FA-86181 / Game economy crafting balance / Open access
Inventory stack insertion: Top-up fills later slots first · case 01
Loot lands in the last partial stack instead of the first.
ROOT CAUSE
Partial stacks are topped up from the end of the bag.
VERIFIED REPAIR
Restore `for s in slots:` at the top-up order step.
Unsuccessful approach: Filling fullest stacks first still ignores slot order.
Case contract
slots = list of None or [name, count]; names are case sensitive. First top up partial stacks (count < max_stack) of the same item in slot order, then fill empty slots in order with new stacks of at most max_stack. Reserved placeholders [name, 0] count as partial stacks. Legacy stacks above max_stack are left untouched. Returns {slots, leftover}.
Why this case matters
Game economies leak or destroy currency when one crafting or pricing rule is off by one boundary, rounding stage or state update; the defect is observable in exact integer outcomes.
1 / The failure
Exit 1"""Failure Map reference implementation. Python standard library only."""
import json
N = 1
observations = []
def solve(slots, item, qty, max_stack):
slots = [s if s is None else list(s) for s in slots]
left = qty
for s in reversed(slots):
if left == 0:
break
if s is not None and s[0] == item and s[1] < max_stack:
add = min(left, max_stack - s[1])
s[1] += add
left -= add
for i in range(len(slots)):
if left == 0:
break
if slots[i] is None:
add = min(left, max_stack)
slots[i] = [item, add]
left -= add
return {'slots': slots, 'leftover': left}
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
cases = [[('two partial stacks #1',
[[['Arrow', 18], ['Arrow', 15], None], 'Arrow', 4, 20],
{'slots': [['Arrow', 20], ['Arrow', 17], None], 'leftover': 0}),
('fault site top-up order #1',
[[None, ['Potion', 1], ['Potion', 25], None, ['Arrow', 19], ['Arrow', 15]], 'Arrow', 1, 20],
{'slots': [None, ['Potion', 1], ['Potion', 25], None, ['Arrow', 20], ['Arrow', 15]], 'leftover': 0}),
('fault site top-up order #2',
[[None, ['Arrow', 0], ['Potion', 19], None, ['Arrow', 14], ['Potion', 1]], 'Potion', 1, 20],
{'slots': [None, ['Arrow', 0], ['Potion', 20], None, ['Arrow', 14], ['Potion', 1]], 'leftover': 0}),
('regression top-up order #1',
[[['arrow', 0], ['arrow', 19]], 'arrow', 7, 20],
{'slots': [['arrow', 7], ['arrow', 19]], 'leftover': 0}),
('regression top-up order #2',
[[['Arrow', 5], ['arrow', 1], ['arrow', 25], None, ['Arrow', 19]], 'Arrow', 1, 20],
{'slots': [['Arrow', 6], ['arrow', 1], ['arrow', 25], None, ['Arrow', 19]], 'leftover': 0}),
('legacy overfull stack #1',
[[['Arrow', 25], None], 'Arrow', 3, 20],
{'slots': [['Arrow', 25], ['Arrow', 3]], 'leftover': 0}),
('case distinct item #1', [[['arrow', 3]], 'Arrow', 2, 20], {'slots': [['arrow', 3]], 'leftover': 2}),
('control #1',
[[['Arrow', 6], None, ['arrow', 5]], 'Potion', 0, 20],
{'slots': [['Arrow', 6], None, ['arrow', 5]], 'leftover': 0})],
[('two partial stacks #1',
[[['Arrow', 18], ['Arrow', 15], None], 'Arrow', 4, 20],
{'slots': [['Arrow', 20], ['Arrow', 17], None], 'leftover': 0}),
('fault site top-up order #1',
[[None, ['Arrow', 0], ['Potion', 19], None, ['Arrow', 14], ['Potion', 1]], 'Potion', 1, 20],
{'slots': [None, ['Arrow', 0], ['Potion', 20], None, ['Arrow', 14], ['Potion', 1]], 'leftover': 0}),
('fault site top-up order #2',
[[['Potion', 8], ['Potion', 20], ['arrow', 1], ['Potion', 0], ['arrow', 20], None], 'Potion', 7, 10],
{'slots': [['Potion', 10], ['Potion', 20], ['arrow', 1], ['Potion', 5], ['arrow', 20], None],
'leftover': 0}),
('regression top-up order #1',
[[['arrow', 0], ['arrow', 19]], 'arrow', 7, 20],
{'slots': [['arrow', 7], ['arrow', 19]], 'leftover': 0}),
('regression top-up order #2',
[[['Arrow', 5], ['arrow', 1], ['arrow', 25], None, ['Arrow', 19]], 'Arrow', 1, 20],
{'slots': [['Arrow', 6], ['arrow', 1], ['arrow', 25], None, ['Arrow', 19]], 'leftover': 0}),
('legacy overfull stack #1',
[[['Arrow', 25], None], 'Arrow', 3, 20],
{'slots': [['Arrow', 25], ['Arrow', 3]], 'leftover': 0}),
('case distinct item #1', [[['arrow', 3]], 'Arrow', 2, 20], {'slots': [['arrow', 3]], 'leftover': 2}),
('control #1',
[[['Arrow', 6], None, ['arrow', 5]], 'Potion', 0, 20],
{'slots': [['Arrow', 6], None, ['arrow', 5]], 'leftover': 0})],
[('two partial stacks #1',
[[['Arrow', 18], ['Arrow', 15], None], 'Arrow', 4, 20],
{'slots': [['Arrow', 20], ['Arrow', 17], None], 'leftover': 0}),
('fault site top-up order #1',
[[['arrow', 25], ['arrow', 4], ['Arrow', 0], ['arrow', 0], ['arrow', 25]], 'arrow', 1, 10],
{'slots': [['arrow', 25], ['arrow', 5], ['Arrow', 0], ['arrow', 0], ['arrow', 25]], 'leftover': 0}),
('fault site top-up order #2',
[[['Potion', 0], ['Arrow', 1], ['Arrow', 0]], 'Arrow', 7, 20],
{'slots': [['Potion', 0], ['Arrow', 8], ['Arrow', 0]], 'leftover': 0}),
('regression top-up order #1',
[[['arrow', 0], ['arrow', 19]], 'arrow', 7, 20],
{'slots': [['arrow', 7], ['arrow', 19]], 'leftover': 0}),
('regression top-up order #2',
[[['Arrow', 5], ['arrow', 1], ['arrow', 25], None, ['Arrow', 19]], 'Arrow', 1, 20],
{'slots': [['Arrow', 6], ['arrow', 1], ['arrow', 25], None, ['Arrow', 19]], 'leftover': 0}),
('legacy overfull stack #1',
[[['Arrow', 25], None], 'Arrow', 3, 20],
{'slots': [['Arrow', 25], ['Arrow', 3]], 'leftover': 0}),
('case distinct item #1', [[['arrow', 3]], 'Arrow', 2, 20], {'slots': [['arrow', 3]], 'leftover': 2}),
('control #1',
[[['Arrow', 6], None, ['arrow', 5]], 'Potion', 0, 20],
{'slots': [['Arrow', 6], None, ['arrow', 5]], 'leftover': 0})],
[('two partial stacks #1',
[[['Arrow', 18], ['Arrow', 15], None], 'Arrow', 4, 20],
{'slots': [['Arrow', 20], ['Arrow', 17], None], 'leftover': 0}),
('fault site top-up order #1',
[[['Arrow', 19], ['Arrow', 5]], 'Arrow', 7, 20],
{'slots': [['Arrow', 20], ['Arrow', 11]], 'leftover': 0}),
('fault site top-up order #2',
[[['arrow', 3], None, ['arrow', 0]], 'arrow', 1, 10],
{'slots': [['arrow', 4], None, ['arrow', 0]], 'leftover': 0}),
('regression top-up order #1',
[[['arrow', 0], ['arrow', 19]], 'arrow', 7, 20],
{'slots': [['arrow', 7], ['arrow', 19]], 'leftover': 0}),
('regression top-up order #2',
[[['Arrow', 5], ['arrow', 1], ['arrow', 25], None, ['Arrow', 19]], 'Arrow', 1, 20],
{'slots': [['Arrow', 6], ['arrow', 1], ['arrow', 25], None, ['Arrow', 19]], 'leftover': 0}),
('legacy overfull stack #1',
[[['Arrow', 25], None], 'Arrow', 3, 20],
{'slots': [['Arrow', 25], ['Arrow', 3]], 'leftover': 0}),
('case distinct item #1', [[['arrow', 3]], 'Arrow', 2, 20], {'slots': [['arrow', 3]], 'leftover': 2}),
('control #1',
[[None, ['Arrow', 16], ['arrow', 20], None, ['Arrow', 25], None], 'Potion', 20, 10],
{'slots': [['Potion', 10], ['Arrow', 16], ['arrow', 20], ['Potion', 10], ['Arrow', 25], None],
'leftover': 0})],
[('two partial stacks #1',
[[['Arrow', 18], ['Arrow', 15], None], 'Arrow', 4, 20],
{'slots': [['Arrow', 20], ['Arrow', 17], None], 'leftover': 0}),
('regression top-up order #1',
[[['arrow', 0], ['arrow', 19]], 'arrow', 7, 20],
{'slots': [['arrow', 7], ['arrow', 19]], 'leftover': 0}),
('regression top-up order #2',
[[['Arrow', 5], ['arrow', 1], ['arrow', 25], None, ['Arrow', 19]], 'Arrow', 1, 20],
{'slots': [['Arrow', 6], ['arrow', 1], ['arrow', 25], None, ['Arrow', 19]], 'leftover': 0}),
('legacy overfull stack #1',
[[['Arrow', 25], None], 'Arrow', 3, 20],
{'slots': [['Arrow', 25], ['Arrow', 3]], 'leftover': 0}),
('case distinct item #1', [[['arrow', 3]], 'Arrow', 2, 20], {'slots': [['arrow', 3]], 'leftover': 2}),
('control #1', [[None], 'Arrow', 11, 20], {'slots': [['Arrow', 11]], 'leftover': 0}),
('control #2', [[['Potion', 20]], 'Arrow', 0, 20], {'slots': [['Potion', 20]], 'leftover': 0}),
('control #3', [[], 'arrow', 45, 5], {'slots': [], 'leftover': 45})]]
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 |
|---|---|---|---|
| two partial stacks #1 | {'leftover': 0, 'slots': [['Arrow', 18], ['Arrow', 19], None]} | {'leftover': 0, 'slots': [['Arrow', 20], ['Arrow', 17], None]} | Failed |
| fault site top-up order #1 | {'leftover': 0, 'slots': [None, ['Potion', 1], ['Potion', 25], None, ['Arrow', 19], ['Arrow', 16]]} | {'leftover': 0, 'slots': [None, ['Potion', 1], ['Potion', 25], None, ['Arrow', 20], ['Arrow', 15]]} | Failed |
| fault site top-up order #2 | {'leftover': 0, 'slots': [None, ['Arrow', 0], ['Potion', 19], None, ['Arrow', 14], ['Potion', 2]]} | {'leftover': 0, 'slots': [None, ['Arrow', 0], ['Potion', 20], None, ['Arrow', 14], ['Potion', 1]]} | Failed |
| regression top-up order #1 | {'leftover': 0, 'slots': [['arrow', 6], ['arrow', 20]]} | {'leftover': 0, 'slots': [['arrow', 7], ['arrow', 19]]} | Failed |
| regression top-up order #2 | {'leftover': 0, 'slots': [['Arrow', 5], ['arrow', 1], ['arrow', 25], None, ['Arrow', 20]]} | {'leftover': 0, 'slots': [['Arrow', 6], ['arrow', 1], ['arrow', 25], None, ['Arrow', 19]]} | Failed |
| legacy overfull stack #1 | {'leftover': 0, 'slots': [['Arrow', 25], ['Arrow', 3]]} | {'leftover': 0, 'slots': [['Arrow', 25], ['Arrow', 3]]} | Passed |
| case distinct item #1 | {'leftover': 2, 'slots': [['arrow', 3]]} | {'leftover': 2, 'slots': [['arrow', 3]]} | Passed |
| control #1 | {'leftover': 0, 'slots': [['Arrow', 6], None, ['arrow', 5]]} | {'leftover': 0, 'slots': [['Arrow', 6], None, ['arrow', 5]]} | Passed |
SHA-256 / 11a0395fdf97ede3a36cd5d768e6c764c465da292854f3712071d66ee62d8940
2 / The unsuccessful fix
Exit 1"""Failure Map reference implementation. Python standard library only."""
import json
N = 1
observations = []
def solve(slots, item, qty, max_stack):
slots = [s if s is None else list(s) for s in slots]
left = qty
for s in sorted((s for s in slots if s), key=lambda s: -s[1]):
if left == 0:
break
if s is not None and s[0] == item and s[1] < max_stack:
add = min(left, max_stack - s[1])
s[1] += add
left -= add
for i in range(len(slots)):
if left == 0:
break
if slots[i] is None:
add = min(left, max_stack)
slots[i] = [item, add]
left -= add
return {'slots': slots, 'leftover': left}
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
cases = [[('two partial stacks #1',
[[['Arrow', 18], ['Arrow', 15], None], 'Arrow', 4, 20],
{'slots': [['Arrow', 20], ['Arrow', 17], None], 'leftover': 0}),
('fault site top-up order #1',
[[None, ['Potion', 1], ['Potion', 25], None, ['Arrow', 19], ['Arrow', 15]], 'Arrow', 1, 20],
{'slots': [None, ['Potion', 1], ['Potion', 25], None, ['Arrow', 20], ['Arrow', 15]], 'leftover': 0}),
('fault site top-up order #2',
[[None, ['Arrow', 0], ['Potion', 19], None, ['Arrow', 14], ['Potion', 1]], 'Potion', 1, 20],
{'slots': [None, ['Arrow', 0], ['Potion', 20], None, ['Arrow', 14], ['Potion', 1]], 'leftover': 0}),
('regression top-up order #1',
[[['arrow', 0], ['arrow', 19]], 'arrow', 7, 20],
{'slots': [['arrow', 7], ['arrow', 19]], 'leftover': 0}),
('regression top-up order #2',
[[['Arrow', 5], ['arrow', 1], ['arrow', 25], None, ['Arrow', 19]], 'Arrow', 1, 20],
{'slots': [['Arrow', 6], ['arrow', 1], ['arrow', 25], None, ['Arrow', 19]], 'leftover': 0}),
('legacy overfull stack #1',
[[['Arrow', 25], None], 'Arrow', 3, 20],
{'slots': [['Arrow', 25], ['Arrow', 3]], 'leftover': 0}),
('case distinct item #1', [[['arrow', 3]], 'Arrow', 2, 20], {'slots': [['arrow', 3]], 'leftover': 2}),
('control #1',
[[['Arrow', 6], None, ['arrow', 5]], 'Potion', 0, 20],
{'slots': [['Arrow', 6], None, ['arrow', 5]], 'leftover': 0})],
[('two partial stacks #1',
[[['Arrow', 18], ['Arrow', 15], None], 'Arrow', 4, 20],
{'slots': [['Arrow', 20], ['Arrow', 17], None], 'leftover': 0}),
('fault site top-up order #1',
[[None, ['Arrow', 0], ['Potion', 19], None, ['Arrow', 14], ['Potion', 1]], 'Potion', 1, 20],
{'slots': [None, ['Arrow', 0], ['Potion', 20], None, ['Arrow', 14], ['Potion', 1]], 'leftover': 0}),
('fault site top-up order #2',
[[['Potion', 8], ['Potion', 20], ['arrow', 1], ['Potion', 0], ['arrow', 20], None], 'Potion', 7, 10],
{'slots': [['Potion', 10], ['Potion', 20], ['arrow', 1], ['Potion', 5], ['arrow', 20], None],
'leftover': 0}),
('regression top-up order #1',
[[['arrow', 0], ['arrow', 19]], 'arrow', 7, 20],
{'slots': [['arrow', 7], ['arrow', 19]], 'leftover': 0}),
('regression top-up order #2',
[[['Arrow', 5], ['arrow', 1], ['arrow', 25], None, ['Arrow', 19]], 'Arrow', 1, 20],
{'slots': [['Arrow', 6], ['arrow', 1], ['arrow', 25], None, ['Arrow', 19]], 'leftover': 0}),
('legacy overfull stack #1',
[[['Arrow', 25], None], 'Arrow', 3, 20],
{'slots': [['Arrow', 25], ['Arrow', 3]], 'leftover': 0}),
('case distinct item #1', [[['arrow', 3]], 'Arrow', 2, 20], {'slots': [['arrow', 3]], 'leftover': 2}),
('control #1',
[[['Arrow', 6], None, ['arrow', 5]], 'Potion', 0, 20],
{'slots': [['Arrow', 6], None, ['arrow', 5]], 'leftover': 0})],
[('two partial stacks #1',
[[['Arrow', 18], ['Arrow', 15], None], 'Arrow', 4, 20],
{'slots': [['Arrow', 20], ['Arrow', 17], None], 'leftover': 0}),
('fault site top-up order #1',
[[['arrow', 25], ['arrow', 4], ['Arrow', 0], ['arrow', 0], ['arrow', 25]], 'arrow', 1, 10],
{'slots': [['arrow', 25], ['arrow', 5], ['Arrow', 0], ['arrow', 0], ['arrow', 25]], 'leftover': 0}),
('fault site top-up order #2',
[[['Potion', 0], ['Arrow', 1], ['Arrow', 0]], 'Arrow', 7, 20],
{'slots': [['Potion', 0], ['Arrow', 8], ['Arrow', 0]], 'leftover': 0}),
('regression top-up order #1',
[[['arrow', 0], ['arrow', 19]], 'arrow', 7, 20],
{'slots': [['arrow', 7], ['arrow', 19]], 'leftover': 0}),
('regression top-up order #2',
[[['Arrow', 5], ['arrow', 1], ['arrow', 25], None, ['Arrow', 19]], 'Arrow', 1, 20],
{'slots': [['Arrow', 6], ['arrow', 1], ['arrow', 25], None, ['Arrow', 19]], 'leftover': 0}),
('legacy overfull stack #1',
[[['Arrow', 25], None], 'Arrow', 3, 20],
{'slots': [['Arrow', 25], ['Arrow', 3]], 'leftover': 0}),
('case distinct item #1', [[['arrow', 3]], 'Arrow', 2, 20], {'slots': [['arrow', 3]], 'leftover': 2}),
('control #1',
[[['Arrow', 6], None, ['arrow', 5]], 'Potion', 0, 20],
{'slots': [['Arrow', 6], None, ['arrow', 5]], 'leftover': 0})],
[('two partial stacks #1',
[[['Arrow', 18], ['Arrow', 15], None], 'Arrow', 4, 20],
{'slots': [['Arrow', 20], ['Arrow', 17], None], 'leftover': 0}),
('fault site top-up order #1',
[[['Arrow', 19], ['Arrow', 5]], 'Arrow', 7, 20],
{'slots': [['Arrow', 20], ['Arrow', 11]], 'leftover': 0}),
('fault site top-up order #2',
[[['arrow', 3], None, ['arrow', 0]], 'arrow', 1, 10],
{'slots': [['arrow', 4], None, ['arrow', 0]], 'leftover': 0}),
('regression top-up order #1',
[[['arrow', 0], ['arrow', 19]], 'arrow', 7, 20],
{'slots': [['arrow', 7], ['arrow', 19]], 'leftover': 0}),
('regression top-up order #2',
[[['Arrow', 5], ['arrow', 1], ['arrow', 25], None, ['Arrow', 19]], 'Arrow', 1, 20],
{'slots': [['Arrow', 6], ['arrow', 1], ['arrow', 25], None, ['Arrow', 19]], 'leftover': 0}),
('legacy overfull stack #1',
[[['Arrow', 25], None], 'Arrow', 3, 20],
{'slots': [['Arrow', 25], ['Arrow', 3]], 'leftover': 0}),
('case distinct item #1', [[['arrow', 3]], 'Arrow', 2, 20], {'slots': [['arrow', 3]], 'leftover': 2}),
('control #1',
[[None, ['Arrow', 16], ['arrow', 20], None, ['Arrow', 25], None], 'Potion', 20, 10],
{'slots': [['Potion', 10], ['Arrow', 16], ['arrow', 20], ['Potion', 10], ['Arrow', 25], None],
'leftover': 0})],
[('two partial stacks #1',
[[['Arrow', 18], ['Arrow', 15], None], 'Arrow', 4, 20],
{'slots': [['Arrow', 20], ['Arrow', 17], None], 'leftover': 0}),
('regression top-up order #1',
[[['arrow', 0], ['arrow', 19]], 'arrow', 7, 20],
{'slots': [['arrow', 7], ['arrow', 19]], 'leftover': 0}),
('regression top-up order #2',
[[['Arrow', 5], ['arrow', 1], ['arrow', 25], None, ['Arrow', 19]], 'Arrow', 1, 20],
{'slots': [['Arrow', 6], ['arrow', 1], ['arrow', 25], None, ['Arrow', 19]], 'leftover': 0}),
('legacy overfull stack #1',
[[['Arrow', 25], None], 'Arrow', 3, 20],
{'slots': [['Arrow', 25], ['Arrow', 3]], 'leftover': 0}),
('case distinct item #1', [[['arrow', 3]], 'Arrow', 2, 20], {'slots': [['arrow', 3]], 'leftover': 2}),
('control #1', [[None], 'Arrow', 11, 20], {'slots': [['Arrow', 11]], 'leftover': 0}),
('control #2', [[['Potion', 20]], 'Arrow', 0, 20], {'slots': [['Potion', 20]], 'leftover': 0}),
('control #3', [[], 'arrow', 45, 5], {'slots': [], 'leftover': 45})]]
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 |
|---|---|---|---|
| two partial stacks #1 | {'leftover': 0, 'slots': [['Arrow', 20], ['Arrow', 17], None]} | {'leftover': 0, 'slots': [['Arrow', 20], ['Arrow', 17], None]} | Passed |
| fault site top-up order #1 | {'leftover': 0, 'slots': [None, ['Potion', 1], ['Potion', 25], None, ['Arrow', 20], ['Arrow', 15]]} | {'leftover': 0, 'slots': [None, ['Potion', 1], ['Potion', 25], None, ['Arrow', 20], ['Arrow', 15]]} | Passed |
| fault site top-up order #2 | {'leftover': 0, 'slots': [None, ['Arrow', 0], ['Potion', 20], None, ['Arrow', 14], ['Potion', 1]]} | {'leftover': 0, 'slots': [None, ['Arrow', 0], ['Potion', 20], None, ['Arrow', 14], ['Potion', 1]]} | Passed |
| regression top-up order #1 | {'leftover': 0, 'slots': [['arrow', 6], ['arrow', 20]]} | {'leftover': 0, 'slots': [['arrow', 7], ['arrow', 19]]} | Failed |
| regression top-up order #2 | {'leftover': 0, 'slots': [['Arrow', 5], ['arrow', 1], ['arrow', 25], None, ['Arrow', 20]]} | {'leftover': 0, 'slots': [['Arrow', 6], ['arrow', 1], ['arrow', 25], None, ['Arrow', 19]]} | Failed |
| legacy overfull stack #1 | {'leftover': 0, 'slots': [['Arrow', 25], ['Arrow', 3]]} | {'leftover': 0, 'slots': [['Arrow', 25], ['Arrow', 3]]} | Passed |
| case distinct item #1 | {'leftover': 2, 'slots': [['arrow', 3]]} | {'leftover': 2, 'slots': [['arrow', 3]]} | Passed |
| control #1 | {'leftover': 0, 'slots': [['Arrow', 6], None, ['arrow', 5]]} | {'leftover': 0, 'slots': [['Arrow', 6], None, ['arrow', 5]]} | Passed |
SHA-256 / a951a8fd627bd6c7618fd0028d513f7aa7194ee91e3929ad6fd94026d0f36e0b
3 / The verified repair
Exit 0"""Failure Map reference implementation. Python standard library only."""
import json
N = 1
observations = []
def solve(slots, item, qty, max_stack):
slots = [s if s is None else list(s) for s in slots]
left = qty
for s in slots:
if left == 0:
break
if s is not None and s[0] == item and s[1] < max_stack:
add = min(left, max_stack - s[1])
s[1] += add
left -= add
for i in range(len(slots)):
if left == 0:
break
if slots[i] is None:
add = min(left, max_stack)
slots[i] = [item, add]
left -= add
return {'slots': slots, 'leftover': left}
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
cases = [[('two partial stacks #1',
[[['Arrow', 18], ['Arrow', 15], None], 'Arrow', 4, 20],
{'slots': [['Arrow', 20], ['Arrow', 17], None], 'leftover': 0}),
('fault site top-up order #1',
[[None, ['Potion', 1], ['Potion', 25], None, ['Arrow', 19], ['Arrow', 15]], 'Arrow', 1, 20],
{'slots': [None, ['Potion', 1], ['Potion', 25], None, ['Arrow', 20], ['Arrow', 15]], 'leftover': 0}),
('fault site top-up order #2',
[[None, ['Arrow', 0], ['Potion', 19], None, ['Arrow', 14], ['Potion', 1]], 'Potion', 1, 20],
{'slots': [None, ['Arrow', 0], ['Potion', 20], None, ['Arrow', 14], ['Potion', 1]], 'leftover': 0}),
('regression top-up order #1',
[[['arrow', 0], ['arrow', 19]], 'arrow', 7, 20],
{'slots': [['arrow', 7], ['arrow', 19]], 'leftover': 0}),
('regression top-up order #2',
[[['Arrow', 5], ['arrow', 1], ['arrow', 25], None, ['Arrow', 19]], 'Arrow', 1, 20],
{'slots': [['Arrow', 6], ['arrow', 1], ['arrow', 25], None, ['Arrow', 19]], 'leftover': 0}),
('legacy overfull stack #1',
[[['Arrow', 25], None], 'Arrow', 3, 20],
{'slots': [['Arrow', 25], ['Arrow', 3]], 'leftover': 0}),
('case distinct item #1', [[['arrow', 3]], 'Arrow', 2, 20], {'slots': [['arrow', 3]], 'leftover': 2}),
('control #1',
[[['Arrow', 6], None, ['arrow', 5]], 'Potion', 0, 20],
{'slots': [['Arrow', 6], None, ['arrow', 5]], 'leftover': 0})],
[('two partial stacks #1',
[[['Arrow', 18], ['Arrow', 15], None], 'Arrow', 4, 20],
{'slots': [['Arrow', 20], ['Arrow', 17], None], 'leftover': 0}),
('fault site top-up order #1',
[[None, ['Arrow', 0], ['Potion', 19], None, ['Arrow', 14], ['Potion', 1]], 'Potion', 1, 20],
{'slots': [None, ['Arrow', 0], ['Potion', 20], None, ['Arrow', 14], ['Potion', 1]], 'leftover': 0}),
('fault site top-up order #2',
[[['Potion', 8], ['Potion', 20], ['arrow', 1], ['Potion', 0], ['arrow', 20], None], 'Potion', 7, 10],
{'slots': [['Potion', 10], ['Potion', 20], ['arrow', 1], ['Potion', 5], ['arrow', 20], None],
'leftover': 0}),
('regression top-up order #1',
[[['arrow', 0], ['arrow', 19]], 'arrow', 7, 20],
{'slots': [['arrow', 7], ['arrow', 19]], 'leftover': 0}),
('regression top-up order #2',
[[['Arrow', 5], ['arrow', 1], ['arrow', 25], None, ['Arrow', 19]], 'Arrow', 1, 20],
{'slots': [['Arrow', 6], ['arrow', 1], ['arrow', 25], None, ['Arrow', 19]], 'leftover': 0}),
('legacy overfull stack #1',
[[['Arrow', 25], None], 'Arrow', 3, 20],
{'slots': [['Arrow', 25], ['Arrow', 3]], 'leftover': 0}),
('case distinct item #1', [[['arrow', 3]], 'Arrow', 2, 20], {'slots': [['arrow', 3]], 'leftover': 2}),
('control #1',
[[['Arrow', 6], None, ['arrow', 5]], 'Potion', 0, 20],
{'slots': [['Arrow', 6], None, ['arrow', 5]], 'leftover': 0})],
[('two partial stacks #1',
[[['Arrow', 18], ['Arrow', 15], None], 'Arrow', 4, 20],
{'slots': [['Arrow', 20], ['Arrow', 17], None], 'leftover': 0}),
('fault site top-up order #1',
[[['arrow', 25], ['arrow', 4], ['Arrow', 0], ['arrow', 0], ['arrow', 25]], 'arrow', 1, 10],
{'slots': [['arrow', 25], ['arrow', 5], ['Arrow', 0], ['arrow', 0], ['arrow', 25]], 'leftover': 0}),
('fault site top-up order #2',
[[['Potion', 0], ['Arrow', 1], ['Arrow', 0]], 'Arrow', 7, 20],
{'slots': [['Potion', 0], ['Arrow', 8], ['Arrow', 0]], 'leftover': 0}),
('regression top-up order #1',
[[['arrow', 0], ['arrow', 19]], 'arrow', 7, 20],
{'slots': [['arrow', 7], ['arrow', 19]], 'leftover': 0}),
('regression top-up order #2',
[[['Arrow', 5], ['arrow', 1], ['arrow', 25], None, ['Arrow', 19]], 'Arrow', 1, 20],
{'slots': [['Arrow', 6], ['arrow', 1], ['arrow', 25], None, ['Arrow', 19]], 'leftover': 0}),
('legacy overfull stack #1',
[[['Arrow', 25], None], 'Arrow', 3, 20],
{'slots': [['Arrow', 25], ['Arrow', 3]], 'leftover': 0}),
('case distinct item #1', [[['arrow', 3]], 'Arrow', 2, 20], {'slots': [['arrow', 3]], 'leftover': 2}),
('control #1',
[[['Arrow', 6], None, ['arrow', 5]], 'Potion', 0, 20],
{'slots': [['Arrow', 6], None, ['arrow', 5]], 'leftover': 0})],
[('two partial stacks #1',
[[['Arrow', 18], ['Arrow', 15], None], 'Arrow', 4, 20],
{'slots': [['Arrow', 20], ['Arrow', 17], None], 'leftover': 0}),
('fault site top-up order #1',
[[['Arrow', 19], ['Arrow', 5]], 'Arrow', 7, 20],
{'slots': [['Arrow', 20], ['Arrow', 11]], 'leftover': 0}),
('fault site top-up order #2',
[[['arrow', 3], None, ['arrow', 0]], 'arrow', 1, 10],
{'slots': [['arrow', 4], None, ['arrow', 0]], 'leftover': 0}),
('regression top-up order #1',
[[['arrow', 0], ['arrow', 19]], 'arrow', 7, 20],
{'slots': [['arrow', 7], ['arrow', 19]], 'leftover': 0}),
('regression top-up order #2',
[[['Arrow', 5], ['arrow', 1], ['arrow', 25], None, ['Arrow', 19]], 'Arrow', 1, 20],
{'slots': [['Arrow', 6], ['arrow', 1], ['arrow', 25], None, ['Arrow', 19]], 'leftover': 0}),
('legacy overfull stack #1',
[[['Arrow', 25], None], 'Arrow', 3, 20],
{'slots': [['Arrow', 25], ['Arrow', 3]], 'leftover': 0}),
('case distinct item #1', [[['arrow', 3]], 'Arrow', 2, 20], {'slots': [['arrow', 3]], 'leftover': 2}),
('control #1',
[[None, ['Arrow', 16], ['arrow', 20], None, ['Arrow', 25], None], 'Potion', 20, 10],
{'slots': [['Potion', 10], ['Arrow', 16], ['arrow', 20], ['Potion', 10], ['Arrow', 25], None],
'leftover': 0})],
[('two partial stacks #1',
[[['Arrow', 18], ['Arrow', 15], None], 'Arrow', 4, 20],
{'slots': [['Arrow', 20], ['Arrow', 17], None], 'leftover': 0}),
('regression top-up order #1',
[[['arrow', 0], ['arrow', 19]], 'arrow', 7, 20],
{'slots': [['arrow', 7], ['arrow', 19]], 'leftover': 0}),
('regression top-up order #2',
[[['Arrow', 5], ['arrow', 1], ['arrow', 25], None, ['Arrow', 19]], 'Arrow', 1, 20],
{'slots': [['Arrow', 6], ['arrow', 1], ['arrow', 25], None, ['Arrow', 19]], 'leftover': 0}),
('legacy overfull stack #1',
[[['Arrow', 25], None], 'Arrow', 3, 20],
{'slots': [['Arrow', 25], ['Arrow', 3]], 'leftover': 0}),
('case distinct item #1', [[['arrow', 3]], 'Arrow', 2, 20], {'slots': [['arrow', 3]], 'leftover': 2}),
('control #1', [[None], 'Arrow', 11, 20], {'slots': [['Arrow', 11]], 'leftover': 0}),
('control #2', [[['Potion', 20]], 'Arrow', 0, 20], {'slots': [['Potion', 20]], 'leftover': 0}),
('control #3', [[], 'arrow', 45, 5], {'slots': [], 'leftover': 45})]]
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 |
|---|---|---|---|
| two partial stacks #1 | {'leftover': 0, 'slots': [['Arrow', 20], ['Arrow', 17], None]} | {'leftover': 0, 'slots': [['Arrow', 20], ['Arrow', 17], None]} | Passed |
| fault site top-up order #1 | {'leftover': 0, 'slots': [None, ['Potion', 1], ['Potion', 25], None, ['Arrow', 20], ['Arrow', 15]]} | {'leftover': 0, 'slots': [None, ['Potion', 1], ['Potion', 25], None, ['Arrow', 20], ['Arrow', 15]]} | Passed |
| fault site top-up order #2 | {'leftover': 0, 'slots': [None, ['Arrow', 0], ['Potion', 20], None, ['Arrow', 14], ['Potion', 1]]} | {'leftover': 0, 'slots': [None, ['Arrow', 0], ['Potion', 20], None, ['Arrow', 14], ['Potion', 1]]} | Passed |
| regression top-up order #1 | {'leftover': 0, 'slots': [['arrow', 7], ['arrow', 19]]} | {'leftover': 0, 'slots': [['arrow', 7], ['arrow', 19]]} | Passed |
| regression top-up order #2 | {'leftover': 0, 'slots': [['Arrow', 6], ['arrow', 1], ['arrow', 25], None, ['Arrow', 19]]} | {'leftover': 0, 'slots': [['Arrow', 6], ['arrow', 1], ['arrow', 25], None, ['Arrow', 19]]} | Passed |
| legacy overfull stack #1 | {'leftover': 0, 'slots': [['Arrow', 25], ['Arrow', 3]]} | {'leftover': 0, 'slots': [['Arrow', 25], ['Arrow', 3]]} | Passed |
| case distinct item #1 | {'leftover': 2, 'slots': [['arrow', 3]]} | {'leftover': 2, 'slots': [['arrow', 3]]} | Passed |
| control #1 | {'leftover': 0, 'slots': [['Arrow', 6], None, ['arrow', 5]]} | {'leftover': 0, 'slots': [['Arrow', 6], None, ['arrow', 5]]} | Passed |
SHA-256 / 53d7b872ff7d41bff60a44161cc92305257ee63bb9fd39f0ff8aee4e0dc11d34
Verification & scope
Deterministic toy contract stipulated for this model; integer or exact arithmetic only, not a reproduction of any specific game engine. 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 2026-09-29T14:50:47.286967+00:00.
Case digest / 4facc7f882a0a71c276b5c6aa8f982bb37eb152a8af7acdbd0300c0264da5d32