FA-86691 / Procedural level generation constraints / Open access
Decoration scatter with quadrant quota: Quadrants take one extra prop · case 01
Each quadrant holds one more prop than configured.
ROOT CAUSE
The quota comparison is strict.
VERIFIED REPAIR
Restore `if quota.get(q, 0) >= per_quadrant:` at the quota check step.
Unsuccessful approach: A global cap lets one quadrant take every prop.
Case contract
Candidates [x, y] (grid[y][x]) are tried in order. Accept when in bounds on '.', its quadrant (x*2//w, y*2//h) holds fewer than per_quadrant accepted props, and its squared Euclidean distance to every accepted prop is at least radius*radius. Returns accepted [x, y].
Why this case matters
Procedural generators silently emit unplayable or unfair levels when a single constraint check uses the wrong boundary, axis, neighborhood or update order; the defect is visible in exact generated geometry.
1 / The failure
Exit 1"""Failure Map reference implementation. Python standard library only."""
import json
N = 1
observations = []
def solve(grid, candidates, radius, per_quadrant):
h = len(grid)
w = len(grid[0])
placed = []
quota = {}
for x, y in candidates:
if not (0 <= y < h and 0 <= x < w) or grid[y][x] != '.':
continue
q = (x * 2 // w, y * 2 // h)
if quota.get(q, 0) > per_quadrant:
continue
if any((x - px) ** 2 + (y - py) ** 2 < radius * radius for px, py in placed):
continue
placed.append([x, y])
quota[q] = quota.get(q, 0) + 1
return placed
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
cases = [[('quadrant full #1', [['....', '....'], [[0, 0], [1, 0], [3, 0]], 1, 1], [[0, 0], [3, 0]]),
('regression quota check #1',
[['~~..#', '.....', '....#'], [[3, 1], [1, 2], [5, 2], [2, 3], [0, 3], [3, 0], [1, 1], [0, 1]], 1, 1],
[[3, 1], [1, 2], [1, 1]]),
('regression quota check #2',
[['...~.#', '.#....'], [[0, 2], [6, 1], [2, 0], [6, 0], [2, 1], [2, 1], [1, 2], [0, 1]], 1, 1],
[[2, 0], [2, 1]]),
('regression quota check #3',
[['.....#..', '..#..~~.', '~.~...~.', '.~~..~.#', '.~~.~~..'],
[[1, 1], [0, 1], [0, 0], [4, 2], [2, 4]],
1,
2],
[[1, 1], [0, 1], [4, 2]]),
('regression quota check #4',
[['.##', '.#.', '...', '~..', '~.~', '..#', '...'],
[[3, 0], [1, 6], [3, 0], [0, 0], [0, 6], [0, 5], [1, 3]],
2,
1],
[[1, 6], [0, 0]]),
('exact radius spacing #1', [['.....'], [[0, 0], [2, 0]], 2, 3], [[0, 0], [2, 0]]),
('diagonal within radius #1', [['...', '...', '...'], [[0, 0], [1, 1]], 2, 3], [[0, 0]]),
('control #1',
[['~..~.', '.#...', '~..#.', '..~#.'], [[1, 2], [4, 3], [1, 2], [4, 3], [1, 1]], 2, 3],
[[1, 2], [4, 3]])],
[('quadrant full #1', [['....', '....'], [[0, 0], [1, 0], [3, 0]], 1, 1], [[0, 0], [3, 0]]),
('regression quota check #1',
[['...~.#', '.#....'], [[0, 2], [6, 1], [2, 0], [6, 0], [2, 1], [2, 1], [1, 2], [0, 1]], 1, 1],
[[2, 0], [2, 1]]),
('regression quota check #2',
[['.....#..', '..#..~~.', '~.~...~.', '.~~..~.#', '.~~.~~..'],
[[1, 1], [0, 1], [0, 0], [4, 2], [2, 4]],
1,
2],
[[1, 1], [0, 1], [4, 2]]),
('regression quota check #3',
[['.##', '.#.', '...', '~..', '~.~', '..#', '...'],
[[3, 0], [1, 6], [3, 0], [0, 0], [0, 6], [0, 5], [1, 3]],
2,
1],
[[1, 6], [0, 0]]),
('regression quota check #4',
[['..~..~..', '...~.~.#', '~~..~~..', '.....~~~', '~..~~#..', '...#....', '.~~.~.#.', '#.......'],
[[6, 4], [7, 1], [8, 4], [7, 7], [6, 3], [4, 5], [8, 4], [1, 8], [0, 6], [8, 6]],
3,
1],
[[6, 4], [0, 6]]),
('exact radius spacing #1', [['.....'], [[0, 0], [2, 0]], 2, 3], [[0, 0], [2, 0]]),
('diagonal within radius #1', [['...', '...', '...'], [[0, 0], [1, 1]], 2, 3], [[0, 0]]),
('control #1',
[['~..~.', '.#...', '~..#.', '..~#.'], [[1, 2], [4, 3], [1, 2], [4, 3], [1, 1]], 2, 3],
[[1, 2], [4, 3]])],
[('quadrant full #1', [['....', '....'], [[0, 0], [1, 0], [3, 0]], 1, 1], [[0, 0], [3, 0]]),
('regression quota check #1',
[['.##', '.#.', '...', '~..', '~.~', '..#', '...'],
[[3, 0], [1, 6], [3, 0], [0, 0], [0, 6], [0, 5], [1, 3]],
2,
1],
[[1, 6], [0, 0]]),
('regression quota check #2',
[['..~..~..', '...~.~.#', '~~..~~..', '.....~~~', '~..~~#..', '...#....', '.~~.~.#.', '#.......'],
[[6, 4], [7, 1], [8, 4], [7, 7], [6, 3], [4, 5], [8, 4], [1, 8], [0, 6], [8, 6]],
3,
1],
[[6, 4], [0, 6]]),
('regression quota check #3',
[['##', '#.', '#.', '##', '..', '.#', '..'], [[1, 4], [1, 6]], 1, 1],
[[1, 4]]),
('regression quota check #4',
[['##......', '~#..#..#', '......~#', '.#~.~..#', '#.#...~#', '#..~..~~', '..~..##.', '.......~'],
[[8, 8], [0, 1], [3, 0], [8, 7], [5, 1], [0, 8], [6, 8], [3, 5], [1, 7], [1, 4], [2, 5], [4, 5]],
3,
1],
[[3, 0], [1, 7], [4, 5]]),
('exact radius spacing #1', [['.....'], [[0, 0], [2, 0]], 2, 3], [[0, 0], [2, 0]]),
('diagonal within radius #1', [['...', '...', '...'], [[0, 0], [1, 1]], 2, 3], [[0, 0]]),
('control #1',
[['~..~.', '.#...', '~..#.', '..~#.'], [[1, 2], [4, 3], [1, 2], [4, 3], [1, 1]], 2, 3],
[[1, 2], [4, 3]])],
[('quadrant full #1', [['....', '....'], [[0, 0], [1, 0], [3, 0]], 1, 1], [[0, 0], [3, 0]]),
('regression quota check #1',
[['##', '#.', '#.', '##', '..', '.#', '..'], [[1, 4], [1, 6]], 1, 1],
[[1, 4]]),
('regression quota check #2',
[['##......', '~#..#..#', '......~#', '.#~.~..#', '#.#...~#', '#..~..~~', '..~..##.', '.......~'],
[[8, 8], [0, 1], [3, 0], [8, 7], [5, 1], [0, 8], [6, 8], [3, 5], [1, 7], [1, 4], [2, 5], [4, 5]],
3,
1],
[[3, 0], [1, 7], [4, 5]]),
('regression quota check #3',
[['.....', '.#.##', '.....', '#.~.#', '.~.#.'],
[[3, 1], [3, 2], [5, 4], [3, 5], [2, 1], [0, 0], [4, 1], [4, 0], [1, 1], [3, 2]],
2,
1],
[[3, 2], [0, 0]]),
('regression quota check #4',
[['####..', '.~..##', '#.~~..', '.#...#', '...#~.'],
[[1, 3], [3, 3], [6, 0], [2, 0], [5, 4], [2, 5]],
1,
1],
[[3, 3]]),
('exact radius spacing #1', [['.....'], [[0, 0], [2, 0]], 2, 3], [[0, 0], [2, 0]]),
('diagonal within radius #1', [['...', '...', '...'], [[0, 0], [1, 1]], 2, 3], [[0, 0]]),
('control #1', [['#..', '..#'], [[1, 1]], 1, 1], [[1, 1]])],
[('quadrant full #1', [['....', '....'], [[0, 0], [1, 0], [3, 0]], 1, 1], [[0, 0], [3, 0]]),
('regression quota check #1',
[['.....', '.#.##', '.....', '#.~.#', '.~.#.'],
[[3, 1], [3, 2], [5, 4], [3, 5], [2, 1], [0, 0], [4, 1], [4, 0], [1, 1], [3, 2]],
2,
1],
[[3, 2], [0, 0]]),
('regression quota check #2',
[['####..', '.~..##', '#.~~..', '.#...#', '...#~.'],
[[1, 3], [3, 3], [6, 0], [2, 0], [5, 4], [2, 5]],
1,
1],
[[3, 3]]),
('regression quota check #3',
[['...~#~.', '~.~~...', '..~.##.', '......#', '#~.~~.#', '......#', '~#.....'],
[[0, 1], [0, 7], [2, 6], [2, 6], [6, 0], [7, 3], [6, 3], [0, 1], [7, 1], [3, 6], [6, 3], [1, 3]],
1,
1],
[[2, 6], [6, 0], [1, 3]]),
('regression quota check #4',
[['......#', '#...#..'], [[2, 1], [3, 1], [7, 2], [6, 2], [7, 1], [1, 1], [5, 0], [3, 1]], 1, 2],
[[2, 1], [3, 1], [5, 0]]),
('exact radius spacing #1', [['.....'], [[0, 0], [2, 0]], 2, 3], [[0, 0], [2, 0]]),
('diagonal within radius #1', [['...', '...', '...'], [[0, 0], [1, 1]], 2, 3], [[0, 0]]),
('control #1',
[['..', '~.'],
[[2, 1], [1, 2], [2, 0], [2, 0], [0, 1], [2, 1], [0, 0], [2, 2], [0, 0], [1, 1], [2, 0]],
3,
2],
[[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 |
|---|---|---|---|
| quadrant full #1 | [[0, 0], [1, 0], [3, 0]] | [[0, 0], [3, 0]] | Failed |
| regression quota check #1 | [[3, 1], [1, 2], [3, 0], [1, 1], [0, 1]] | [[3, 1], [1, 2], [1, 1]] | Failed |
| regression quota check #2 | [[2, 0], [2, 1], [0, 1]] | [[2, 0], [2, 1]] | Failed |
| regression quota check #3 | [[1, 1], [0, 1], [0, 0], [4, 2]] | [[1, 1], [0, 1], [4, 2]] | Failed |
| regression quota check #4 | [[1, 6], [0, 0], [1, 3]] | [[1, 6], [0, 0]] | Failed |
| exact radius spacing #1 | [[0, 0], [2, 0]] | [[0, 0], [2, 0]] | Passed |
| diagonal within radius #1 | [[0, 0]] | [[0, 0]] | Passed |
| control #1 | [[1, 2], [4, 3]] | [[1, 2], [4, 3]] | Passed |
SHA-256 / d972914c9c8ef1efd8befe67c86a20c502a8f896944ecb3c597a8ae73fecbc15
2 / The unsuccessful fix
Exit 1"""Failure Map reference implementation. Python standard library only."""
import json
N = 1
observations = []
def solve(grid, candidates, radius, per_quadrant):
h = len(grid)
w = len(grid[0])
placed = []
quota = {}
for x, y in candidates:
if not (0 <= y < h and 0 <= x < w) or grid[y][x] != '.':
continue
q = (x * 2 // w, y * 2 // h)
if len(placed) >= per_quadrant * 4:
continue
if any((x - px) ** 2 + (y - py) ** 2 < radius * radius for px, py in placed):
continue
placed.append([x, y])
quota[q] = quota.get(q, 0) + 1
return placed
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
cases = [[('quadrant full #1', [['....', '....'], [[0, 0], [1, 0], [3, 0]], 1, 1], [[0, 0], [3, 0]]),
('regression quota check #1',
[['~~..#', '.....', '....#'], [[3, 1], [1, 2], [5, 2], [2, 3], [0, 3], [3, 0], [1, 1], [0, 1]], 1, 1],
[[3, 1], [1, 2], [1, 1]]),
('regression quota check #2',
[['...~.#', '.#....'], [[0, 2], [6, 1], [2, 0], [6, 0], [2, 1], [2, 1], [1, 2], [0, 1]], 1, 1],
[[2, 0], [2, 1]]),
('regression quota check #3',
[['.....#..', '..#..~~.', '~.~...~.', '.~~..~.#', '.~~.~~..'],
[[1, 1], [0, 1], [0, 0], [4, 2], [2, 4]],
1,
2],
[[1, 1], [0, 1], [4, 2]]),
('regression quota check #4',
[['.##', '.#.', '...', '~..', '~.~', '..#', '...'],
[[3, 0], [1, 6], [3, 0], [0, 0], [0, 6], [0, 5], [1, 3]],
2,
1],
[[1, 6], [0, 0]]),
('exact radius spacing #1', [['.....'], [[0, 0], [2, 0]], 2, 3], [[0, 0], [2, 0]]),
('diagonal within radius #1', [['...', '...', '...'], [[0, 0], [1, 1]], 2, 3], [[0, 0]]),
('control #1',
[['~..~.', '.#...', '~..#.', '..~#.'], [[1, 2], [4, 3], [1, 2], [4, 3], [1, 1]], 2, 3],
[[1, 2], [4, 3]])],
[('quadrant full #1', [['....', '....'], [[0, 0], [1, 0], [3, 0]], 1, 1], [[0, 0], [3, 0]]),
('regression quota check #1',
[['...~.#', '.#....'], [[0, 2], [6, 1], [2, 0], [6, 0], [2, 1], [2, 1], [1, 2], [0, 1]], 1, 1],
[[2, 0], [2, 1]]),
('regression quota check #2',
[['.....#..', '..#..~~.', '~.~...~.', '.~~..~.#', '.~~.~~..'],
[[1, 1], [0, 1], [0, 0], [4, 2], [2, 4]],
1,
2],
[[1, 1], [0, 1], [4, 2]]),
('regression quota check #3',
[['.##', '.#.', '...', '~..', '~.~', '..#', '...'],
[[3, 0], [1, 6], [3, 0], [0, 0], [0, 6], [0, 5], [1, 3]],
2,
1],
[[1, 6], [0, 0]]),
('regression quota check #4',
[['..~..~..', '...~.~.#', '~~..~~..', '.....~~~', '~..~~#..', '...#....', '.~~.~.#.', '#.......'],
[[6, 4], [7, 1], [8, 4], [7, 7], [6, 3], [4, 5], [8, 4], [1, 8], [0, 6], [8, 6]],
3,
1],
[[6, 4], [0, 6]]),
('exact radius spacing #1', [['.....'], [[0, 0], [2, 0]], 2, 3], [[0, 0], [2, 0]]),
('diagonal within radius #1', [['...', '...', '...'], [[0, 0], [1, 1]], 2, 3], [[0, 0]]),
('control #1',
[['~..~.', '.#...', '~..#.', '..~#.'], [[1, 2], [4, 3], [1, 2], [4, 3], [1, 1]], 2, 3],
[[1, 2], [4, 3]])],
[('quadrant full #1', [['....', '....'], [[0, 0], [1, 0], [3, 0]], 1, 1], [[0, 0], [3, 0]]),
('regression quota check #1',
[['.##', '.#.', '...', '~..', '~.~', '..#', '...'],
[[3, 0], [1, 6], [3, 0], [0, 0], [0, 6], [0, 5], [1, 3]],
2,
1],
[[1, 6], [0, 0]]),
('regression quota check #2',
[['..~..~..', '...~.~.#', '~~..~~..', '.....~~~', '~..~~#..', '...#....', '.~~.~.#.', '#.......'],
[[6, 4], [7, 1], [8, 4], [7, 7], [6, 3], [4, 5], [8, 4], [1, 8], [0, 6], [8, 6]],
3,
1],
[[6, 4], [0, 6]]),
('regression quota check #3',
[['##', '#.', '#.', '##', '..', '.#', '..'], [[1, 4], [1, 6]], 1, 1],
[[1, 4]]),
('regression quota check #4',
[['##......', '~#..#..#', '......~#', '.#~.~..#', '#.#...~#', '#..~..~~', '..~..##.', '.......~'],
[[8, 8], [0, 1], [3, 0], [8, 7], [5, 1], [0, 8], [6, 8], [3, 5], [1, 7], [1, 4], [2, 5], [4, 5]],
3,
1],
[[3, 0], [1, 7], [4, 5]]),
('exact radius spacing #1', [['.....'], [[0, 0], [2, 0]], 2, 3], [[0, 0], [2, 0]]),
('diagonal within radius #1', [['...', '...', '...'], [[0, 0], [1, 1]], 2, 3], [[0, 0]]),
('control #1',
[['~..~.', '.#...', '~..#.', '..~#.'], [[1, 2], [4, 3], [1, 2], [4, 3], [1, 1]], 2, 3],
[[1, 2], [4, 3]])],
[('quadrant full #1', [['....', '....'], [[0, 0], [1, 0], [3, 0]], 1, 1], [[0, 0], [3, 0]]),
('regression quota check #1',
[['##', '#.', '#.', '##', '..', '.#', '..'], [[1, 4], [1, 6]], 1, 1],
[[1, 4]]),
('regression quota check #2',
[['##......', '~#..#..#', '......~#', '.#~.~..#', '#.#...~#', '#..~..~~', '..~..##.', '.......~'],
[[8, 8], [0, 1], [3, 0], [8, 7], [5, 1], [0, 8], [6, 8], [3, 5], [1, 7], [1, 4], [2, 5], [4, 5]],
3,
1],
[[3, 0], [1, 7], [4, 5]]),
('regression quota check #3',
[['.....', '.#.##', '.....', '#.~.#', '.~.#.'],
[[3, 1], [3, 2], [5, 4], [3, 5], [2, 1], [0, 0], [4, 1], [4, 0], [1, 1], [3, 2]],
2,
1],
[[3, 2], [0, 0]]),
('regression quota check #4',
[['####..', '.~..##', '#.~~..', '.#...#', '...#~.'],
[[1, 3], [3, 3], [6, 0], [2, 0], [5, 4], [2, 5]],
1,
1],
[[3, 3]]),
('exact radius spacing #1', [['.....'], [[0, 0], [2, 0]], 2, 3], [[0, 0], [2, 0]]),
('diagonal within radius #1', [['...', '...', '...'], [[0, 0], [1, 1]], 2, 3], [[0, 0]]),
('control #1', [['#..', '..#'], [[1, 1]], 1, 1], [[1, 1]])],
[('quadrant full #1', [['....', '....'], [[0, 0], [1, 0], [3, 0]], 1, 1], [[0, 0], [3, 0]]),
('regression quota check #1',
[['.....', '.#.##', '.....', '#.~.#', '.~.#.'],
[[3, 1], [3, 2], [5, 4], [3, 5], [2, 1], [0, 0], [4, 1], [4, 0], [1, 1], [3, 2]],
2,
1],
[[3, 2], [0, 0]]),
('regression quota check #2',
[['####..', '.~..##', '#.~~..', '.#...#', '...#~.'],
[[1, 3], [3, 3], [6, 0], [2, 0], [5, 4], [2, 5]],
1,
1],
[[3, 3]]),
('regression quota check #3',
[['...~#~.', '~.~~...', '..~.##.', '......#', '#~.~~.#', '......#', '~#.....'],
[[0, 1], [0, 7], [2, 6], [2, 6], [6, 0], [7, 3], [6, 3], [0, 1], [7, 1], [3, 6], [6, 3], [1, 3]],
1,
1],
[[2, 6], [6, 0], [1, 3]]),
('regression quota check #4',
[['......#', '#...#..'], [[2, 1], [3, 1], [7, 2], [6, 2], [7, 1], [1, 1], [5, 0], [3, 1]], 1, 2],
[[2, 1], [3, 1], [5, 0]]),
('exact radius spacing #1', [['.....'], [[0, 0], [2, 0]], 2, 3], [[0, 0], [2, 0]]),
('diagonal within radius #1', [['...', '...', '...'], [[0, 0], [1, 1]], 2, 3], [[0, 0]]),
('control #1',
[['..', '~.'],
[[2, 1], [1, 2], [2, 0], [2, 0], [0, 1], [2, 1], [0, 0], [2, 2], [0, 0], [1, 1], [2, 0]],
3,
2],
[[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 |
|---|---|---|---|
| quadrant full #1 | [[0, 0], [1, 0], [3, 0]] | [[0, 0], [3, 0]] | Failed |
| regression quota check #1 | [[3, 1], [1, 2], [3, 0], [1, 1]] | [[3, 1], [1, 2], [1, 1]] | Failed |
| regression quota check #2 | [[2, 0], [2, 1], [0, 1]] | [[2, 0], [2, 1]] | Failed |
| regression quota check #3 | [[1, 1], [0, 1], [0, 0], [4, 2]] | [[1, 1], [0, 1], [4, 2]] | Failed |
| regression quota check #4 | [[1, 6], [0, 0], [1, 3]] | [[1, 6], [0, 0]] | Failed |
| exact radius spacing #1 | [[0, 0], [2, 0]] | [[0, 0], [2, 0]] | Passed |
| diagonal within radius #1 | [[0, 0]] | [[0, 0]] | Passed |
| control #1 | [[1, 2], [4, 3]] | [[1, 2], [4, 3]] | Passed |
SHA-256 / fe118536dee967e7ee26fe2156ca467352d8807dccaa8b7ef575ea6c66397304
3 / The verified repair
Exit 0"""Failure Map reference implementation. Python standard library only."""
import json
N = 1
observations = []
def solve(grid, candidates, radius, per_quadrant):
h = len(grid)
w = len(grid[0])
placed = []
quota = {}
for x, y in candidates:
if not (0 <= y < h and 0 <= x < w) or grid[y][x] != '.':
continue
q = (x * 2 // w, y * 2 // h)
if quota.get(q, 0) >= per_quadrant:
continue
if any((x - px) ** 2 + (y - py) ** 2 < radius * radius for px, py in placed):
continue
placed.append([x, y])
quota[q] = quota.get(q, 0) + 1
return placed
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
cases = [[('quadrant full #1', [['....', '....'], [[0, 0], [1, 0], [3, 0]], 1, 1], [[0, 0], [3, 0]]),
('regression quota check #1',
[['~~..#', '.....', '....#'], [[3, 1], [1, 2], [5, 2], [2, 3], [0, 3], [3, 0], [1, 1], [0, 1]], 1, 1],
[[3, 1], [1, 2], [1, 1]]),
('regression quota check #2',
[['...~.#', '.#....'], [[0, 2], [6, 1], [2, 0], [6, 0], [2, 1], [2, 1], [1, 2], [0, 1]], 1, 1],
[[2, 0], [2, 1]]),
('regression quota check #3',
[['.....#..', '..#..~~.', '~.~...~.', '.~~..~.#', '.~~.~~..'],
[[1, 1], [0, 1], [0, 0], [4, 2], [2, 4]],
1,
2],
[[1, 1], [0, 1], [4, 2]]),
('regression quota check #4',
[['.##', '.#.', '...', '~..', '~.~', '..#', '...'],
[[3, 0], [1, 6], [3, 0], [0, 0], [0, 6], [0, 5], [1, 3]],
2,
1],
[[1, 6], [0, 0]]),
('exact radius spacing #1', [['.....'], [[0, 0], [2, 0]], 2, 3], [[0, 0], [2, 0]]),
('diagonal within radius #1', [['...', '...', '...'], [[0, 0], [1, 1]], 2, 3], [[0, 0]]),
('control #1',
[['~..~.', '.#...', '~..#.', '..~#.'], [[1, 2], [4, 3], [1, 2], [4, 3], [1, 1]], 2, 3],
[[1, 2], [4, 3]])],
[('quadrant full #1', [['....', '....'], [[0, 0], [1, 0], [3, 0]], 1, 1], [[0, 0], [3, 0]]),
('regression quota check #1',
[['...~.#', '.#....'], [[0, 2], [6, 1], [2, 0], [6, 0], [2, 1], [2, 1], [1, 2], [0, 1]], 1, 1],
[[2, 0], [2, 1]]),
('regression quota check #2',
[['.....#..', '..#..~~.', '~.~...~.', '.~~..~.#', '.~~.~~..'],
[[1, 1], [0, 1], [0, 0], [4, 2], [2, 4]],
1,
2],
[[1, 1], [0, 1], [4, 2]]),
('regression quota check #3',
[['.##', '.#.', '...', '~..', '~.~', '..#', '...'],
[[3, 0], [1, 6], [3, 0], [0, 0], [0, 6], [0, 5], [1, 3]],
2,
1],
[[1, 6], [0, 0]]),
('regression quota check #4',
[['..~..~..', '...~.~.#', '~~..~~..', '.....~~~', '~..~~#..', '...#....', '.~~.~.#.', '#.......'],
[[6, 4], [7, 1], [8, 4], [7, 7], [6, 3], [4, 5], [8, 4], [1, 8], [0, 6], [8, 6]],
3,
1],
[[6, 4], [0, 6]]),
('exact radius spacing #1', [['.....'], [[0, 0], [2, 0]], 2, 3], [[0, 0], [2, 0]]),
('diagonal within radius #1', [['...', '...', '...'], [[0, 0], [1, 1]], 2, 3], [[0, 0]]),
('control #1',
[['~..~.', '.#...', '~..#.', '..~#.'], [[1, 2], [4, 3], [1, 2], [4, 3], [1, 1]], 2, 3],
[[1, 2], [4, 3]])],
[('quadrant full #1', [['....', '....'], [[0, 0], [1, 0], [3, 0]], 1, 1], [[0, 0], [3, 0]]),
('regression quota check #1',
[['.##', '.#.', '...', '~..', '~.~', '..#', '...'],
[[3, 0], [1, 6], [3, 0], [0, 0], [0, 6], [0, 5], [1, 3]],
2,
1],
[[1, 6], [0, 0]]),
('regression quota check #2',
[['..~..~..', '...~.~.#', '~~..~~..', '.....~~~', '~..~~#..', '...#....', '.~~.~.#.', '#.......'],
[[6, 4], [7, 1], [8, 4], [7, 7], [6, 3], [4, 5], [8, 4], [1, 8], [0, 6], [8, 6]],
3,
1],
[[6, 4], [0, 6]]),
('regression quota check #3',
[['##', '#.', '#.', '##', '..', '.#', '..'], [[1, 4], [1, 6]], 1, 1],
[[1, 4]]),
('regression quota check #4',
[['##......', '~#..#..#', '......~#', '.#~.~..#', '#.#...~#', '#..~..~~', '..~..##.', '.......~'],
[[8, 8], [0, 1], [3, 0], [8, 7], [5, 1], [0, 8], [6, 8], [3, 5], [1, 7], [1, 4], [2, 5], [4, 5]],
3,
1],
[[3, 0], [1, 7], [4, 5]]),
('exact radius spacing #1', [['.....'], [[0, 0], [2, 0]], 2, 3], [[0, 0], [2, 0]]),
('diagonal within radius #1', [['...', '...', '...'], [[0, 0], [1, 1]], 2, 3], [[0, 0]]),
('control #1',
[['~..~.', '.#...', '~..#.', '..~#.'], [[1, 2], [4, 3], [1, 2], [4, 3], [1, 1]], 2, 3],
[[1, 2], [4, 3]])],
[('quadrant full #1', [['....', '....'], [[0, 0], [1, 0], [3, 0]], 1, 1], [[0, 0], [3, 0]]),
('regression quota check #1',
[['##', '#.', '#.', '##', '..', '.#', '..'], [[1, 4], [1, 6]], 1, 1],
[[1, 4]]),
('regression quota check #2',
[['##......', '~#..#..#', '......~#', '.#~.~..#', '#.#...~#', '#..~..~~', '..~..##.', '.......~'],
[[8, 8], [0, 1], [3, 0], [8, 7], [5, 1], [0, 8], [6, 8], [3, 5], [1, 7], [1, 4], [2, 5], [4, 5]],
3,
1],
[[3, 0], [1, 7], [4, 5]]),
('regression quota check #3',
[['.....', '.#.##', '.....', '#.~.#', '.~.#.'],
[[3, 1], [3, 2], [5, 4], [3, 5], [2, 1], [0, 0], [4, 1], [4, 0], [1, 1], [3, 2]],
2,
1],
[[3, 2], [0, 0]]),
('regression quota check #4',
[['####..', '.~..##', '#.~~..', '.#...#', '...#~.'],
[[1, 3], [3, 3], [6, 0], [2, 0], [5, 4], [2, 5]],
1,
1],
[[3, 3]]),
('exact radius spacing #1', [['.....'], [[0, 0], [2, 0]], 2, 3], [[0, 0], [2, 0]]),
('diagonal within radius #1', [['...', '...', '...'], [[0, 0], [1, 1]], 2, 3], [[0, 0]]),
('control #1', [['#..', '..#'], [[1, 1]], 1, 1], [[1, 1]])],
[('quadrant full #1', [['....', '....'], [[0, 0], [1, 0], [3, 0]], 1, 1], [[0, 0], [3, 0]]),
('regression quota check #1',
[['.....', '.#.##', '.....', '#.~.#', '.~.#.'],
[[3, 1], [3, 2], [5, 4], [3, 5], [2, 1], [0, 0], [4, 1], [4, 0], [1, 1], [3, 2]],
2,
1],
[[3, 2], [0, 0]]),
('regression quota check #2',
[['####..', '.~..##', '#.~~..', '.#...#', '...#~.'],
[[1, 3], [3, 3], [6, 0], [2, 0], [5, 4], [2, 5]],
1,
1],
[[3, 3]]),
('regression quota check #3',
[['...~#~.', '~.~~...', '..~.##.', '......#', '#~.~~.#', '......#', '~#.....'],
[[0, 1], [0, 7], [2, 6], [2, 6], [6, 0], [7, 3], [6, 3], [0, 1], [7, 1], [3, 6], [6, 3], [1, 3]],
1,
1],
[[2, 6], [6, 0], [1, 3]]),
('regression quota check #4',
[['......#', '#...#..'], [[2, 1], [3, 1], [7, 2], [6, 2], [7, 1], [1, 1], [5, 0], [3, 1]], 1, 2],
[[2, 1], [3, 1], [5, 0]]),
('exact radius spacing #1', [['.....'], [[0, 0], [2, 0]], 2, 3], [[0, 0], [2, 0]]),
('diagonal within radius #1', [['...', '...', '...'], [[0, 0], [1, 1]], 2, 3], [[0, 0]]),
('control #1',
[['..', '~.'],
[[2, 1], [1, 2], [2, 0], [2, 0], [0, 1], [2, 1], [0, 0], [2, 2], [0, 0], [1, 1], [2, 0]],
3,
2],
[[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 |
|---|---|---|---|
| quadrant full #1 | [[0, 0], [3, 0]] | [[0, 0], [3, 0]] | Passed |
| regression quota check #1 | [[3, 1], [1, 2], [1, 1]] | [[3, 1], [1, 2], [1, 1]] | Passed |
| regression quota check #2 | [[2, 0], [2, 1]] | [[2, 0], [2, 1]] | Passed |
| regression quota check #3 | [[1, 1], [0, 1], [4, 2]] | [[1, 1], [0, 1], [4, 2]] | Passed |
| regression quota check #4 | [[1, 6], [0, 0]] | [[1, 6], [0, 0]] | Passed |
| exact radius spacing #1 | [[0, 0], [2, 0]] | [[0, 0], [2, 0]] | Passed |
| diagonal within radius #1 | [[0, 0]] | [[0, 0]] | Passed |
| control #1 | [[1, 2], [4, 3]] | [[1, 2], [4, 3]] | Passed |
SHA-256 / 4a9ae367097340519a43ebb1393259e62d97ab50ef82cc1ed01ee8710f991431
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 2026-09-29T14:50:51.908291+00:00.
Case digest / b1839e1d6f0184fb804af0b1c714d6510289a40cdef14d56d21163c66feccb3d