FA-86426 / Procedural level generation constraints / Open access
Enemy spawn point selection: Diagonal spawns count as far away · case 01
Enemies spawn diagonally next to the player.
ROOT CAUSE
Player distance uses Manhattan instead of Chebyshev distance.
VERIFIED REPAIR
Restore `max(abs(r - pr), abs(c - pc))` at the player distance metric step.
Unsuccessful approach: Using the smaller axis distance underestimates separation everywhere.
Case contract
Candidates [row, col] are tried in order until count spawns are chosen. A spawn must be in bounds on a '.' tile, at Chebyshev distance >= min_dist from the player and at Chebyshev distance >= 2 from every chosen spawn (no touching spawns, diagonals included). Returns chosen cells.
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, player, candidates, min_dist, count):
chosen = []
pr, pc = player
for r, c in candidates:
if len(chosen) >= count:
break
if not (0 <= r < len(grid) and 0 <= c < len(grid[0])) or grid[r][c] != '.':
continue
if abs(r - pr) + abs(c - pc) < min_dist:
continue
if any(max(abs(r - a), abs(c - b)) < 2 for a, b in chosen):
continue
chosen.append([r, c])
return chosen
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
cases = [[('exact safe radius #1', [['.....', '.....'], [0, 0], [[1, 1], [0, 2]], 2, 2], [[0, 2]]),
('negative index candidate #1', [['...', '...', '..#'], [0, 0], [[-1, -1], [2, 0]], 1, 2], [[2, 0]]),
('regression player distance metric #1',
[['......', '..#...', '...~..', '.~#...', '~..~~.'],
[1, 3],
[[0, 0], [-1, 4], [-1, 2], [5, 4], [5, 1], [5, 1], [3, 5], [5, 6], [1, 4], [5, 2]],
3,
3],
[[0, 0]]),
('fault site player distance metric #1',
[['..~##.', '~..~..', '.~~#.~'], [0, 3], [[1, 4], [-1, 6], [1, 1], [2, 4], [2, 2], [1, 0]], 3, 5],
[]),
('partial repair boundary #1',
[['...#', '.#..', '#.#~', '~~.~', '~~#.', '~##.', '....', '...#'],
[1, 2],
[[0, 1], [6, 4], [5, 4], [4, 1], [4, 0], [6, 1], [0, 4], [7, 2], [5, 3], [-1, 1]],
3,
2],
[[6, 1], [5, 3]]),
('partial repair boundary #2',
[['~..~.#.', '.....#.', '.......', '#......', '##....~'],
[1, 4],
[[5, 0], [2, 0], [1, 6], [-1, 7], [0, 2], [1, 1], [3, 5], [2, 3], [5, 4]],
1,
3],
[[2, 0], [1, 6], [0, 2]]),
('diagonal neighbour spawn #1', [['....', '....', '....'], [0, 0], [[1, 2], [2, 3]], 1, 3], [[1, 2]]),
('control #1',
[['#.#', '...', '#.#', '.#.', '...', '...', '...', '##.'], [6, 2], [[2, -1], [7, 2]], 0, 0],
[])],
[('exact safe radius #1', [['.....', '.....'], [0, 0], [[1, 1], [0, 2]], 2, 2], [[0, 2]]),
('negative index candidate #1', [['...', '...', '..#'], [0, 0], [[-1, -1], [2, 0]], 1, 2], [[2, 0]]),
('fault site player distance metric #1',
[['..~##.', '~..~..', '.~~#.~'], [0, 3], [[1, 4], [-1, 6], [1, 1], [2, 4], [2, 2], [1, 0]], 3, 5],
[]),
('fault site player distance metric #2',
[['...', '#..', '.~~', '#~.', '.~.', '~..'], [2, 1], [[-1, 0], [1, 1], [3, 2], [4, 3]], 2, 1],
[]),
('partial repair boundary #1',
[['...#', '.#..', '#.#~', '~~.~', '~~#.', '~##.', '....', '...#'],
[1, 2],
[[0, 1], [6, 4], [5, 4], [4, 1], [4, 0], [6, 1], [0, 4], [7, 2], [5, 3], [-1, 1]],
3,
2],
[[6, 1], [5, 3]]),
('partial repair boundary #2',
[['~..~.#.', '.....#.', '.......', '#......', '##....~'],
[1, 4],
[[5, 0], [2, 0], [1, 6], [-1, 7], [0, 2], [1, 1], [3, 5], [2, 3], [5, 4]],
1,
3],
[[2, 0], [1, 6], [0, 2]]),
('diagonal neighbour spawn #1', [['....', '....', '....'], [0, 0], [[1, 2], [2, 3]], 1, 3], [[1, 2]]),
('control #1',
[['#.#', '...', '#.#', '.#.', '...', '...', '...', '##.'], [6, 2], [[2, -1], [7, 2]], 0, 0],
[])],
[('exact safe radius #1', [['.....', '.....'], [0, 0], [[1, 1], [0, 2]], 2, 2], [[0, 2]]),
('negative index candidate #1', [['...', '...', '..#'], [0, 0], [[-1, -1], [2, 0]], 1, 2], [[2, 0]]),
('fault site player distance metric #1',
[['~...', '.~..', '.#..', '#.~.', '....', '...#', '..#.', '~~.#'],
[5, 2],
[[8, 4], [4, -1], [8, -1], [4, 3]],
2,
1],
[]),
('regression player distance metric #1',
[['~...', '....', '~~..', '.#..', '...~', '~.~.', '..~.'],
[2, 2],
[[3, 3], [3, 2], [2, 0], [6, 3], [7, 2], [7, 1], [7, 2], [0, 3]],
3,
3],
[[6, 3]]),
('partial repair boundary #1',
[['.~.', '#..', '.#.', '...', '..#', '.~.', '#..', '~..'],
[0, 2],
[[3, 3], [3, 1], [3, 0], [7, -1], [4, 3], [7, 1]],
3,
2],
[[3, 1], [7, 1]]),
('regression player distance metric #2',
[['......', '..#...', '...~..', '.~#...', '~..~~.'],
[1, 3],
[[0, 0], [-1, 4], [-1, 2], [5, 4], [5, 1], [5, 1], [3, 5], [5, 6], [1, 4], [5, 2]],
3,
3],
[[0, 0]]),
('diagonal neighbour spawn #1', [['....', '....', '....'], [0, 0], [[1, 2], [2, 3]], 1, 3], [[1, 2]]),
('control #1',
[['.#~', '...', '~.#', '#.~', '..#', '#~.'], [3, 1], [[5, 0], [1, 0], [6, -1], [6, -1]], 0, 5],
[[1, 0]])],
[('exact safe radius #1', [['.....', '.....'], [0, 0], [[1, 1], [0, 2]], 2, 2], [[0, 2]]),
('negative index candidate #1', [['...', '...', '..#'], [0, 0], [[-1, -1], [2, 0]], 1, 2], [[2, 0]]),
('regression player distance metric #1',
[['.~....##', '......#.', '~...#..#', '~......~'],
[2, 3],
[[-1, 3], [0, 1], [1, -1], [1, 2], [2, 5], [1, 3]],
2,
1],
[[2, 5]]),
('regression player distance metric #2',
[['.~.~....', '....~~~#', '......~~', '....#...'],
[1, 5],
[[-1, 7], [0, 7], [2, 5], [0, 8], [2, 1], [-1, 3], [1, 5]],
3,
3],
[[2, 1]]),
('partial repair boundary #1',
[['..~...', '#.~...', '.#....'],
[0, 5],
[[0, 3], [0, 0], [1, 1], [3, 3], [2, 1], [0, 1], [0, 5], [2, 4], [2, 3], [1, 4]],
1,
3],
[[0, 3], [0, 0], [2, 4]]),
('partial repair boundary #2',
[['.~..', '#...', '..~~', '#...', '..~.'],
[3, 0],
[[0, 4], [5, 3], [3, 2], [4, -1], [-1, -1], [2, 0], [1, 2], [1, -1], [0, 1]],
1,
3],
[[3, 2], [2, 0], [1, 2]]),
('diagonal neighbour spawn #1', [['....', '....', '....'], [0, 0], [[1, 2], [2, 3]], 1, 3], [[1, 2]]),
('control #1',
[['...#...', '......~', '~~.....', '..~....', '.~....~', '.....#.'], [5, 2], [[1, 5]], 0, 0],
[])],
[('exact safe radius #1', [['.....', '.....'], [0, 0], [[1, 1], [0, 2]], 2, 2], [[0, 2]]),
('negative index candidate #1', [['...', '...', '..#'], [0, 0], [[-1, -1], [2, 0]], 1, 2], [[2, 0]]),
('fault site player distance metric #1',
[['..~#.', '.~...', '~..~.', '..~..', '~..#.', '##...', '....~', '...#.'],
[5, 0],
[[5, 1], [2, 4], [3, 5], [6, 1], [4, 0], [8, 1], [2, 4], [8, 1], [6, 5], [7, 2]],
3,
5],
[[2, 4]]),
('regression player distance metric #1',
[['..~.~', '..#..', '.~...', '..~.~', '.~#..', '.....', '.....'],
[0, 2],
[[2, 0], [4, 5], [5, 0], [0, 5], [5, 4], [7, 1], [-1, -1], [4, 0], [7, 3]],
3,
3],
[[5, 0], [5, 4]]),
('regression player distance metric #2',
[['~...', '....', '~~..', '.#..', '...~', '~.~.', '..~.'],
[2, 2],
[[3, 3], [3, 2], [2, 0], [6, 3], [7, 2], [7, 1], [7, 2], [0, 3]],
3,
3],
[[6, 3]]),
('partial repair boundary #1',
[['.#~', '...', '...', '.~.', '#.~', '.#.', '~..'],
[2, 0],
[[4, 2], [0, -1], [0, 3], [6, 1], [4, 0], [4, 2], [7, 2], [3, 2], [1, 2]],
3,
1],
[[6, 1]]),
('diagonal neighbour spawn #1', [['....', '....', '....'], [0, 0], [[1, 2], [2, 3]], 1, 3], [[1, 2]]),
('control #1',
[['....', '.#.~', '..~~', '...#'], [2, 0], [[4, -1], [3, 3], [3, 1], [1, 0], [1, 3]], 0, 2],
[[3, 1], [1, 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 |
|---|---|---|---|
| exact safe radius #1 | [[1, 1]] | [[0, 2]] | Failed |
| negative index candidate #1 | [[2, 0]] | [[2, 0]] | Passed |
| regression player distance metric #1 | [[0, 0], [3, 5]] | [[0, 0]] | Failed |
| fault site player distance metric #1 | [[1, 1], [2, 4]] | [] | Failed |
| partial repair boundary #1 | [[6, 1], [5, 3]] | [[6, 1], [5, 3]] | Passed |
| partial repair boundary #2 | [[2, 0], [1, 6], [0, 2]] | [[2, 0], [1, 6], [0, 2]] | Passed |
| diagonal neighbour spawn #1 | [[1, 2]] | [[1, 2]] | Passed |
| control #1 | [] | [] | Passed |
SHA-256 / c1d7890a1b4b97fa03cbf12376cb0560966357bcddae6146736336358634af09
2 / The unsuccessful fix
Exit 1"""Failure Map reference implementation. Python standard library only."""
import json
N = 1
observations = []
def solve(grid, player, candidates, min_dist, count):
chosen = []
pr, pc = player
for r, c in candidates:
if len(chosen) >= count:
break
if not (0 <= r < len(grid) and 0 <= c < len(grid[0])) or grid[r][c] != '.':
continue
if min(abs(r - pr), abs(c - pc)) < min_dist:
continue
if any(max(abs(r - a), abs(c - b)) < 2 for a, b in chosen):
continue
chosen.append([r, c])
return chosen
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
cases = [[('exact safe radius #1', [['.....', '.....'], [0, 0], [[1, 1], [0, 2]], 2, 2], [[0, 2]]),
('negative index candidate #1', [['...', '...', '..#'], [0, 0], [[-1, -1], [2, 0]], 1, 2], [[2, 0]]),
('regression player distance metric #1',
[['......', '..#...', '...~..', '.~#...', '~..~~.'],
[1, 3],
[[0, 0], [-1, 4], [-1, 2], [5, 4], [5, 1], [5, 1], [3, 5], [5, 6], [1, 4], [5, 2]],
3,
3],
[[0, 0]]),
('fault site player distance metric #1',
[['..~##.', '~..~..', '.~~#.~'], [0, 3], [[1, 4], [-1, 6], [1, 1], [2, 4], [2, 2], [1, 0]], 3, 5],
[]),
('partial repair boundary #1',
[['...#', '.#..', '#.#~', '~~.~', '~~#.', '~##.', '....', '...#'],
[1, 2],
[[0, 1], [6, 4], [5, 4], [4, 1], [4, 0], [6, 1], [0, 4], [7, 2], [5, 3], [-1, 1]],
3,
2],
[[6, 1], [5, 3]]),
('partial repair boundary #2',
[['~..~.#.', '.....#.', '.......', '#......', '##....~'],
[1, 4],
[[5, 0], [2, 0], [1, 6], [-1, 7], [0, 2], [1, 1], [3, 5], [2, 3], [5, 4]],
1,
3],
[[2, 0], [1, 6], [0, 2]]),
('diagonal neighbour spawn #1', [['....', '....', '....'], [0, 0], [[1, 2], [2, 3]], 1, 3], [[1, 2]]),
('control #1',
[['#.#', '...', '#.#', '.#.', '...', '...', '...', '##.'], [6, 2], [[2, -1], [7, 2]], 0, 0],
[])],
[('exact safe radius #1', [['.....', '.....'], [0, 0], [[1, 1], [0, 2]], 2, 2], [[0, 2]]),
('negative index candidate #1', [['...', '...', '..#'], [0, 0], [[-1, -1], [2, 0]], 1, 2], [[2, 0]]),
('fault site player distance metric #1',
[['..~##.', '~..~..', '.~~#.~'], [0, 3], [[1, 4], [-1, 6], [1, 1], [2, 4], [2, 2], [1, 0]], 3, 5],
[]),
('fault site player distance metric #2',
[['...', '#..', '.~~', '#~.', '.~.', '~..'], [2, 1], [[-1, 0], [1, 1], [3, 2], [4, 3]], 2, 1],
[]),
('partial repair boundary #1',
[['...#', '.#..', '#.#~', '~~.~', '~~#.', '~##.', '....', '...#'],
[1, 2],
[[0, 1], [6, 4], [5, 4], [4, 1], [4, 0], [6, 1], [0, 4], [7, 2], [5, 3], [-1, 1]],
3,
2],
[[6, 1], [5, 3]]),
('partial repair boundary #2',
[['~..~.#.', '.....#.', '.......', '#......', '##....~'],
[1, 4],
[[5, 0], [2, 0], [1, 6], [-1, 7], [0, 2], [1, 1], [3, 5], [2, 3], [5, 4]],
1,
3],
[[2, 0], [1, 6], [0, 2]]),
('diagonal neighbour spawn #1', [['....', '....', '....'], [0, 0], [[1, 2], [2, 3]], 1, 3], [[1, 2]]),
('control #1',
[['#.#', '...', '#.#', '.#.', '...', '...', '...', '##.'], [6, 2], [[2, -1], [7, 2]], 0, 0],
[])],
[('exact safe radius #1', [['.....', '.....'], [0, 0], [[1, 1], [0, 2]], 2, 2], [[0, 2]]),
('negative index candidate #1', [['...', '...', '..#'], [0, 0], [[-1, -1], [2, 0]], 1, 2], [[2, 0]]),
('fault site player distance metric #1',
[['~...', '.~..', '.#..', '#.~.', '....', '...#', '..#.', '~~.#'],
[5, 2],
[[8, 4], [4, -1], [8, -1], [4, 3]],
2,
1],
[]),
('regression player distance metric #1',
[['~...', '....', '~~..', '.#..', '...~', '~.~.', '..~.'],
[2, 2],
[[3, 3], [3, 2], [2, 0], [6, 3], [7, 2], [7, 1], [7, 2], [0, 3]],
3,
3],
[[6, 3]]),
('partial repair boundary #1',
[['.~.', '#..', '.#.', '...', '..#', '.~.', '#..', '~..'],
[0, 2],
[[3, 3], [3, 1], [3, 0], [7, -1], [4, 3], [7, 1]],
3,
2],
[[3, 1], [7, 1]]),
('regression player distance metric #2',
[['......', '..#...', '...~..', '.~#...', '~..~~.'],
[1, 3],
[[0, 0], [-1, 4], [-1, 2], [5, 4], [5, 1], [5, 1], [3, 5], [5, 6], [1, 4], [5, 2]],
3,
3],
[[0, 0]]),
('diagonal neighbour spawn #1', [['....', '....', '....'], [0, 0], [[1, 2], [2, 3]], 1, 3], [[1, 2]]),
('control #1',
[['.#~', '...', '~.#', '#.~', '..#', '#~.'], [3, 1], [[5, 0], [1, 0], [6, -1], [6, -1]], 0, 5],
[[1, 0]])],
[('exact safe radius #1', [['.....', '.....'], [0, 0], [[1, 1], [0, 2]], 2, 2], [[0, 2]]),
('negative index candidate #1', [['...', '...', '..#'], [0, 0], [[-1, -1], [2, 0]], 1, 2], [[2, 0]]),
('regression player distance metric #1',
[['.~....##', '......#.', '~...#..#', '~......~'],
[2, 3],
[[-1, 3], [0, 1], [1, -1], [1, 2], [2, 5], [1, 3]],
2,
1],
[[2, 5]]),
('regression player distance metric #2',
[['.~.~....', '....~~~#', '......~~', '....#...'],
[1, 5],
[[-1, 7], [0, 7], [2, 5], [0, 8], [2, 1], [-1, 3], [1, 5]],
3,
3],
[[2, 1]]),
('partial repair boundary #1',
[['..~...', '#.~...', '.#....'],
[0, 5],
[[0, 3], [0, 0], [1, 1], [3, 3], [2, 1], [0, 1], [0, 5], [2, 4], [2, 3], [1, 4]],
1,
3],
[[0, 3], [0, 0], [2, 4]]),
('partial repair boundary #2',
[['.~..', '#...', '..~~', '#...', '..~.'],
[3, 0],
[[0, 4], [5, 3], [3, 2], [4, -1], [-1, -1], [2, 0], [1, 2], [1, -1], [0, 1]],
1,
3],
[[3, 2], [2, 0], [1, 2]]),
('diagonal neighbour spawn #1', [['....', '....', '....'], [0, 0], [[1, 2], [2, 3]], 1, 3], [[1, 2]]),
('control #1',
[['...#...', '......~', '~~.....', '..~....', '.~....~', '.....#.'], [5, 2], [[1, 5]], 0, 0],
[])],
[('exact safe radius #1', [['.....', '.....'], [0, 0], [[1, 1], [0, 2]], 2, 2], [[0, 2]]),
('negative index candidate #1', [['...', '...', '..#'], [0, 0], [[-1, -1], [2, 0]], 1, 2], [[2, 0]]),
('fault site player distance metric #1',
[['..~#.', '.~...', '~..~.', '..~..', '~..#.', '##...', '....~', '...#.'],
[5, 0],
[[5, 1], [2, 4], [3, 5], [6, 1], [4, 0], [8, 1], [2, 4], [8, 1], [6, 5], [7, 2]],
3,
5],
[[2, 4]]),
('regression player distance metric #1',
[['..~.~', '..#..', '.~...', '..~.~', '.~#..', '.....', '.....'],
[0, 2],
[[2, 0], [4, 5], [5, 0], [0, 5], [5, 4], [7, 1], [-1, -1], [4, 0], [7, 3]],
3,
3],
[[5, 0], [5, 4]]),
('regression player distance metric #2',
[['~...', '....', '~~..', '.#..', '...~', '~.~.', '..~.'],
[2, 2],
[[3, 3], [3, 2], [2, 0], [6, 3], [7, 2], [7, 1], [7, 2], [0, 3]],
3,
3],
[[6, 3]]),
('partial repair boundary #1',
[['.#~', '...', '...', '.~.', '#.~', '.#.', '~..'],
[2, 0],
[[4, 2], [0, -1], [0, 3], [6, 1], [4, 0], [4, 2], [7, 2], [3, 2], [1, 2]],
3,
1],
[[6, 1]]),
('diagonal neighbour spawn #1', [['....', '....', '....'], [0, 0], [[1, 2], [2, 3]], 1, 3], [[1, 2]]),
('control #1',
[['....', '.#.~', '..~~', '...#'], [2, 0], [[4, -1], [3, 3], [3, 1], [1, 0], [1, 3]], 0, 2],
[[3, 1], [1, 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 |
|---|---|---|---|
| exact safe radius #1 | [] | [[0, 2]] | Failed |
| negative index candidate #1 | [] | [[2, 0]] | Failed |
| regression player distance metric #1 | [] | [[0, 0]] | Failed |
| fault site player distance metric #1 | [] | [] | Passed |
| partial repair boundary #1 | [] | [[6, 1], [5, 3]] | Failed |
| partial repair boundary #2 | [[2, 0], [0, 2], [3, 5]] | [[2, 0], [1, 6], [0, 2]] | Failed |
| diagonal neighbour spawn #1 | [[1, 2]] | [[1, 2]] | Passed |
| control #1 | [] | [] | Passed |
SHA-256 / ca328a898bb40740207a1223cb68fd71a975e155c64125b34ffe2ed4bbae27e5
3 / The verified repair
Exit 0"""Failure Map reference implementation. Python standard library only."""
import json
N = 1
observations = []
def solve(grid, player, candidates, min_dist, count):
chosen = []
pr, pc = player
for r, c in candidates:
if len(chosen) >= count:
break
if not (0 <= r < len(grid) and 0 <= c < len(grid[0])) or grid[r][c] != '.':
continue
if max(abs(r - pr), abs(c - pc)) < min_dist:
continue
if any(max(abs(r - a), abs(c - b)) < 2 for a, b in chosen):
continue
chosen.append([r, c])
return chosen
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
cases = [[('exact safe radius #1', [['.....', '.....'], [0, 0], [[1, 1], [0, 2]], 2, 2], [[0, 2]]),
('negative index candidate #1', [['...', '...', '..#'], [0, 0], [[-1, -1], [2, 0]], 1, 2], [[2, 0]]),
('regression player distance metric #1',
[['......', '..#...', '...~..', '.~#...', '~..~~.'],
[1, 3],
[[0, 0], [-1, 4], [-1, 2], [5, 4], [5, 1], [5, 1], [3, 5], [5, 6], [1, 4], [5, 2]],
3,
3],
[[0, 0]]),
('fault site player distance metric #1',
[['..~##.', '~..~..', '.~~#.~'], [0, 3], [[1, 4], [-1, 6], [1, 1], [2, 4], [2, 2], [1, 0]], 3, 5],
[]),
('partial repair boundary #1',
[['...#', '.#..', '#.#~', '~~.~', '~~#.', '~##.', '....', '...#'],
[1, 2],
[[0, 1], [6, 4], [5, 4], [4, 1], [4, 0], [6, 1], [0, 4], [7, 2], [5, 3], [-1, 1]],
3,
2],
[[6, 1], [5, 3]]),
('partial repair boundary #2',
[['~..~.#.', '.....#.', '.......', '#......', '##....~'],
[1, 4],
[[5, 0], [2, 0], [1, 6], [-1, 7], [0, 2], [1, 1], [3, 5], [2, 3], [5, 4]],
1,
3],
[[2, 0], [1, 6], [0, 2]]),
('diagonal neighbour spawn #1', [['....', '....', '....'], [0, 0], [[1, 2], [2, 3]], 1, 3], [[1, 2]]),
('control #1',
[['#.#', '...', '#.#', '.#.', '...', '...', '...', '##.'], [6, 2], [[2, -1], [7, 2]], 0, 0],
[])],
[('exact safe radius #1', [['.....', '.....'], [0, 0], [[1, 1], [0, 2]], 2, 2], [[0, 2]]),
('negative index candidate #1', [['...', '...', '..#'], [0, 0], [[-1, -1], [2, 0]], 1, 2], [[2, 0]]),
('fault site player distance metric #1',
[['..~##.', '~..~..', '.~~#.~'], [0, 3], [[1, 4], [-1, 6], [1, 1], [2, 4], [2, 2], [1, 0]], 3, 5],
[]),
('fault site player distance metric #2',
[['...', '#..', '.~~', '#~.', '.~.', '~..'], [2, 1], [[-1, 0], [1, 1], [3, 2], [4, 3]], 2, 1],
[]),
('partial repair boundary #1',
[['...#', '.#..', '#.#~', '~~.~', '~~#.', '~##.', '....', '...#'],
[1, 2],
[[0, 1], [6, 4], [5, 4], [4, 1], [4, 0], [6, 1], [0, 4], [7, 2], [5, 3], [-1, 1]],
3,
2],
[[6, 1], [5, 3]]),
('partial repair boundary #2',
[['~..~.#.', '.....#.', '.......', '#......', '##....~'],
[1, 4],
[[5, 0], [2, 0], [1, 6], [-1, 7], [0, 2], [1, 1], [3, 5], [2, 3], [5, 4]],
1,
3],
[[2, 0], [1, 6], [0, 2]]),
('diagonal neighbour spawn #1', [['....', '....', '....'], [0, 0], [[1, 2], [2, 3]], 1, 3], [[1, 2]]),
('control #1',
[['#.#', '...', '#.#', '.#.', '...', '...', '...', '##.'], [6, 2], [[2, -1], [7, 2]], 0, 0],
[])],
[('exact safe radius #1', [['.....', '.....'], [0, 0], [[1, 1], [0, 2]], 2, 2], [[0, 2]]),
('negative index candidate #1', [['...', '...', '..#'], [0, 0], [[-1, -1], [2, 0]], 1, 2], [[2, 0]]),
('fault site player distance metric #1',
[['~...', '.~..', '.#..', '#.~.', '....', '...#', '..#.', '~~.#'],
[5, 2],
[[8, 4], [4, -1], [8, -1], [4, 3]],
2,
1],
[]),
('regression player distance metric #1',
[['~...', '....', '~~..', '.#..', '...~', '~.~.', '..~.'],
[2, 2],
[[3, 3], [3, 2], [2, 0], [6, 3], [7, 2], [7, 1], [7, 2], [0, 3]],
3,
3],
[[6, 3]]),
('partial repair boundary #1',
[['.~.', '#..', '.#.', '...', '..#', '.~.', '#..', '~..'],
[0, 2],
[[3, 3], [3, 1], [3, 0], [7, -1], [4, 3], [7, 1]],
3,
2],
[[3, 1], [7, 1]]),
('regression player distance metric #2',
[['......', '..#...', '...~..', '.~#...', '~..~~.'],
[1, 3],
[[0, 0], [-1, 4], [-1, 2], [5, 4], [5, 1], [5, 1], [3, 5], [5, 6], [1, 4], [5, 2]],
3,
3],
[[0, 0]]),
('diagonal neighbour spawn #1', [['....', '....', '....'], [0, 0], [[1, 2], [2, 3]], 1, 3], [[1, 2]]),
('control #1',
[['.#~', '...', '~.#', '#.~', '..#', '#~.'], [3, 1], [[5, 0], [1, 0], [6, -1], [6, -1]], 0, 5],
[[1, 0]])],
[('exact safe radius #1', [['.....', '.....'], [0, 0], [[1, 1], [0, 2]], 2, 2], [[0, 2]]),
('negative index candidate #1', [['...', '...', '..#'], [0, 0], [[-1, -1], [2, 0]], 1, 2], [[2, 0]]),
('regression player distance metric #1',
[['.~....##', '......#.', '~...#..#', '~......~'],
[2, 3],
[[-1, 3], [0, 1], [1, -1], [1, 2], [2, 5], [1, 3]],
2,
1],
[[2, 5]]),
('regression player distance metric #2',
[['.~.~....', '....~~~#', '......~~', '....#...'],
[1, 5],
[[-1, 7], [0, 7], [2, 5], [0, 8], [2, 1], [-1, 3], [1, 5]],
3,
3],
[[2, 1]]),
('partial repair boundary #1',
[['..~...', '#.~...', '.#....'],
[0, 5],
[[0, 3], [0, 0], [1, 1], [3, 3], [2, 1], [0, 1], [0, 5], [2, 4], [2, 3], [1, 4]],
1,
3],
[[0, 3], [0, 0], [2, 4]]),
('partial repair boundary #2',
[['.~..', '#...', '..~~', '#...', '..~.'],
[3, 0],
[[0, 4], [5, 3], [3, 2], [4, -1], [-1, -1], [2, 0], [1, 2], [1, -1], [0, 1]],
1,
3],
[[3, 2], [2, 0], [1, 2]]),
('diagonal neighbour spawn #1', [['....', '....', '....'], [0, 0], [[1, 2], [2, 3]], 1, 3], [[1, 2]]),
('control #1',
[['...#...', '......~', '~~.....', '..~....', '.~....~', '.....#.'], [5, 2], [[1, 5]], 0, 0],
[])],
[('exact safe radius #1', [['.....', '.....'], [0, 0], [[1, 1], [0, 2]], 2, 2], [[0, 2]]),
('negative index candidate #1', [['...', '...', '..#'], [0, 0], [[-1, -1], [2, 0]], 1, 2], [[2, 0]]),
('fault site player distance metric #1',
[['..~#.', '.~...', '~..~.', '..~..', '~..#.', '##...', '....~', '...#.'],
[5, 0],
[[5, 1], [2, 4], [3, 5], [6, 1], [4, 0], [8, 1], [2, 4], [8, 1], [6, 5], [7, 2]],
3,
5],
[[2, 4]]),
('regression player distance metric #1',
[['..~.~', '..#..', '.~...', '..~.~', '.~#..', '.....', '.....'],
[0, 2],
[[2, 0], [4, 5], [5, 0], [0, 5], [5, 4], [7, 1], [-1, -1], [4, 0], [7, 3]],
3,
3],
[[5, 0], [5, 4]]),
('regression player distance metric #2',
[['~...', '....', '~~..', '.#..', '...~', '~.~.', '..~.'],
[2, 2],
[[3, 3], [3, 2], [2, 0], [6, 3], [7, 2], [7, 1], [7, 2], [0, 3]],
3,
3],
[[6, 3]]),
('partial repair boundary #1',
[['.#~', '...', '...', '.~.', '#.~', '.#.', '~..'],
[2, 0],
[[4, 2], [0, -1], [0, 3], [6, 1], [4, 0], [4, 2], [7, 2], [3, 2], [1, 2]],
3,
1],
[[6, 1]]),
('diagonal neighbour spawn #1', [['....', '....', '....'], [0, 0], [[1, 2], [2, 3]], 1, 3], [[1, 2]]),
('control #1',
[['....', '.#.~', '..~~', '...#'], [2, 0], [[4, -1], [3, 3], [3, 1], [1, 0], [1, 3]], 0, 2],
[[3, 1], [1, 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 |
|---|---|---|---|
| exact safe radius #1 | [[0, 2]] | [[0, 2]] | Passed |
| negative index candidate #1 | [[2, 0]] | [[2, 0]] | Passed |
| regression player distance metric #1 | [[0, 0]] | [[0, 0]] | Passed |
| fault site player distance metric #1 | [] | [] | Passed |
| partial repair boundary #1 | [[6, 1], [5, 3]] | [[6, 1], [5, 3]] | Passed |
| partial repair boundary #2 | [[2, 0], [1, 6], [0, 2]] | [[2, 0], [1, 6], [0, 2]] | Passed |
| diagonal neighbour spawn #1 | [[1, 2]] | [[1, 2]] | Passed |
| control #1 | [] | [] | Passed |
SHA-256 / 4c1c1d919ce2957b5545ae6b3d5651ed83fd44422b0af78448ae6dca0aa09da2
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 2026-09-29T14:50:49.501666+00:00.
Case digest / 8128d8e14fad966f9b379ab4de964876d18b91a3cf1ad9c0f9835fcc7be145aa