FA-73046 / Probabilistic sketches / Open access
Count-Min sketch with conservative update: target computed from a running minimum · case 01
Early rows are raised from a partial minimum, overestimating keys whose smallest cell is in a later row.
ROOT CAUSE
The minimum is accumulated while cells are being updated, so the target for early rows ignores later rows.
VERIFIED REPAIR
Compute the full minimum across rows before updating any cell.
Unsuccessful approach: Using the maximum cell as the base raises every row to the most contaminated value.
Case contract
Input {w, d, ops}. Row r hashes key to ((A_r*key + B_r) mod 2^31-1) mod w with fixed A and B. add with count <= 0 is "rejected" (conservative update cannot represent deletions). Otherwise the current estimate e is the minimum of the key's cells, and each cell is raised to max(cell, e + count). The stream total counts accepted mass and the overestimate bound is ceil(e/w * total). q returns the minimum of the key's cells. Return [results, total, bound, table].
Why this case matters
Conservative update reduces Count-Min overestimation in heavy-hitter monitors, but only if the raise-to-target rule is applied exactly.
1 / The failure
Exit 1"""Failure Map reference implementation. Python standard library only."""
import json
import math
N = 1
observations = []
def solve(x):
w = x['w']
A = [1103515245, 1812433253, 1664525017, 2013265921, 1597334677]
B = [12345, 1013904223, 7, 99991, 31337]
P = 2147483647
d = x['d']
t = [[0] * w for _ in range(d)]
def bucket(r, key):
return (A[r] * key + B[r]) % P % w
total = 0
res = []
for op in x['ops']:
if op[0] == 'add':
key, cnt = op[1], op[2]
if cnt <= 0:
res.append('rejected')
continue
est = None
for r in range(d):
b = bucket(r, key)
est = t[r][b] if est is None else min(est, t[r][b])
t[r][b] = max(t[r][b], est + cnt)
total += cnt
res.append('ok')
else:
res.append(min(t[r][bucket(r, op[1])] for r in range(d)))
return [res, total, math.ceil(math.e / w * total), t]
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
cases = [[['colliding keys',
{'d': 3,
'ops': [['add', 1, 4], ['add', 6, 2], ['add', 1, 1], ['q', 1], ['q', 6], ['q', 11]],
'w': 5},
[['ok', 'ok', 'ok', 5, 2, 0], 7, 4, [[5, 0, 0, 0, 2], [0, 2, 0, 0, 5], [0, 2, 0, 0, 5]]]],
['zero and negative counts',
{'d': 2, 'ops': [['add', 3, 0], ['add', 3, -2], ['add', 3, 5], ['q', 3]], 'w': 7},
[['rejected', 'rejected', 'ok', 5], 5, 2, [[0, 0, 0, 5, 0, 0, 0], [0, 0, 0, 5, 0, 0, 0]]]],
['huge keys wrap prime',
{'d': 3,
'ops': [['add', 900000007, 3],
['add', 2700000021, 2],
['q', 900000007],
['q', 2700000021],
['q', 7]],
'w': 7},
[['ok', 'ok', 3, 2, 0],
5,
2,
[[0, 3, 0, 0, 0, 0, 0], [2, 0, 0, 0, 3, 0, 0], [2, 0, 0, 3, 0, 0, 0]]]],
['uneven rows',
{'d': 4,
'ops': [['add', 2, 3],
['add', 9, 5],
['add', 2, 2],
['add', 5, 2],
['q', 2],
['q', 9],
['q', 5]],
'w': 4},
[['ok', 'ok', 'ok', 'ok', 5, 5, 2],
12,
9,
[[5, 0, 5, 0], [5, 0, 0, 5], [0, 0, 5, 2], [5, 0, 5, 0]]]],
['single row',
{'d': 1, 'ops': [['add', 1, 2], ['add', 4, 3], ['q', 1], ['add', 0, 0]], 'w': 3},
[['ok', 'ok', 2, 'rejected'], 5, 5, [[2, 3, 0]]]],
['many keys',
{'d': 3,
'ops': [['add', 0, 1],
['add', 1, 2],
['add', 2, 3],
['add', 3, 4],
['add', 4, 1],
['add', 5, 2],
['add', 6, 3],
['add', 7, 4],
['add', 8, 1],
['add', 9, 2],
['add', 10, 3],
['add', 11, 4],
['q', 0],
['q', 3],
['q', 6],
['q', 9],
['add', 2, 0]],
'w': 5},
[['ok',
'ok',
'ok',
'ok',
'ok',
'ok',
'ok',
'ok',
'ok',
'ok',
'ok',
'ok',
1,
4,
4,
2,
'rejected'],
30,
17,
[[5, 2, 2, 4, 4], [3, 4, 5, 5, 2], [0, 4, 1, 5, 4]]]]],
[['colliding keys',
{'d': 3,
'ops': [['add', 1, 4], ['add', 6, 2], ['add', 1, 1], ['q', 1], ['q', 6], ['q', 11]],
'w': 5},
[['ok', 'ok', 'ok', 5, 2, 0], 7, 4, [[5, 0, 0, 0, 2], [0, 2, 0, 0, 5], [0, 2, 0, 0, 5]]]],
['zero and negative counts',
{'d': 2, 'ops': [['add', 3, 0], ['add', 3, -2], ['add', 3, 5], ['q', 3]], 'w': 7},
[['rejected', 'rejected', 'ok', 5], 5, 2, [[0, 0, 0, 5, 0, 0, 0], [0, 0, 0, 5, 0, 0, 0]]]],
['huge keys wrap prime',
{'d': 3,
'ops': [['add', 900000014, 3],
['add', 2700000042, 2],
['q', 900000014],
['q', 2700000042],
['q', 7]],
'w': 8},
[['ok', 'ok', 3, 2, 0],
5,
2,
[[0, 0, 0, 2, 0, 0, 0, 3], [0, 0, 2, 3, 0, 0, 0, 0], [3, 0, 2, 0, 0, 0, 0, 0]]]],
['uneven rows',
{'d': 4,
'ops': [['add', 2, 3],
['add', 9, 5],
['add', 2, 2],
['add', 5, 3],
['q', 2],
['q', 9],
['q', 5]],
'w': 4},
[['ok', 'ok', 'ok', 'ok', 5, 5, 3],
13,
9,
[[5, 0, 5, 0], [5, 0, 0, 5], [0, 0, 5, 3], [5, 0, 5, 0]]]],
['single row',
{'d': 1, 'ops': [['add', 1, 2], ['add', 4, 3], ['q', 1], ['add', 0, 0]], 'w': 3},
[['ok', 'ok', 2, 'rejected'], 5, 5, [[2, 3, 0]]]],
['many keys',
{'d': 3,
'ops': [['add', 0, 1],
['add', 1, 3],
['add', 2, 1],
['add', 3, 3],
['add', 4, 1],
['add', 5, 3],
['add', 6, 1],
['add', 7, 3],
['add', 8, 1],
['add', 9, 3],
['add', 10, 1],
['add', 11, 3],
['q', 0],
['q', 3],
['q', 6],
['q', 9],
['add', 2, 0]],
'w': 5},
[['ok',
'ok',
'ok',
'ok',
'ok',
'ok',
'ok',
'ok',
'ok',
'ok',
'ok',
'ok',
1,
3,
3,
3,
'rejected'],
24,
14,
[[4, 3, 3, 3, 3], [3, 3, 4, 4, 3], [0, 3, 1, 4, 3]]]]],
[['colliding keys',
{'d': 3,
'ops': [['add', 1, 4], ['add', 6, 2], ['add', 1, 1], ['q', 1], ['q', 6], ['q', 11]],
'w': 5},
[['ok', 'ok', 'ok', 5, 2, 0], 7, 4, [[5, 0, 0, 0, 2], [0, 2, 0, 0, 5], [0, 2, 0, 0, 5]]]],
['zero and negative counts',
{'d': 2, 'ops': [['add', 3, 0], ['add', 3, -2], ['add', 3, 5], ['q', 3]], 'w': 7},
[['rejected', 'rejected', 'ok', 5], 5, 2, [[0, 0, 0, 5, 0, 0, 0], [0, 0, 0, 5, 0, 0, 0]]]],
['huge keys wrap prime',
{'d': 3,
'ops': [['add', 900000021, 3],
['add', 2700000063, 2],
['q', 900000021],
['q', 2700000063],
['q', 7]],
'w': 9},
[['ok', 'ok', 3, 2, 0],
5,
2,
[[0, 0, 2, 0, 0, 3, 0, 0, 0], [0, 0, 3, 0, 0, 0, 0, 0, 0], [0, 3, 0, 0, 0, 0, 2, 0, 0]]]],
['uneven rows',
{'d': 4,
'ops': [['add', 2, 3],
['add', 9, 5],
['add', 2, 2],
['add', 5, 4],
['q', 2],
['q', 9],
['q', 5]],
'w': 4},
[['ok', 'ok', 'ok', 'ok', 5, 5, 4],
14,
10,
[[5, 0, 5, 0], [5, 0, 0, 5], [0, 0, 5, 4], [5, 0, 5, 0]]]],
['single row',
{'d': 1, 'ops': [['add', 1, 2], ['add', 4, 3], ['q', 1], ['add', 0, 0]], 'w': 3},
[['ok', 'ok', 2, 'rejected'], 5, 5, [[2, 3, 0]]]],
['many keys',
{'d': 3,
'ops': [['add', 0, 1],
['add', 1, 4],
['add', 2, 3],
['add', 3, 2],
['add', 4, 1],
['add', 5, 4],
['add', 6, 3],
['add', 7, 2],
['add', 8, 1],
['add', 9, 4],
['add', 10, 3],
['add', 11, 2],
['q', 0],
['q', 3],
['q', 6],
['q', 9],
['add', 2, 0]],
'w': 5},
[['ok',
'ok',
'ok',
'ok',
'ok',
'ok',
'ok',
'ok',
'ok',
'ok',
'ok',
'ok',
1,
3,
3,
4,
'rejected'],
30,
17,
[[5, 4, 4, 3, 3], [4, 3, 5, 3, 4], [0, 4, 1, 5, 4]]]]],
[['colliding keys',
{'d': 3,
'ops': [['add', 1, 4], ['add', 6, 2], ['add', 1, 1], ['q', 1], ['q', 6], ['q', 11]],
'w': 5},
[['ok', 'ok', 'ok', 5, 2, 0], 7, 4, [[5, 0, 0, 0, 2], [0, 2, 0, 0, 5], [0, 2, 0, 0, 5]]]],
['zero and negative counts',
{'d': 2, 'ops': [['add', 3, 0], ['add', 3, -2], ['add', 3, 5], ['q', 3]], 'w': 7},
[['rejected', 'rejected', 'ok', 5], 5, 2, [[0, 0, 0, 5, 0, 0, 0], [0, 0, 0, 5, 0, 0, 0]]]],
['huge keys wrap prime',
{'d': 3,
'ops': [['add', 900000028, 3],
['add', 2700000084, 2],
['q', 900000028],
['q', 2700000084],
['q', 7]],
'w': 10},
[['ok', 'ok', 3, 2, 0],
5,
2,
[[0, 0, 0, 0, 2, 0, 0, 0, 3, 0],
[0, 0, 0, 0, 0, 3, 2, 0, 0, 0],
[0, 0, 0, 0, 3, 0, 0, 0, 0, 0]]]],
['uneven rows',
{'d': 4,
'ops': [['add', 2, 3],
['add', 9, 5],
['add', 2, 2],
['add', 5, 5],
['q', 2],
['q', 9],
['q', 5]],
'w': 4},
[['ok', 'ok', 'ok', 'ok', 5, 5, 5],
15,
11,
[[5, 0, 5, 0], [5, 0, 0, 5], [0, 0, 5, 5], [5, 0, 5, 0]]]],
['single row',
{'d': 1, 'ops': [['add', 1, 2], ['add', 4, 3], ['q', 1], ['add', 0, 0]], 'w': 3},
[['ok', 'ok', 2, 'rejected'], 5, 5, [[2, 3, 0]]]],
['many keys',
{'d': 3,
'ops': [['add', 0, 1],
['add', 1, 1],
['add', 2, 1],
['add', 3, 1],
['add', 4, 1],
['add', 5, 1],
['add', 6, 1],
['add', 7, 1],
['add', 8, 1],
['add', 9, 1],
['add', 10, 1],
['add', 11, 1],
['q', 0],
['q', 3],
['q', 6],
['q', 9],
['add', 2, 0]],
'w': 5},
[['ok',
'ok',
'ok',
'ok',
'ok',
'ok',
'ok',
'ok',
'ok',
'ok',
'ok',
'ok',
1,
1,
1,
1,
'rejected'],
12,
7,
[[2, 1, 1, 1, 1], [1, 1, 2, 2, 1], [0, 1, 1, 2, 1]]]]],
[['colliding keys',
{'d': 3,
'ops': [['add', 1, 4], ['add', 6, 2], ['add', 1, 1], ['q', 1], ['q', 6], ['q', 11]],
'w': 5},
[['ok', 'ok', 'ok', 5, 2, 0], 7, 4, [[5, 0, 0, 0, 2], [0, 2, 0, 0, 5], [0, 2, 0, 0, 5]]]],
['zero and negative counts',
{'d': 2, 'ops': [['add', 3, 0], ['add', 3, -2], ['add', 3, 5], ['q', 3]], 'w': 7},
[['rejected', 'rejected', 'ok', 5], 5, 2, [[0, 0, 0, 5, 0, 0, 0], [0, 0, 0, 5, 0, 0, 0]]]],
['huge keys wrap prime',
{'d': 3,
'ops': [['add', 900000035, 3],
['add', 2700000105, 2],
['q', 900000035],
['q', 2700000105],
['q', 7]],
'w': 11},
[['ok', 'ok', 3, 2, 0],
5,
2,
[[0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 2],
[0, 0, 0, 3, 2, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 2, 3, 0, 0, 0]]]],
['uneven rows',
{'d': 4,
'ops': [['add', 2, 3],
['add', 9, 5],
['add', 2, 2],
['add', 5, 6],
['q', 2],
['q', 9],
['q', 5]],
'w': 4},
[['ok', 'ok', 'ok', 'ok', 5, 5, 6],
16,
11,
[[6, 0, 5, 0], [6, 0, 0, 5], [0, 0, 5, 6], [6, 0, 5, 0]]]],
['single row',
{'d': 1, 'ops': [['add', 1, 2], ['add', 4, 3], ['q', 1], ['add', 0, 0]], 'w': 3},
[['ok', 'ok', 2, 'rejected'], 5, 5, [[2, 3, 0]]]],
['many keys',
{'d': 3,
'ops': [['add', 0, 1],
['add', 1, 2],
['add', 2, 3],
['add', 3, 4],
['add', 4, 1],
['add', 5, 2],
['add', 6, 3],
['add', 7, 4],
['add', 8, 1],
['add', 9, 2],
['add', 10, 3],
['add', 11, 4],
['q', 0],
['q', 3],
['q', 6],
['q', 9],
['add', 2, 0]],
'w': 5},
[['ok',
'ok',
'ok',
'ok',
'ok',
'ok',
'ok',
'ok',
'ok',
'ok',
'ok',
'ok',
1,
4,
4,
2,
'rejected'],
30,
17,
[[5, 2, 2, 4, 4], [3, 4, 5, 5, 2], [0, 4, 1, 5, 4]]]]]]
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 |
|---|---|---|---|
| colliding keys | [['ok', 'ok', 'ok', 5, 2, 0], 7, 4, [[5, 0, 0, 0, 2], [0, 2, 0, 0, 5], [0, 2, 0, 0, 5]]] | [['ok', 'ok', 'ok', 5, 2, 0], 7, 4, [[5, 0, 0, 0, 2], [0, 2, 0, 0, 5], [0, 2, 0, 0, 5]]] | Passed |
| zero and negative counts | [['rejected', 'rejected', 'ok', 5], 5, 2, [[0, 0, 0, 5, 0, 0, 0], [0, 0, 0, 5, 0, 0, 0]]] | [['rejected', 'rejected', 'ok', 5], 5, 2, [[0, 0, 0, 5, 0, 0, 0], [0, 0, 0, 5, 0, 0, 0]]] | Passed |
| huge keys wrap prime | [['ok', 'ok', 3, 2, 0], 5, 2, [[0, 5, 0, 0, 0, 0, 0], [2, 0, 0, 0, 3, 0, 0], [2, 0, 0, 3, 0, 0, 0]]] | [['ok', 'ok', 3, 2, 0], 5, 2, [[0, 3, 0, 0, 0, 0, 0], [2, 0, 0, 0, 3, 0, 0], [2, 0, 0, 3, 0, 0, 0]]] | Failed |
| uneven rows | [['ok', 'ok', 'ok', 'ok', 5, 5, 2], 12, 9, [[7, 0, 5, 0], [7, 0, 0, 5], [0, 0, 5, 2], [5, 0, 5, 0]]] | [['ok', 'ok', 'ok', 'ok', 5, 5, 2], 12, 9, [[5, 0, 5, 0], [5, 0, 0, 5], [0, 0, 5, 2], [5, 0, 5, 0]]] | Failed |
| single row | [['ok', 'ok', 2, 'rejected'], 5, 5, [[2, 3, 0]]] | [['ok', 'ok', 2, 'rejected'], 5, 5, [[2, 3, 0]]] | Passed |
| many keys | [['ok', 'ok', 'ok', 'ok', 'ok', 'ok', 'ok', 'ok', 'ok', 'ok', 'ok', 'ok', 1, 4, 4, 3, 'rejected'], 30, 17, [[10, 3, 3, 7, 7], [3, 4, 6, 5, 3], [0, 4, 1, 5, 4]]] | [['ok', 'ok', 'ok', 'ok', 'ok', 'ok', 'ok', 'ok', 'ok', 'ok', 'ok', 'ok', 1, 4, 4, 2, 'rejected'], 30, 17, [[5, 2, 2, 4, 4], [3, 4, 5, 5, 2], [0, 4, 1, 5, 4]]] | Failed |
SHA-256 / 3e182ba1a22a701ad8ed5b24556b059c1e81e709df9722ad5a2aa398e6ca1fec
2 / The unsuccessful fix
Exit 1"""Failure Map reference implementation. Python standard library only."""
import json
import math
N = 1
observations = []
def solve(x):
w = x['w']
A = [1103515245, 1812433253, 1664525017, 2013265921, 1597334677]
B = [12345, 1013904223, 7, 99991, 31337]
P = 2147483647
d = x['d']
t = [[0] * w for _ in range(d)]
def bucket(r, key):
return (A[r] * key + B[r]) % P % w
total = 0
res = []
for op in x['ops']:
if op[0] == 'add':
key, cnt = op[1], op[2]
if cnt <= 0:
res.append('rejected')
continue
est = max(t[r][bucket(r, key)] for r in range(d))
for r in range(d):
b = bucket(r, key)
t[r][b] = max(t[r][b], est + cnt)
total += cnt
res.append('ok')
else:
res.append(min(t[r][bucket(r, op[1])] for r in range(d)))
return [res, total, math.ceil(math.e / w * total), t]
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
cases = [[['colliding keys',
{'d': 3,
'ops': [['add', 1, 4], ['add', 6, 2], ['add', 1, 1], ['q', 1], ['q', 6], ['q', 11]],
'w': 5},
[['ok', 'ok', 'ok', 5, 2, 0], 7, 4, [[5, 0, 0, 0, 2], [0, 2, 0, 0, 5], [0, 2, 0, 0, 5]]]],
['zero and negative counts',
{'d': 2, 'ops': [['add', 3, 0], ['add', 3, -2], ['add', 3, 5], ['q', 3]], 'w': 7},
[['rejected', 'rejected', 'ok', 5], 5, 2, [[0, 0, 0, 5, 0, 0, 0], [0, 0, 0, 5, 0, 0, 0]]]],
['huge keys wrap prime',
{'d': 3,
'ops': [['add', 900000007, 3],
['add', 2700000021, 2],
['q', 900000007],
['q', 2700000021],
['q', 7]],
'w': 7},
[['ok', 'ok', 3, 2, 0],
5,
2,
[[0, 3, 0, 0, 0, 0, 0], [2, 0, 0, 0, 3, 0, 0], [2, 0, 0, 3, 0, 0, 0]]]],
['uneven rows',
{'d': 4,
'ops': [['add', 2, 3],
['add', 9, 5],
['add', 2, 2],
['add', 5, 2],
['q', 2],
['q', 9],
['q', 5]],
'w': 4},
[['ok', 'ok', 'ok', 'ok', 5, 5, 2],
12,
9,
[[5, 0, 5, 0], [5, 0, 0, 5], [0, 0, 5, 2], [5, 0, 5, 0]]]],
['single row',
{'d': 1, 'ops': [['add', 1, 2], ['add', 4, 3], ['q', 1], ['add', 0, 0]], 'w': 3},
[['ok', 'ok', 2, 'rejected'], 5, 5, [[2, 3, 0]]]],
['many keys',
{'d': 3,
'ops': [['add', 0, 1],
['add', 1, 2],
['add', 2, 3],
['add', 3, 4],
['add', 4, 1],
['add', 5, 2],
['add', 6, 3],
['add', 7, 4],
['add', 8, 1],
['add', 9, 2],
['add', 10, 3],
['add', 11, 4],
['q', 0],
['q', 3],
['q', 6],
['q', 9],
['add', 2, 0]],
'w': 5},
[['ok',
'ok',
'ok',
'ok',
'ok',
'ok',
'ok',
'ok',
'ok',
'ok',
'ok',
'ok',
1,
4,
4,
2,
'rejected'],
30,
17,
[[5, 2, 2, 4, 4], [3, 4, 5, 5, 2], [0, 4, 1, 5, 4]]]]],
[['colliding keys',
{'d': 3,
'ops': [['add', 1, 4], ['add', 6, 2], ['add', 1, 1], ['q', 1], ['q', 6], ['q', 11]],
'w': 5},
[['ok', 'ok', 'ok', 5, 2, 0], 7, 4, [[5, 0, 0, 0, 2], [0, 2, 0, 0, 5], [0, 2, 0, 0, 5]]]],
['zero and negative counts',
{'d': 2, 'ops': [['add', 3, 0], ['add', 3, -2], ['add', 3, 5], ['q', 3]], 'w': 7},
[['rejected', 'rejected', 'ok', 5], 5, 2, [[0, 0, 0, 5, 0, 0, 0], [0, 0, 0, 5, 0, 0, 0]]]],
['huge keys wrap prime',
{'d': 3,
'ops': [['add', 900000014, 3],
['add', 2700000042, 2],
['q', 900000014],
['q', 2700000042],
['q', 7]],
'w': 8},
[['ok', 'ok', 3, 2, 0],
5,
2,
[[0, 0, 0, 2, 0, 0, 0, 3], [0, 0, 2, 3, 0, 0, 0, 0], [3, 0, 2, 0, 0, 0, 0, 0]]]],
['uneven rows',
{'d': 4,
'ops': [['add', 2, 3],
['add', 9, 5],
['add', 2, 2],
['add', 5, 3],
['q', 2],
['q', 9],
['q', 5]],
'w': 4},
[['ok', 'ok', 'ok', 'ok', 5, 5, 3],
13,
9,
[[5, 0, 5, 0], [5, 0, 0, 5], [0, 0, 5, 3], [5, 0, 5, 0]]]],
['single row',
{'d': 1, 'ops': [['add', 1, 2], ['add', 4, 3], ['q', 1], ['add', 0, 0]], 'w': 3},
[['ok', 'ok', 2, 'rejected'], 5, 5, [[2, 3, 0]]]],
['many keys',
{'d': 3,
'ops': [['add', 0, 1],
['add', 1, 3],
['add', 2, 1],
['add', 3, 3],
['add', 4, 1],
['add', 5, 3],
['add', 6, 1],
['add', 7, 3],
['add', 8, 1],
['add', 9, 3],
['add', 10, 1],
['add', 11, 3],
['q', 0],
['q', 3],
['q', 6],
['q', 9],
['add', 2, 0]],
'w': 5},
[['ok',
'ok',
'ok',
'ok',
'ok',
'ok',
'ok',
'ok',
'ok',
'ok',
'ok',
'ok',
1,
3,
3,
3,
'rejected'],
24,
14,
[[4, 3, 3, 3, 3], [3, 3, 4, 4, 3], [0, 3, 1, 4, 3]]]]],
[['colliding keys',
{'d': 3,
'ops': [['add', 1, 4], ['add', 6, 2], ['add', 1, 1], ['q', 1], ['q', 6], ['q', 11]],
'w': 5},
[['ok', 'ok', 'ok', 5, 2, 0], 7, 4, [[5, 0, 0, 0, 2], [0, 2, 0, 0, 5], [0, 2, 0, 0, 5]]]],
['zero and negative counts',
{'d': 2, 'ops': [['add', 3, 0], ['add', 3, -2], ['add', 3, 5], ['q', 3]], 'w': 7},
[['rejected', 'rejected', 'ok', 5], 5, 2, [[0, 0, 0, 5, 0, 0, 0], [0, 0, 0, 5, 0, 0, 0]]]],
['huge keys wrap prime',
{'d': 3,
'ops': [['add', 900000021, 3],
['add', 2700000063, 2],
['q', 900000021],
['q', 2700000063],
['q', 7]],
'w': 9},
[['ok', 'ok', 3, 2, 0],
5,
2,
[[0, 0, 2, 0, 0, 3, 0, 0, 0], [0, 0, 3, 0, 0, 0, 0, 0, 0], [0, 3, 0, 0, 0, 0, 2, 0, 0]]]],
['uneven rows',
{'d': 4,
'ops': [['add', 2, 3],
['add', 9, 5],
['add', 2, 2],
['add', 5, 4],
['q', 2],
['q', 9],
['q', 5]],
'w': 4},
[['ok', 'ok', 'ok', 'ok', 5, 5, 4],
14,
10,
[[5, 0, 5, 0], [5, 0, 0, 5], [0, 0, 5, 4], [5, 0, 5, 0]]]],
['single row',
{'d': 1, 'ops': [['add', 1, 2], ['add', 4, 3], ['q', 1], ['add', 0, 0]], 'w': 3},
[['ok', 'ok', 2, 'rejected'], 5, 5, [[2, 3, 0]]]],
['many keys',
{'d': 3,
'ops': [['add', 0, 1],
['add', 1, 4],
['add', 2, 3],
['add', 3, 2],
['add', 4, 1],
['add', 5, 4],
['add', 6, 3],
['add', 7, 2],
['add', 8, 1],
['add', 9, 4],
['add', 10, 3],
['add', 11, 2],
['q', 0],
['q', 3],
['q', 6],
['q', 9],
['add', 2, 0]],
'w': 5},
[['ok',
'ok',
'ok',
'ok',
'ok',
'ok',
'ok',
'ok',
'ok',
'ok',
'ok',
'ok',
1,
3,
3,
4,
'rejected'],
30,
17,
[[5, 4, 4, 3, 3], [4, 3, 5, 3, 4], [0, 4, 1, 5, 4]]]]],
[['colliding keys',
{'d': 3,
'ops': [['add', 1, 4], ['add', 6, 2], ['add', 1, 1], ['q', 1], ['q', 6], ['q', 11]],
'w': 5},
[['ok', 'ok', 'ok', 5, 2, 0], 7, 4, [[5, 0, 0, 0, 2], [0, 2, 0, 0, 5], [0, 2, 0, 0, 5]]]],
['zero and negative counts',
{'d': 2, 'ops': [['add', 3, 0], ['add', 3, -2], ['add', 3, 5], ['q', 3]], 'w': 7},
[['rejected', 'rejected', 'ok', 5], 5, 2, [[0, 0, 0, 5, 0, 0, 0], [0, 0, 0, 5, 0, 0, 0]]]],
['huge keys wrap prime',
{'d': 3,
'ops': [['add', 900000028, 3],
['add', 2700000084, 2],
['q', 900000028],
['q', 2700000084],
['q', 7]],
'w': 10},
[['ok', 'ok', 3, 2, 0],
5,
2,
[[0, 0, 0, 0, 2, 0, 0, 0, 3, 0],
[0, 0, 0, 0, 0, 3, 2, 0, 0, 0],
[0, 0, 0, 0, 3, 0, 0, 0, 0, 0]]]],
['uneven rows',
{'d': 4,
'ops': [['add', 2, 3],
['add', 9, 5],
['add', 2, 2],
['add', 5, 5],
['q', 2],
['q', 9],
['q', 5]],
'w': 4},
[['ok', 'ok', 'ok', 'ok', 5, 5, 5],
15,
11,
[[5, 0, 5, 0], [5, 0, 0, 5], [0, 0, 5, 5], [5, 0, 5, 0]]]],
['single row',
{'d': 1, 'ops': [['add', 1, 2], ['add', 4, 3], ['q', 1], ['add', 0, 0]], 'w': 3},
[['ok', 'ok', 2, 'rejected'], 5, 5, [[2, 3, 0]]]],
['many keys',
{'d': 3,
'ops': [['add', 0, 1],
['add', 1, 1],
['add', 2, 1],
['add', 3, 1],
['add', 4, 1],
['add', 5, 1],
['add', 6, 1],
['add', 7, 1],
['add', 8, 1],
['add', 9, 1],
['add', 10, 1],
['add', 11, 1],
['q', 0],
['q', 3],
['q', 6],
['q', 9],
['add', 2, 0]],
'w': 5},
[['ok',
'ok',
'ok',
'ok',
'ok',
'ok',
'ok',
'ok',
'ok',
'ok',
'ok',
'ok',
1,
1,
1,
1,
'rejected'],
12,
7,
[[2, 1, 1, 1, 1], [1, 1, 2, 2, 1], [0, 1, 1, 2, 1]]]]],
[['colliding keys',
{'d': 3,
'ops': [['add', 1, 4], ['add', 6, 2], ['add', 1, 1], ['q', 1], ['q', 6], ['q', 11]],
'w': 5},
[['ok', 'ok', 'ok', 5, 2, 0], 7, 4, [[5, 0, 0, 0, 2], [0, 2, 0, 0, 5], [0, 2, 0, 0, 5]]]],
['zero and negative counts',
{'d': 2, 'ops': [['add', 3, 0], ['add', 3, -2], ['add', 3, 5], ['q', 3]], 'w': 7},
[['rejected', 'rejected', 'ok', 5], 5, 2, [[0, 0, 0, 5, 0, 0, 0], [0, 0, 0, 5, 0, 0, 0]]]],
['huge keys wrap prime',
{'d': 3,
'ops': [['add', 900000035, 3],
['add', 2700000105, 2],
['q', 900000035],
['q', 2700000105],
['q', 7]],
'w': 11},
[['ok', 'ok', 3, 2, 0],
5,
2,
[[0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 2],
[0, 0, 0, 3, 2, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 2, 3, 0, 0, 0]]]],
['uneven rows',
{'d': 4,
'ops': [['add', 2, 3],
['add', 9, 5],
['add', 2, 2],
['add', 5, 6],
['q', 2],
['q', 9],
['q', 5]],
'w': 4},
[['ok', 'ok', 'ok', 'ok', 5, 5, 6],
16,
11,
[[6, 0, 5, 0], [6, 0, 0, 5], [0, 0, 5, 6], [6, 0, 5, 0]]]],
['single row',
{'d': 1, 'ops': [['add', 1, 2], ['add', 4, 3], ['q', 1], ['add', 0, 0]], 'w': 3},
[['ok', 'ok', 2, 'rejected'], 5, 5, [[2, 3, 0]]]],
['many keys',
{'d': 3,
'ops': [['add', 0, 1],
['add', 1, 2],
['add', 2, 3],
['add', 3, 4],
['add', 4, 1],
['add', 5, 2],
['add', 6, 3],
['add', 7, 4],
['add', 8, 1],
['add', 9, 2],
['add', 10, 3],
['add', 11, 4],
['q', 0],
['q', 3],
['q', 6],
['q', 9],
['add', 2, 0]],
'w': 5},
[['ok',
'ok',
'ok',
'ok',
'ok',
'ok',
'ok',
'ok',
'ok',
'ok',
'ok',
'ok',
1,
4,
4,
2,
'rejected'],
30,
17,
[[5, 2, 2, 4, 4], [3, 4, 5, 5, 2], [0, 4, 1, 5, 4]]]]]]
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 |
|---|---|---|---|
| colliding keys | [['ok', 'ok', 'ok', 5, 2, 0], 7, 4, [[5, 0, 0, 0, 2], [0, 2, 0, 0, 5], [0, 2, 0, 0, 5]]] | [['ok', 'ok', 'ok', 5, 2, 0], 7, 4, [[5, 0, 0, 0, 2], [0, 2, 0, 0, 5], [0, 2, 0, 0, 5]]] | Passed |
| zero and negative counts | [['rejected', 'rejected', 'ok', 5], 5, 2, [[0, 0, 0, 5, 0, 0, 0], [0, 0, 0, 5, 0, 0, 0]]] | [['rejected', 'rejected', 'ok', 5], 5, 2, [[0, 0, 0, 5, 0, 0, 0], [0, 0, 0, 5, 0, 0, 0]]] | Passed |
| huge keys wrap prime | [['ok', 'ok', 3, 5, 0], 5, 2, [[0, 5, 0, 0, 0, 0, 0], [5, 0, 0, 0, 3, 0, 0], [5, 0, 0, 3, 0, 0, 0]]] | [['ok', 'ok', 3, 2, 0], 5, 2, [[0, 3, 0, 0, 0, 0, 0], [2, 0, 0, 0, 3, 0, 0], [2, 0, 0, 3, 0, 0, 0]]] | Failed |
| uneven rows | [['ok', 'ok', 'ok', 'ok', 10, 8, 12], 12, 9, [[12, 0, 8, 0], [12, 0, 0, 10], [0, 0, 10, 12], [12, 0, 10, 0]]] | [['ok', 'ok', 'ok', 'ok', 5, 5, 2], 12, 9, [[5, 0, 5, 0], [5, 0, 0, 5], [0, 0, 5, 2], [5, 0, 5, 0]]] | Failed |
| single row | [['ok', 'ok', 2, 'rejected'], 5, 5, [[2, 3, 0]]] | [['ok', 'ok', 2, 'rejected'], 5, 5, [[2, 3, 0]]] | Passed |
| many keys | [['ok', 'ok', 'ok', 'ok', 'ok', 'ok', 'ok', 'ok', 'ok', 'ok', 'ok', 'ok', 1, 10, 16, 23, 'rejected'], 30, 17, [[30, 13, 23, 10, 20], [13, 16, 26, 30, 23], [0, 21, 1, 30, 11]]] | [['ok', 'ok', 'ok', 'ok', 'ok', 'ok', 'ok', 'ok', 'ok', 'ok', 'ok', 'ok', 1, 4, 4, 2, 'rejected'], 30, 17, [[5, 2, 2, 4, 4], [3, 4, 5, 5, 2], [0, 4, 1, 5, 4]]] | Failed |
SHA-256 / 7d54571cb40e9fade4b8c416d62ab60bd07f406aad2a576c0055905a23789e0a
3 / The verified repair
Exit 0"""Failure Map reference implementation. Python standard library only."""
import json
import math
N = 1
observations = []
def solve(x):
w = x['w']
A = [1103515245, 1812433253, 1664525017, 2013265921, 1597334677]
B = [12345, 1013904223, 7, 99991, 31337]
P = 2147483647
d = x['d']
t = [[0] * w for _ in range(d)]
def bucket(r, key):
return (A[r] * key + B[r]) % P % w
total = 0
res = []
for op in x['ops']:
if op[0] == 'add':
key, cnt = op[1], op[2]
if cnt <= 0:
res.append('rejected')
continue
est = min(t[r][bucket(r, key)] for r in range(d))
for r in range(d):
b = bucket(r, key)
t[r][b] = max(t[r][b], est + cnt)
total += cnt
res.append('ok')
else:
res.append(min(t[r][bucket(r, op[1])] for r in range(d)))
return [res, total, math.ceil(math.e / w * total), t]
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
cases = [[['colliding keys',
{'d': 3,
'ops': [['add', 1, 4], ['add', 6, 2], ['add', 1, 1], ['q', 1], ['q', 6], ['q', 11]],
'w': 5},
[['ok', 'ok', 'ok', 5, 2, 0], 7, 4, [[5, 0, 0, 0, 2], [0, 2, 0, 0, 5], [0, 2, 0, 0, 5]]]],
['zero and negative counts',
{'d': 2, 'ops': [['add', 3, 0], ['add', 3, -2], ['add', 3, 5], ['q', 3]], 'w': 7},
[['rejected', 'rejected', 'ok', 5], 5, 2, [[0, 0, 0, 5, 0, 0, 0], [0, 0, 0, 5, 0, 0, 0]]]],
['huge keys wrap prime',
{'d': 3,
'ops': [['add', 900000007, 3],
['add', 2700000021, 2],
['q', 900000007],
['q', 2700000021],
['q', 7]],
'w': 7},
[['ok', 'ok', 3, 2, 0],
5,
2,
[[0, 3, 0, 0, 0, 0, 0], [2, 0, 0, 0, 3, 0, 0], [2, 0, 0, 3, 0, 0, 0]]]],
['uneven rows',
{'d': 4,
'ops': [['add', 2, 3],
['add', 9, 5],
['add', 2, 2],
['add', 5, 2],
['q', 2],
['q', 9],
['q', 5]],
'w': 4},
[['ok', 'ok', 'ok', 'ok', 5, 5, 2],
12,
9,
[[5, 0, 5, 0], [5, 0, 0, 5], [0, 0, 5, 2], [5, 0, 5, 0]]]],
['single row',
{'d': 1, 'ops': [['add', 1, 2], ['add', 4, 3], ['q', 1], ['add', 0, 0]], 'w': 3},
[['ok', 'ok', 2, 'rejected'], 5, 5, [[2, 3, 0]]]],
['many keys',
{'d': 3,
'ops': [['add', 0, 1],
['add', 1, 2],
['add', 2, 3],
['add', 3, 4],
['add', 4, 1],
['add', 5, 2],
['add', 6, 3],
['add', 7, 4],
['add', 8, 1],
['add', 9, 2],
['add', 10, 3],
['add', 11, 4],
['q', 0],
['q', 3],
['q', 6],
['q', 9],
['add', 2, 0]],
'w': 5},
[['ok',
'ok',
'ok',
'ok',
'ok',
'ok',
'ok',
'ok',
'ok',
'ok',
'ok',
'ok',
1,
4,
4,
2,
'rejected'],
30,
17,
[[5, 2, 2, 4, 4], [3, 4, 5, 5, 2], [0, 4, 1, 5, 4]]]]],
[['colliding keys',
{'d': 3,
'ops': [['add', 1, 4], ['add', 6, 2], ['add', 1, 1], ['q', 1], ['q', 6], ['q', 11]],
'w': 5},
[['ok', 'ok', 'ok', 5, 2, 0], 7, 4, [[5, 0, 0, 0, 2], [0, 2, 0, 0, 5], [0, 2, 0, 0, 5]]]],
['zero and negative counts',
{'d': 2, 'ops': [['add', 3, 0], ['add', 3, -2], ['add', 3, 5], ['q', 3]], 'w': 7},
[['rejected', 'rejected', 'ok', 5], 5, 2, [[0, 0, 0, 5, 0, 0, 0], [0, 0, 0, 5, 0, 0, 0]]]],
['huge keys wrap prime',
{'d': 3,
'ops': [['add', 900000014, 3],
['add', 2700000042, 2],
['q', 900000014],
['q', 2700000042],
['q', 7]],
'w': 8},
[['ok', 'ok', 3, 2, 0],
5,
2,
[[0, 0, 0, 2, 0, 0, 0, 3], [0, 0, 2, 3, 0, 0, 0, 0], [3, 0, 2, 0, 0, 0, 0, 0]]]],
['uneven rows',
{'d': 4,
'ops': [['add', 2, 3],
['add', 9, 5],
['add', 2, 2],
['add', 5, 3],
['q', 2],
['q', 9],
['q', 5]],
'w': 4},
[['ok', 'ok', 'ok', 'ok', 5, 5, 3],
13,
9,
[[5, 0, 5, 0], [5, 0, 0, 5], [0, 0, 5, 3], [5, 0, 5, 0]]]],
['single row',
{'d': 1, 'ops': [['add', 1, 2], ['add', 4, 3], ['q', 1], ['add', 0, 0]], 'w': 3},
[['ok', 'ok', 2, 'rejected'], 5, 5, [[2, 3, 0]]]],
['many keys',
{'d': 3,
'ops': [['add', 0, 1],
['add', 1, 3],
['add', 2, 1],
['add', 3, 3],
['add', 4, 1],
['add', 5, 3],
['add', 6, 1],
['add', 7, 3],
['add', 8, 1],
['add', 9, 3],
['add', 10, 1],
['add', 11, 3],
['q', 0],
['q', 3],
['q', 6],
['q', 9],
['add', 2, 0]],
'w': 5},
[['ok',
'ok',
'ok',
'ok',
'ok',
'ok',
'ok',
'ok',
'ok',
'ok',
'ok',
'ok',
1,
3,
3,
3,
'rejected'],
24,
14,
[[4, 3, 3, 3, 3], [3, 3, 4, 4, 3], [0, 3, 1, 4, 3]]]]],
[['colliding keys',
{'d': 3,
'ops': [['add', 1, 4], ['add', 6, 2], ['add', 1, 1], ['q', 1], ['q', 6], ['q', 11]],
'w': 5},
[['ok', 'ok', 'ok', 5, 2, 0], 7, 4, [[5, 0, 0, 0, 2], [0, 2, 0, 0, 5], [0, 2, 0, 0, 5]]]],
['zero and negative counts',
{'d': 2, 'ops': [['add', 3, 0], ['add', 3, -2], ['add', 3, 5], ['q', 3]], 'w': 7},
[['rejected', 'rejected', 'ok', 5], 5, 2, [[0, 0, 0, 5, 0, 0, 0], [0, 0, 0, 5, 0, 0, 0]]]],
['huge keys wrap prime',
{'d': 3,
'ops': [['add', 900000021, 3],
['add', 2700000063, 2],
['q', 900000021],
['q', 2700000063],
['q', 7]],
'w': 9},
[['ok', 'ok', 3, 2, 0],
5,
2,
[[0, 0, 2, 0, 0, 3, 0, 0, 0], [0, 0, 3, 0, 0, 0, 0, 0, 0], [0, 3, 0, 0, 0, 0, 2, 0, 0]]]],
['uneven rows',
{'d': 4,
'ops': [['add', 2, 3],
['add', 9, 5],
['add', 2, 2],
['add', 5, 4],
['q', 2],
['q', 9],
['q', 5]],
'w': 4},
[['ok', 'ok', 'ok', 'ok', 5, 5, 4],
14,
10,
[[5, 0, 5, 0], [5, 0, 0, 5], [0, 0, 5, 4], [5, 0, 5, 0]]]],
['single row',
{'d': 1, 'ops': [['add', 1, 2], ['add', 4, 3], ['q', 1], ['add', 0, 0]], 'w': 3},
[['ok', 'ok', 2, 'rejected'], 5, 5, [[2, 3, 0]]]],
['many keys',
{'d': 3,
'ops': [['add', 0, 1],
['add', 1, 4],
['add', 2, 3],
['add', 3, 2],
['add', 4, 1],
['add', 5, 4],
['add', 6, 3],
['add', 7, 2],
['add', 8, 1],
['add', 9, 4],
['add', 10, 3],
['add', 11, 2],
['q', 0],
['q', 3],
['q', 6],
['q', 9],
['add', 2, 0]],
'w': 5},
[['ok',
'ok',
'ok',
'ok',
'ok',
'ok',
'ok',
'ok',
'ok',
'ok',
'ok',
'ok',
1,
3,
3,
4,
'rejected'],
30,
17,
[[5, 4, 4, 3, 3], [4, 3, 5, 3, 4], [0, 4, 1, 5, 4]]]]],
[['colliding keys',
{'d': 3,
'ops': [['add', 1, 4], ['add', 6, 2], ['add', 1, 1], ['q', 1], ['q', 6], ['q', 11]],
'w': 5},
[['ok', 'ok', 'ok', 5, 2, 0], 7, 4, [[5, 0, 0, 0, 2], [0, 2, 0, 0, 5], [0, 2, 0, 0, 5]]]],
['zero and negative counts',
{'d': 2, 'ops': [['add', 3, 0], ['add', 3, -2], ['add', 3, 5], ['q', 3]], 'w': 7},
[['rejected', 'rejected', 'ok', 5], 5, 2, [[0, 0, 0, 5, 0, 0, 0], [0, 0, 0, 5, 0, 0, 0]]]],
['huge keys wrap prime',
{'d': 3,
'ops': [['add', 900000028, 3],
['add', 2700000084, 2],
['q', 900000028],
['q', 2700000084],
['q', 7]],
'w': 10},
[['ok', 'ok', 3, 2, 0],
5,
2,
[[0, 0, 0, 0, 2, 0, 0, 0, 3, 0],
[0, 0, 0, 0, 0, 3, 2, 0, 0, 0],
[0, 0, 0, 0, 3, 0, 0, 0, 0, 0]]]],
['uneven rows',
{'d': 4,
'ops': [['add', 2, 3],
['add', 9, 5],
['add', 2, 2],
['add', 5, 5],
['q', 2],
['q', 9],
['q', 5]],
'w': 4},
[['ok', 'ok', 'ok', 'ok', 5, 5, 5],
15,
11,
[[5, 0, 5, 0], [5, 0, 0, 5], [0, 0, 5, 5], [5, 0, 5, 0]]]],
['single row',
{'d': 1, 'ops': [['add', 1, 2], ['add', 4, 3], ['q', 1], ['add', 0, 0]], 'w': 3},
[['ok', 'ok', 2, 'rejected'], 5, 5, [[2, 3, 0]]]],
['many keys',
{'d': 3,
'ops': [['add', 0, 1],
['add', 1, 1],
['add', 2, 1],
['add', 3, 1],
['add', 4, 1],
['add', 5, 1],
['add', 6, 1],
['add', 7, 1],
['add', 8, 1],
['add', 9, 1],
['add', 10, 1],
['add', 11, 1],
['q', 0],
['q', 3],
['q', 6],
['q', 9],
['add', 2, 0]],
'w': 5},
[['ok',
'ok',
'ok',
'ok',
'ok',
'ok',
'ok',
'ok',
'ok',
'ok',
'ok',
'ok',
1,
1,
1,
1,
'rejected'],
12,
7,
[[2, 1, 1, 1, 1], [1, 1, 2, 2, 1], [0, 1, 1, 2, 1]]]]],
[['colliding keys',
{'d': 3,
'ops': [['add', 1, 4], ['add', 6, 2], ['add', 1, 1], ['q', 1], ['q', 6], ['q', 11]],
'w': 5},
[['ok', 'ok', 'ok', 5, 2, 0], 7, 4, [[5, 0, 0, 0, 2], [0, 2, 0, 0, 5], [0, 2, 0, 0, 5]]]],
['zero and negative counts',
{'d': 2, 'ops': [['add', 3, 0], ['add', 3, -2], ['add', 3, 5], ['q', 3]], 'w': 7},
[['rejected', 'rejected', 'ok', 5], 5, 2, [[0, 0, 0, 5, 0, 0, 0], [0, 0, 0, 5, 0, 0, 0]]]],
['huge keys wrap prime',
{'d': 3,
'ops': [['add', 900000035, 3],
['add', 2700000105, 2],
['q', 900000035],
['q', 2700000105],
['q', 7]],
'w': 11},
[['ok', 'ok', 3, 2, 0],
5,
2,
[[0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 2],
[0, 0, 0, 3, 2, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 2, 3, 0, 0, 0]]]],
['uneven rows',
{'d': 4,
'ops': [['add', 2, 3],
['add', 9, 5],
['add', 2, 2],
['add', 5, 6],
['q', 2],
['q', 9],
['q', 5]],
'w': 4},
[['ok', 'ok', 'ok', 'ok', 5, 5, 6],
16,
11,
[[6, 0, 5, 0], [6, 0, 0, 5], [0, 0, 5, 6], [6, 0, 5, 0]]]],
['single row',
{'d': 1, 'ops': [['add', 1, 2], ['add', 4, 3], ['q', 1], ['add', 0, 0]], 'w': 3},
[['ok', 'ok', 2, 'rejected'], 5, 5, [[2, 3, 0]]]],
['many keys',
{'d': 3,
'ops': [['add', 0, 1],
['add', 1, 2],
['add', 2, 3],
['add', 3, 4],
['add', 4, 1],
['add', 5, 2],
['add', 6, 3],
['add', 7, 4],
['add', 8, 1],
['add', 9, 2],
['add', 10, 3],
['add', 11, 4],
['q', 0],
['q', 3],
['q', 6],
['q', 9],
['add', 2, 0]],
'w': 5},
[['ok',
'ok',
'ok',
'ok',
'ok',
'ok',
'ok',
'ok',
'ok',
'ok',
'ok',
'ok',
1,
4,
4,
2,
'rejected'],
30,
17,
[[5, 2, 2, 4, 4], [3, 4, 5, 5, 2], [0, 4, 1, 5, 4]]]]]]
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 |
|---|---|---|---|
| colliding keys | [['ok', 'ok', 'ok', 5, 2, 0], 7, 4, [[5, 0, 0, 0, 2], [0, 2, 0, 0, 5], [0, 2, 0, 0, 5]]] | [['ok', 'ok', 'ok', 5, 2, 0], 7, 4, [[5, 0, 0, 0, 2], [0, 2, 0, 0, 5], [0, 2, 0, 0, 5]]] | Passed |
| zero and negative counts | [['rejected', 'rejected', 'ok', 5], 5, 2, [[0, 0, 0, 5, 0, 0, 0], [0, 0, 0, 5, 0, 0, 0]]] | [['rejected', 'rejected', 'ok', 5], 5, 2, [[0, 0, 0, 5, 0, 0, 0], [0, 0, 0, 5, 0, 0, 0]]] | Passed |
| huge keys wrap prime | [['ok', 'ok', 3, 2, 0], 5, 2, [[0, 3, 0, 0, 0, 0, 0], [2, 0, 0, 0, 3, 0, 0], [2, 0, 0, 3, 0, 0, 0]]] | [['ok', 'ok', 3, 2, 0], 5, 2, [[0, 3, 0, 0, 0, 0, 0], [2, 0, 0, 0, 3, 0, 0], [2, 0, 0, 3, 0, 0, 0]]] | Passed |
| uneven rows | [['ok', 'ok', 'ok', 'ok', 5, 5, 2], 12, 9, [[5, 0, 5, 0], [5, 0, 0, 5], [0, 0, 5, 2], [5, 0, 5, 0]]] | [['ok', 'ok', 'ok', 'ok', 5, 5, 2], 12, 9, [[5, 0, 5, 0], [5, 0, 0, 5], [0, 0, 5, 2], [5, 0, 5, 0]]] | Passed |
| single row | [['ok', 'ok', 2, 'rejected'], 5, 5, [[2, 3, 0]]] | [['ok', 'ok', 2, 'rejected'], 5, 5, [[2, 3, 0]]] | Passed |
| many keys | [['ok', 'ok', 'ok', 'ok', 'ok', 'ok', 'ok', 'ok', 'ok', 'ok', 'ok', 'ok', 1, 4, 4, 2, 'rejected'], 30, 17, [[5, 2, 2, 4, 4], [3, 4, 5, 5, 2], [0, 4, 1, 5, 4]]] | [['ok', 'ok', 'ok', 'ok', 'ok', 'ok', 'ok', 'ok', 'ok', 'ok', 'ok', 'ok', 1, 4, 4, 2, 'rejected'], 30, 17, [[5, 2, 2, 4, 4], [3, 4, 5, 5, 2], [0, 4, 1, 5, 4]]] | Passed |
SHA-256 / 0e18fcfdc61a0aa0508c64b1667c489c348c474f4cfb57183103a8face239005
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 2026-09-29T14:48:43.962065+00:00.
Case digest / e3df3f344f1b4d1bc1970243b3b2a9bd536b56f749c523f213aa29991dd81468