal add and remove',
{'k': 2, 'm': 14, 'ops': [['add', 32], ['add', 33], ['remove', 32], ['has', 32], ['has', 33]]},
[['added', 'added', 'removed', False, True], [0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0]]],
['remove absent from empty',
{'k': 2, 'm': 14, 'ops': [['remove', 9], ['has', 9]]},
[['absent', False], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]],
['saturated then drained',
{'k': 1,
'm': 14,
'ops': [['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['has', 6]]},
[['added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
True],
[0, 0, 0, 0, 0, 0, 15, 0, 0, 0, 0, 0, 0, 0]]]],
[['duplicate probe positions',
{'k': 4,
'm': 15,
'ops': [['add', 63], ['add', 1], ['has', 63], ['remove', 63], ['has', 63], ['has', 1]]},
[['added', 'added', True, 'removed', False, True],
[0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]],
['hot item with repeated positions',
{'k': 4,
'm': 15,
'ops': [['add', 63],
['add', 63],
['add', 63],
['add', 63],
['add', 63],
['add', 63],
['add', 63],
['add', 63],
['remove', 63],
['remove', 63],
['remove', 63],
['remove', 63],
['remove', 63],
['remove', 63],
['remove', 63],
['remove', 63],
['has', 63]]},
[['added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
False],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]],
['wide stride item',
{'k': 3, 'm': 15, 'ops': [['add', 215], ['add', 10], ['has', 215], ['remove', 10]]},
[['added', 'added', True, 'removed'], [0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0]]],
['saturating counter',
{'k': 2,
'm': 15,
'ops': [['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['remove', 4],
['has', 4]]},
[['added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'removed',
True],
[0, 0, 0, 0, 15, 15, 0, 0, 0, 0, 0, 0, 0, 0, 0]]],
['atomic removal of absent item',
{'k': 3, 'm': 15, 'ops': [['add', 8], ['remove', 53], ['has', 8]]},
[['added', 'absent', True], [0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0]]],
['partial overlap membership',
{'k': 3, 'm': 15, 'ops': [['add', 2], ['add', 17], ['has', 32], ['has', 3], ['has', 2]]},
[['added', 'added', False, False, True], [0, 0, 2, 1, 2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0]]],
['normal add and remove',
{'k': 2, 'm': 15, 'ops': [['add', 33], ['add', 34], ['remove', 33], ['has', 33], ['has', 34]]},
[['added', 'added', 'removed', False, True], [0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0]]],
['remove absent from empty',
{'k': 2, 'm': 15, 'ops': [['remove', 9], ['has', 9]]},
[['absent', False], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]],
['saturated then drained',
{'k': 1,
'm': 15,
'ops': [['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['has', 6]]},
[['added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
True],
[0, 0, 0, 0, 0, 0, 15, 0, 0, 0, 0, 0, 0, 0, 0]]]],
[['duplicate probe positions',
{'k': 4,
'm': 16,
'ops': [['add', 115], ['add', 1], ['has', 115], ['remove', 115], ['has', 115], ['has', 1]]},
[['added', 'added', True, 'removed', False, True],
[0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]],
['hot item with repeated positions',
{'k': 4,
'm': 16,
'ops': [['add', 115],
['add', 115],
['add', 115],
['add', 115],
['add', 115],
['add', 115],
['add', 115],
['add', 115],
['remove', 115],
['remove', 115],
['remove', 115],
['remove', 115],
['remove', 115],
['remove', 115],
['remove', 115],
['remove', 115],
['has', 115]]},
[['added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
False],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]],
['wide stride item',
{'k': 3, 'm': 16, 'ops': [['add', 245], ['add', 11], ['has', 245], ['remove', 11]]},
[['added', 'added', True, 'removed'], [0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0]]],
['saturating counter',
{'k': 2,
'm': 16,
'ops': [['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['remove', 4],
['has', 4]]},
[['added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'removed',
True],
[0, 0, 0, 0, 15, 15, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]],
['atomic removal of absent item',
{'k': 3, 'm': 16, 'ops': [['add', 9], ['remove', 57], ['has', 9]]},
[['added', 'absent', True], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0]]],
['partial overlap membership',
{'k': 3, 'm': 16, 'ops': [['add', 2], ['add', 18], ['has', 34], ['has', 3], ['has', 2]]},
[['added', 'added', False, False, True], [0, 0, 2, 1, 2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0]]],
['normal add and remove',
{'k': 2, 'm': 16, 'ops': [['add', 34], ['add', 35], ['remove', 34], ['has', 34], ['has', 35]]},
[['added', 'added', 'removed', False, True], [0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0]]],
['remove absent from empty',
{'k': 2, 'm': 16, 'ops': [['remove', 9], ['has', 9]]},
[['absent', False], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]],
['saturated then drained',
{'k': 1,
'm': 16,
'ops': [['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['has', 6]]},
[['added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
True],
[0, 0, 0, 0, 0, 0, 15, 0, 0, 0, 0, 0, 0, 0, 0, 0]]]],
[['duplicate probe positions',
{'k': 4,
'm': 18,
'ops': [['add', 147], ['add', 1], ['has', 147], ['remove', 147], ['has', 147], ['has', 1]]},
[['added', 'added', True, 'removed', False, True],
[0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]],
['hot item with repeated positions',
{'k': 4,
'm': 18,
'ops': [['add', 147],
['add', 147],
['add', 147],
['add', 147],
['add', 147],
['add', 147],
['add', 147],
['add', 147],
['remove', 147],
['remove', 147],
['remove', 147],
['remove', 147],
['remove', 147],
['remove', 147],
['remove', 147],
['remove', 147],
['has', 147]]},
[['added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
False],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]],
['wide stride item',
{'k': 3, 'm': 18, 'ops': [['add', 311], ['add', 12], ['has', 311], ['remove', 12]]},
[['added', 'added', True, 'removed'], [0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]],
['saturating counter',
{'k': 2,
'm': 18,
'ops': [['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['remove', 4],
['has', 4]]},
[['added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'removed',
True],
[0, 0, 0, 0, 15, 15, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]],
['atomic removal of absent item',
{'k': 3, 'm': 18, 'ops': [['add', 10], ['remove', 64], ['has', 10]]},
[['added', 'absent', True], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0]]],
['partial overlap membership',
{'k': 3, 'm': 18, 'ops': [['add', 2], ['add', 20], ['has', 38], ['has', 3], ['has', 2]]},
[['added', 'added', False, False, True],
[0, 0, 2, 1, 2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]],
['normal add and remove',
{'k': 2, 'm': 18, 'ops': [['add', 35], ['add', 36], ['remove', 35], ['has', 35], ['has', 36]]},
[['added', 'added', 'removed', False, True],
[1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]],
['remove absent from empty',
{'k': 2, 'm': 18, 'ops': [['remove', 9], ['has', 9]]},
[['absent', False], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]],
['saturated then drained',
{'k': 1,
'm': 18,
'ops': [['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['has', 6]]},
[['added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
True],
[0, 0, 0, 0, 0, 0, 15, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]]]]
for label, args, expected in cases[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 |
|---|---|---|---|
| duplicate probe positions | [['added', 'added', True, 'removed', False, True], [0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0]] | [['added', 'added', True, 'removed', False, True], [0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0]] | Passed |
| hot item with repeated positions | [['added', 'added', 'added', 'added', 'added', 'added', 'added', 'added', 'removed', 'removed', 'removed', 'removed', 'removed', 'removed', 'removed', 'removed', False], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]] | [['added', 'added', 'added', 'added', 'added', 'added', 'added', 'added', 'removed', 'removed', 'removed', 'removed', 'removed', 'removed', 'removed', 'removed', False], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]] | Passed |
| wide stride item | [['added', 'added', True, 'removed'], [0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0]] | [['added', 'added', True, 'removed'], [0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0]] | Passed |
| saturating counter | [['added', 'added', 'added', 'added', 'added', 'added', 'added', 'added', 'added', 'added', 'added', 'added', 'added', 'added', 'added', 'added', 'added', 'removed', True], [0, 0, 0, 0, 14, 14, 0, 0, 0, 0, 0, 0]] | [['added', 'added', 'added', 'added', 'added', 'added', 'added', 'added', 'added', 'added', 'added', 'added', 'added', 'added', 'added', 'added', 'added', 'removed', True], [0, 0, 0, 0, 15, 15, 0, 0, 0, 0, 0, 0]] | Failed |
| atomic removal of absent item | [['added', 'absent', True], [0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0]] | [['added', 'absent', True], [0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0]] | Passed |
| partial overlap membership | [['added', 'added', False, False, True], [0, 0, 2, 1, 2, 0, 1, 0, 0, 0, 0, 0]] | [['added', 'added', False, False, True], [0, 0, 2, 1, 2, 0, 1, 0, 0, 0, 0, 0]] | Passed |
| normal add and remove | [['added', 'added', 'removed', False, True], [0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1]] | [['added', 'added', 'removed', False, True], [0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1]] | Passed |
| remove absent from empty | [['absent', False], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]] | [['absent', False], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]] | Passed |
| saturated then drained | [['added', 'added', 'added', 'added', 'added', 'added', 'added', 'added', 'added', 'added', 'added', 'added', 'added', 'added', 'added', 'added', 'removed', 'removed', 'removed', 'removed', 'removed', 'removed', 'removed', 'removed', 'removed', 'removed', 'removed', 'removed', 'removed', 'removed', 'removed', 'absent', False], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]] | [['added', 'added', 'added', 'added', 'added', 'added', 'added', 'added', 'added', 'added', 'added', 'added', 'added', 'added', 'added', 'added', 'removed', 'removed', 'removed', 'removed', 'removed', 'removed', 'removed', 'removed', 'removed', 'removed', 'removed', 'removed', 'removed', 'removed', 'removed', 'removed', True], [0, 0, 0, 0, 0, 0, 15, 0, 0, 0, 0, 0]] | Failed |
SHA-256 / f8030a956fa336dd9e30ae8e91a150946479a46e26886a4e656d891902ceca31
3 / The verified repair
Exit 0"""Failure Map reference implementation. Python standard library only."""
import json
N = 1
observations = []
def solve(x):
m = x['m']
k = x['k']
c = [0] * m
def positions(item):
h1 = item % m
h2 = 1 + (item // m) % (m - 1)
out = []
for i in range(k):
p = (h1 + i * h2) % m
if p not in out:
out.append(p)
return out
res = []
for op, item in x['ops']:
pos = positions(item)
if op == 'add':
for p in pos:
if c[p] < 15:
c[p] = c[p] + 1
res.append('added')
elif op == 'remove':
if any(c[p] == 0 for p in pos):
res.append('absent')
continue
for p in pos:
if c[p] < 15:
c[p] = c[p] - 1
res.append('removed')
else:
res.append(all(c[p] > 0 for p in pos))
return [res, c]
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
cases = [[['duplicate probe positions',
{'k': 4,
'm': 12,
'ops': [['add', 63], ['add', 1], ['has', 63], ['remove', 63], ['has', 63], ['has', 1]]},
[['added', 'added', True, 'removed', False, True], [0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0]]],
['hot item with repeated positions',
{'k': 4,
'm': 12,
'ops': [['add', 63],
['add', 63],
['add', 63],
['add', 63],
['add', 63],
['add', 63],
['add', 63],
['add', 63],
['remove', 63],
['remove', 63],
['remove', 63],
['remove', 63],
['remove', 63],
['remove', 63],
['remove', 63],
['remove', 63],
['has', 63]]},
[['added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
False],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]],
['wide stride item',
{'k': 3, 'm': 12, 'ops': [['add', 137], ['add', 8], ['has', 137], ['remove', 8]]},
[['added', 'added', True, 'removed'], [0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0]]],
['saturating counter',
{'k': 2,
'm': 12,
'ops': [['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['remove', 4],
['has', 4]]},
[['added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'removed',
True],
[0, 0, 0, 0, 15, 15, 0, 0, 0, 0, 0, 0]]],
['atomic removal of absent item',
{'k': 3, 'm': 12, 'ops': [['add', 6], ['remove', 42], ['has', 6]]},
[['added', 'absent', True], [0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0]]],
['partial overlap membership',
{'k': 3, 'm': 12, 'ops': [['add', 2], ['add', 14], ['has', 26], ['has', 3], ['has', 2]]},
[['added', 'added', False, False, True], [0, 0, 2, 1, 2, 0, 1, 0, 0, 0, 0, 0]]],
['normal add and remove',
{'k': 2, 'm': 12, 'ops': [['add', 31], ['add', 32], ['remove', 31], ['has', 31], ['has', 32]]},
[['added', 'added', 'removed', False, True], [0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1]]],
['remove absent from empty',
{'k': 2, 'm': 12, 'ops': [['remove', 9], ['has', 9]]},
[['absent', False], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]],
['saturated then drained',
{'k': 1,
'm': 12,
'ops': [['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['has', 6]]},
[['added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
True],
[0, 0, 0, 0, 0, 0, 15, 0, 0, 0, 0, 0]]]],
[['duplicate probe positions',
{'k': 4,
'm': 14,
'ops': [['add', 87], ['add', 1], ['has', 87], ['remove', 87], ['has', 87], ['has', 1]]},
[['added', 'added', True, 'removed', False, True], [0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0]]],
['hot item with repeated positions',
{'k': 4,
'm': 14,
'ops': [['add', 87],
['add', 87],
['add', 87],
['add', 87],
['add', 87],
['add', 87],
['add', 87],
['add', 87],
['remove', 87],
['remove', 87],
['remove', 87],
['remove', 87],
['remove', 87],
['remove', 87],
['remove', 87],
['remove', 87],
['has', 87]]},
[['added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
False],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]],
['wide stride item',
{'k': 3, 'm': 14, 'ops': [['add', 187], ['add', 9], ['has', 187], ['remove', 9]]},
[['added', 'added', True, 'removed'], [0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0]]],
['saturating counter',
{'k': 2,
'm': 14,
'ops': [['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['remove', 4],
['has', 4]]},
[['added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'removed',
True],
[0, 0, 0, 0, 15, 15, 0, 0, 0, 0, 0, 0, 0, 0]]],
['atomic removal of absent item',
{'k': 3, 'm': 14, 'ops': [['add', 7], ['remove', 49], ['has', 7]]},
[['added', 'absent', True], [0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0]]],
['partial overlap membership',
{'k': 3, 'm': 14, 'ops': [['add', 2], ['add', 16], ['has', 30], ['has', 3], ['has', 2]]},
[['added', 'added', False, False, True], [0, 0, 2, 1, 2, 0, 1, 0, 0, 0, 0, 0, 0, 0]]],
['normal add and remove',
{'k': 2, 'm': 14, 'ops': [['add', 32], ['add', 33], ['remove', 32], ['has', 32], ['has', 33]]},
[['added', 'added', 'removed', False, True], [0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0]]],
['remove absent from empty',
{'k': 2, 'm': 14, 'ops': [['remove', 9], ['has', 9]]},
[['absent', False], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]],
['saturated then drained',
{'k': 1,
'm': 14,
'ops': [['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['has', 6]]},
[['added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
True],
[0, 0, 0, 0, 0, 0, 15, 0, 0, 0, 0, 0, 0, 0]]]],
[['duplicate probe positions',
{'k': 4,
'm': 15,
'ops': [['add', 63], ['add', 1], ['has', 63], ['remove', 63], ['has', 63], ['has', 1]]},
[['added', 'added', True, 'removed', False, True],
[0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]],
['hot item with repeated positions',
{'k': 4,
'm': 15,
'ops': [['add', 63],
['add', 63],
['add', 63],
['add', 63],
['add', 63],
['add', 63],
['add', 63],
['add', 63],
['remove', 63],
['remove', 63],
['remove', 63],
['remove', 63],
['remove', 63],
['remove', 63],
['remove', 63],
['remove', 63],
['has', 63]]},
[['added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
False],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]],
['wide stride item',
{'k': 3, 'm': 15, 'ops': [['add', 215], ['add', 10], ['has', 215], ['remove', 10]]},
[['added', 'added', True, 'removed'], [0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0]]],
['saturating counter',
{'k': 2,
'm': 15,
'ops': [['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['remove', 4],
['has', 4]]},
[['added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'removed',
True],
[0, 0, 0, 0, 15, 15, 0, 0, 0, 0, 0, 0, 0, 0, 0]]],
['atomic removal of absent item',
{'k': 3, 'm': 15, 'ops': [['add', 8], ['remove', 53], ['has', 8]]},
[['added', 'absent', True], [0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0]]],
['partial overlap membership',
{'k': 3, 'm': 15, 'ops': [['add', 2], ['add', 17], ['has', 32], ['has', 3], ['has', 2]]},
[['added', 'added', False, False, True], [0, 0, 2, 1, 2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0]]],
['normal add and remove',
{'k': 2, 'm': 15, 'ops': [['add', 33], ['add', 34], ['remove', 33], ['has', 33], ['has', 34]]},
[['added', 'added', 'removed', False, True], [0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0]]],
['remove absent from empty',
{'k': 2, 'm': 15, 'ops': [['remove', 9], ['has', 9]]},
[['absent', False], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]],
['saturated then drained',
{'k': 1,
'm': 15,
'ops': [['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['has', 6]]},
[['added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
True],
[0, 0, 0, 0, 0, 0, 15, 0, 0, 0, 0, 0, 0, 0, 0]]]],
[['duplicate probe positions',
{'k': 4,
'm': 16,
'ops': [['add', 115], ['add', 1], ['has', 115], ['remove', 115], ['has', 115], ['has', 1]]},
[['added', 'added', True, 'removed', False, True],
[0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]],
['hot item with repeated positions',
{'k': 4,
'm': 16,
'ops': [['add', 115],
['add', 115],
['add', 115],
['add', 115],
['add', 115],
['add', 115],
['add', 115],
['add', 115],
['remove', 115],
['remove', 115],
['remove', 115],
['remove', 115],
['remove', 115],
['remove', 115],
['remove', 115],
['remove', 115],
['has', 115]]},
[['added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
False],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]],
['wide stride item',
{'k': 3, 'm': 16, 'ops': [['add', 245], ['add', 11], ['has', 245], ['remove', 11]]},
[['added', 'added', True, 'removed'], [0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0]]],
['saturating counter',
{'k': 2,
'm': 16,
'ops': [['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['remove', 4],
['has', 4]]},
[['added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'removed',
True],
[0, 0, 0, 0, 15, 15, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]],
['atomic removal of absent item',
{'k': 3, 'm': 16, 'ops': [['add', 9], ['remove', 57], ['has', 9]]},
[['added', 'absent', True], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0]]],
['partial overlap membership',
{'k': 3, 'm': 16, 'ops': [['add', 2], ['add', 18], ['has', 34], ['has', 3], ['has', 2]]},
[['added', 'added', False, False, True], [0, 0, 2, 1, 2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0]]],
['normal add and remove',
{'k': 2, 'm': 16, 'ops': [['add', 34], ['add', 35], ['remove', 34], ['has', 34], ['has', 35]]},
[['added', 'added', 'removed', False, True], [0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0]]],
['remove absent from empty',
{'k': 2, 'm': 16, 'ops': [['remove', 9], ['has', 9]]},
[['absent', False], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]],
['saturated then drained',
{'k': 1,
'm': 16,
'ops': [['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['has', 6]]},
[['added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
True],
[0, 0, 0, 0, 0, 0, 15, 0, 0, 0, 0, 0, 0, 0, 0, 0]]]],
[['duplicate probe positions',
{'k': 4,
'm': 18,
'ops': [['add', 147], ['add', 1], ['has', 147], ['remove', 147], ['has', 147], ['has', 1]]},
[['added', 'added', True, 'removed', False, True],
[0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]],
['hot item with repeated positions',
{'k': 4,
'm': 18,
'ops': [['add', 147],
['add', 147],
['add', 147],
['add', 147],
['add', 147],
['add', 147],
['add', 147],
['add', 147],
['remove', 147],
['remove', 147],
['remove', 147],
['remove', 147],
['remove', 147],
['remove', 147],
['remove', 147],
['remove', 147],
['has', 147]]},
[['added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
False],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]],
['wide stride item',
{'k': 3, 'm': 18, 'ops': [['add', 311], ['add', 12], ['has', 311], ['remove', 12]]},
[['added', 'added', True, 'removed'], [0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]],
['saturating counter',
{'k': 2,
'm': 18,
'ops': [['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['remove', 4],
['has', 4]]},
[['added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'removed',
True],
[0, 0, 0, 0, 15, 15, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]],
['atomic removal of absent item',
{'k': 3, 'm': 18, 'ops': [['add', 10], ['remove', 64], ['has', 10]]},
[['added', 'absent', True], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0]]],
['partial overlap membership',
{'k': 3, 'm': 18, 'ops': [['add', 2], ['add', 20], ['has', 38], ['has', 3], ['has', 2]]},
[['added', 'added', False, False, True],
[0, 0, 2, 1, 2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]],
['normal add and remove',
{'k': 2, 'm': 18, 'ops': [['add', 35], ['add', 36], ['remove', 35], ['has', 35], ['has', 36]]},
[['added', 'added', 'removed', False, True],
[1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]],
['remove absent from empty',
{'k': 2, 'm': 18, 'ops': [['remove', 9], ['has', 9]]},
[['absent', False], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]],
['saturated then drained',
{'k': 1,
'm': 18,
'ops': [['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['has', 6]]},
[['added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
True],
[0, 0, 0, 0, 0, 0, 15, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]]]]
for label, args, expected in cases[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 |
|---|---|---|---|
| duplicate probe positions | [['added', 'added', True, 'removed', False, True], [0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0]] | [['added', 'added', True, 'removed', False, True], [0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0]] | Passed |
| hot item with repeated positions | [['added', 'added', 'added', 'added', 'added', 'added', 'added', 'added', 'removed', 'removed', 'removed', 'removed', 'removed', 'removed', 'removed', 'removed', False], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]] | [['added', 'added', 'added', 'added', 'added', 'added', 'added', 'added', 'removed', 'removed', 'removed', 'removed', 'removed', 'removed', 'removed', 'removed', False], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]] | Passed |
| wide stride item | [['added', 'added', True, 'removed'], [0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0]] | [['added', 'added', True, 'removed'], [0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0]] | Passed |
| saturating counter | [['added', 'added', 'added', 'added', 'added', 'added', 'added', 'added', 'added', 'added', 'added', 'added', 'added', 'added', 'added', 'added', 'added', 'removed', True], [0, 0, 0, 0, 15, 15, 0, 0, 0, 0, 0, 0]] | [['added', 'added', 'added', 'added', 'added', 'added', 'added', 'added', 'added', 'added', 'added', 'added', 'added', 'added', 'added', 'added', 'added', 'removed', True], [0, 0, 0, 0, 15, 15, 0, 0, 0, 0, 0, 0]] | Passed |
| atomic removal of absent item | [['added', 'absent', True], [0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0]] | [['added', 'absent', True], [0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0]] | Passed |
| partial overlap membership | [['added', 'added', False, False, True], [0, 0, 2, 1, 2, 0, 1, 0, 0, 0, 0, 0]] | [['added', 'added', False, False, True], [0, 0, 2, 1, 2, 0, 1, 0, 0, 0, 0, 0]] | Passed |
| normal add and remove | [['added', 'added', 'removed', False, True], [0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1]] | [['added', 'added', 'removed', False, True], [0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1]] | Passed |
| remove absent from empty | [['absent', False], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]] | [['absent', False], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]] | Passed |
| saturated then drained | [['added', 'added', 'added', 'added', 'added', 'added', 'added', 'added', 'added', 'added', 'added', 'added', 'added', 'added', 'added', 'added', 'removed', 'removed', 'removed', 'removed', 'removed', 'removed', 'removed', 'removed', 'removed', 'removed', 'removed', 'removed', 'removed', 'removed', 'removed', 'removed', True], [0, 0, 0, 0, 0, 0, 15, 0, 0, 0, 0, 0]] | [['added', 'added', 'added', 'added', 'added', 'added', 'added', 'added', 'added', 'added', 'added', 'added', 'added', 'added', 'added', 'added', 'removed', 'removed', 'removed', 'removed', 'removed', 'removed', 'removed', 'removed', 'removed', 'removed', 'removed', 'removed', 'removed', 'removed', 'removed', 'removed', True], [0, 0, 0, 0, 0, 0, 15, 0, 0, 0, 0, 0]] | Passed |
SHA-256 / b1752ed904752db5c3830a5b34af03464bdda54fa5d33ac76f7fa036f848ea62
Verification & scope
A deterministic, bounded teaching model with stipulated constants and pre-hashed or explicitly hashed inputs; it is not a production implementation and makes no claim of conformance to any library or paper beyond the stated contract. 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 2026-09-29T14:48:42.870466+00:00.
Case digest / dd574610221462c6aa80f346319cad63ed6b30ed27e29bae9d52f4418fcc843a