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FA-86821 / Procedural level generation constraints / Open access

Aligned stair placement: Stairs scanned column-major · case 01

Stair placement differs from the documented row-major rule.

Verified by executionVariant 1 · 8 checks per implementationDownload source bundle ↓JSON ↗

ROOT CAUSE

The loops iterate columns in the outer loop.

VERIFIED REPAIR

Restore `for y in range(len(floor_a)): for x in range(len(floor_a[0])):` at the scan order step.

Unsuccessful approach: Scanning rows bottom-up still picks a different first cell.

Case contract

Scan floor_a row by row (y), then column (x); choose the first cell where floor_a[y][x] == '.', the cell exists on floor_b and is '.' there, and the Manhattan distance to entrance [x, y] is at least min_dist. Returns [x, y] or None.

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(floor_a, floor_b, entrance, min_dist):
    for x in range(len(floor_a[0])):
        for y in range(len(floor_a)):
            if floor_a[y][x] != '.':
                continue
            if y >= len(floor_b) or x >= len(floor_b[0]) or floor_b[y][x] != '.':
                continue
            if abs(x - entrance[0]) + abs(y - entrance[1]) < min_dist:
                continue
            return [x, y]
    return None
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
cases = [[('first row candidate #1', [['..', '..'], ['#.', '..'], [0, 0], 1], [1, 0]),
  ('regression scan order #1',
   [['#....', '..#..', '#...#', '#..#.', '.#.#.', '.#.#.'],
    ['#~..', '..~.', '..~.', '..#.', '##~~'],
    [1, 4],
    1],
   [2, 0]),
  ('regression scan order #2',
   [['.#..', '....', '....', '#...'], ['~#...', '~.~..', '#~.~.'], [3, 0], 0],
   [2, 0]),
  ('partial repair boundary #1',
   [['..###.', '.#.#..', '...##.', '###...', '.#..##'], ['#', '~', '.', '.', '.', '#'], [2, 2], 2],
   [0, 2]),
  ('partial repair boundary #2',
   [['#', '.', '.', '.', '.', '#'], ['..', '..', '..', '.~', '.~', '##'], [0, 3], 0],
   [0, 1]),
  ('water below #1', [['.'], ['~'], [0, 0], 0], None),
  ('distance exactly min #1', [['...'], ['...'], [0, 0], 2], [2, 0]),
  ('control #1', [['#.#.', '...#'], ['...#~', '.....'], [3, 1], 4], None)],
 [('first row candidate #1', [['..', '..'], ['#.', '..'], [0, 0], 1], [1, 0]),
  ('regression scan order #1',
   [['.#..', '....', '....', '#...'], ['~#...', '~.~..', '#~.~.'], [3, 0], 0],
   [2, 0]),
  ('regression scan order #2',
   [['..#..', '#..#.', '..#..', '.....', '.#...', '##.#.'],
    ['~~.', '##.', '~#~', '###', '.##', '...'],
    [2, 1],
    0],
   [2, 1]),
  ('partial repair boundary #1',
   [['..###.', '.#.#..', '...##.', '###...', '.#..##'], ['#', '~', '.', '.', '.', '#'], [2, 2], 2],
   [0, 2]),
  ('partial repair boundary #2',
   [['#', '.', '.', '.', '.', '#'], ['..', '..', '..', '.~', '.~', '##'], [0, 3], 0],
   [0, 1]),
  ('water below #1', [['.'], ['~'], [0, 0], 0], None),
  ('distance exactly min #1', [['...'], ['...'], [0, 0], 2], [2, 0]),
  ('control #1', [['#.#.', '...#'], ['...#~', '.....'], [3, 1], 4], None)],
 [('first row candidate #1', [['..', '..'], ['#.', '..'], [0, 0], 1], [1, 0]),
  ('regression scan order #1',
   [['###..', '.#.##', '.....', '.....', '#.##.'], ['~#..', '...#'], [0, 0], 3],
   [3, 0]),
  ('regression scan order #2',
   [['..#..', '#....', '##...', '...#.', '..#..'], ['~.~.', '.##.', '~.##', '....', '...~'], [4, 2], 0],
   [1, 0]),
  ('partial repair boundary #1',
   [['#', '.', '.', '.', '.', '#'], ['..', '..', '..', '.~', '.~', '##'], [0, 3], 0],
   [0, 1]),
  ('partial repair boundary #2',
   [['...#', '.##.', '#..#', '.#..', '.#.#', '....'], ['.....', '.#..~', '.#~.#', '.#~.#'], [2, 5], 1],
   [0, 0]),
  ('water below #1', [['.'], ['~'], [0, 0], 0], None),
  ('distance exactly min #1', [['...'], ['...'], [0, 0], 2], [2, 0]),
  ('control #1', [['#.#.', '...#'], ['...#~', '.....'], [3, 1], 4], None)],
 [('first row candidate #1', [['..', '..'], ['#.', '..'], [0, 0], 1], [1, 0]),
  ('regression scan order #1',
   [['...', '...', '###', '...', '###'], ['~.#', '.#~', '~..', '.#~', '.#.'], [1, 3], 2],
   [1, 0]),
  ('regression scan order #2',
   [['..', '..', '.#', '##', '..', '..'], ['~.', '.~', '..', '~.', '~#'], [1, 4], 4],
   [1, 0]),
  ('regression scan order #3',
   [['..#..', '#..#.', '..#..', '.....', '.#...', '##.#.'],
    ['~~.', '##.', '~#~', '###', '.##', '...'],
    [2, 1],
    0],
   [2, 1]),
  ('regression scan order #4',
   [['###..', '.#.##', '.....', '.....', '#.##.'], ['~#..', '...#'], [0, 0], 3],
   [3, 0]),
  ('water below #1', [['.'], ['~'], [0, 0], 0], None),
  ('distance exactly min #1', [['...'], ['...'], [0, 0], 2], [2, 0]),
  ('control #1', [['.', '#', '.', '#'], ['#.....'], [0, 1], 4], None)],
 [('first row candidate #1', [['..', '..'], ['#.', '..'], [0, 0], 1], [1, 0]),
  ('regression scan order #1',
   [['...#', '##..', '.##.', '....', '.#..', '..##'], ['~.', '#.', '##', '~.', '#.', '.#'], [3, 2], 2],
   [1, 0]),
  ('regression scan order #2',
   [['.#...', '.....', '.....', '..##.'], ['~~.', '.#.', '...', '#.~', '~##', '...'], [0, 1], 3],
   [2, 0]),
  ('partial repair boundary #1',
   [['..#', '.#.', '#.#', '...', '..#'], ['#', '.', '#', '.'], [0, 0], 0],
   [0, 1]),
  ('partial repair boundary #2',
   [['.....#', '..#.#.', '.#..#.', '..###.', '#.#..#'], ['.#.~~#', '.#.##.', '~~#~..', '......'], [0, 3], 5],
   [2, 0]),
  ('water below #1', [['.'], ['~'], [0, 0], 0], None),
  ('distance exactly min #1', [['...'], ['...'], [0, 0], 2], [2, 0]),
  ('control #1',
   [['...', '.#.', '...', '..#', '###', '..#'], ['~.#.~', '##~~#', '~~#..', '.~.~.'], [2, 4], 5],
   [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 fixtureActualExpectedOutcome
first row candidate #1[0, 1][1, 0]Failed
regression scan order #1[0, 1][2, 0]Failed
regression scan order #2[1, 1][2, 0]Failed
partial repair boundary #1[0, 2][0, 2]Passed
partial repair boundary #2[0, 1][0, 1]Passed
water below #1NoneNonePassed
distance exactly min #1[2, 0][2, 0]Passed
control #1NoneNonePassed

SHA-256 / 425c0dc9fbb7ae83f3b1a894c85cdd8cb58118c4e16717130cc8e10302ed29a6

2 / The unsuccessful fix

Exit 1
"""Failure Map reference implementation. Python standard library only."""
import json

N = 1
observations = []
def solve(floor_a, floor_b, entrance, min_dist):
    for y in reversed(range(len(floor_a))):
        for x in range(len(floor_a[0])):
            if floor_a[y][x] != '.':
                continue
            if y >= len(floor_b) or x >= len(floor_b[0]) or floor_b[y][x] != '.':
                continue
            if abs(x - entrance[0]) + abs(y - entrance[1]) < min_dist:
                continue
            return [x, y]
    return None
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
cases = [[('first row candidate #1', [['..', '..'], ['#.', '..'], [0, 0], 1], [1, 0]),
  ('regression scan order #1',
   [['#....', '..#..', '#...#', '#..#.', '.#.#.', '.#.#.'],
    ['#~..', '..~.', '..~.', '..#.', '##~~'],
    [1, 4],
    1],
   [2, 0]),
  ('regression scan order #2',
   [['.#..', '....', '....', '#...'], ['~#...', '~.~..', '#~.~.'], [3, 0], 0],
   [2, 0]),
  ('partial repair boundary #1',
   [['..###.', '.#.#..', '...##.', '###...', '.#..##'], ['#', '~', '.', '.', '.', '#'], [2, 2], 2],
   [0, 2]),
  ('partial repair boundary #2',
   [['#', '.', '.', '.', '.', '#'], ['..', '..', '..', '.~', '.~', '##'], [0, 3], 0],
   [0, 1]),
  ('water below #1', [['.'], ['~'], [0, 0], 0], None),
  ('distance exactly min #1', [['...'], ['...'], [0, 0], 2], [2, 0]),
  ('control #1', [['#.#.', '...#'], ['...#~', '.....'], [3, 1], 4], None)],
 [('first row candidate #1', [['..', '..'], ['#.', '..'], [0, 0], 1], [1, 0]),
  ('regression scan order #1',
   [['.#..', '....', '....', '#...'], ['~#...', '~.~..', '#~.~.'], [3, 0], 0],
   [2, 0]),
  ('regression scan order #2',
   [['..#..', '#..#.', '..#..', '.....', '.#...', '##.#.'],
    ['~~.', '##.', '~#~', '###', '.##', '...'],
    [2, 1],
    0],
   [2, 1]),
  ('partial repair boundary #1',
   [['..###.', '.#.#..', '...##.', '###...', '.#..##'], ['#', '~', '.', '.', '.', '#'], [2, 2], 2],
   [0, 2]),
  ('partial repair boundary #2',
   [['#', '.', '.', '.', '.', '#'], ['..', '..', '..', '.~', '.~', '##'], [0, 3], 0],
   [0, 1]),
  ('water below #1', [['.'], ['~'], [0, 0], 0], None),
  ('distance exactly min #1', [['...'], ['...'], [0, 0], 2], [2, 0]),
  ('control #1', [['#.#.', '...#'], ['...#~', '.....'], [3, 1], 4], None)],
 [('first row candidate #1', [['..', '..'], ['#.', '..'], [0, 0], 1], [1, 0]),
  ('regression scan order #1',
   [['###..', '.#.##', '.....', '.....', '#.##.'], ['~#..', '...#'], [0, 0], 3],
   [3, 0]),
  ('regression scan order #2',
   [['..#..', '#....', '##...', '...#.', '..#..'], ['~.~.', '.##.', '~.##', '....', '...~'], [4, 2], 0],
   [1, 0]),
  ('partial repair boundary #1',
   [['#', '.', '.', '.', '.', '#'], ['..', '..', '..', '.~', '.~', '##'], [0, 3], 0],
   [0, 1]),
  ('partial repair boundary #2',
   [['...#', '.##.', '#..#', '.#..', '.#.#', '....'], ['.....', '.#..~', '.#~.#', '.#~.#'], [2, 5], 1],
   [0, 0]),
  ('water below #1', [['.'], ['~'], [0, 0], 0], None),
  ('distance exactly min #1', [['...'], ['...'], [0, 0], 2], [2, 0]),
  ('control #1', [['#.#.', '...#'], ['...#~', '.....'], [3, 1], 4], None)],
 [('first row candidate #1', [['..', '..'], ['#.', '..'], [0, 0], 1], [1, 0]),
  ('regression scan order #1',
   [['...', '...', '###', '...', '###'], ['~.#', '.#~', '~..', '.#~', '.#.'], [1, 3], 2],
   [1, 0]),
  ('regression scan order #2',
   [['..', '..', '.#', '##', '..', '..'], ['~.', '.~', '..', '~.', '~#'], [1, 4], 4],
   [1, 0]),
  ('regression scan order #3',
   [['..#..', '#..#.', '..#..', '.....', '.#...', '##.#.'],
    ['~~.', '##.', '~#~', '###', '.##', '...'],
    [2, 1],
    0],
   [2, 1]),
  ('regression scan order #4',
   [['###..', '.#.##', '.....', '.....', '#.##.'], ['~#..', '...#'], [0, 0], 3],
   [3, 0]),
  ('water below #1', [['.'], ['~'], [0, 0], 0], None),
  ('distance exactly min #1', [['...'], ['...'], [0, 0], 2], [2, 0]),
  ('control #1', [['.', '#', '.', '#'], ['#.....'], [0, 1], 4], None)],
 [('first row candidate #1', [['..', '..'], ['#.', '..'], [0, 0], 1], [1, 0]),
  ('regression scan order #1',
   [['...#', '##..', '.##.', '....', '.#..', '..##'], ['~.', '#.', '##', '~.', '#.', '.#'], [3, 2], 2],
   [1, 0]),
  ('regression scan order #2',
   [['.#...', '.....', '.....', '..##.'], ['~~.', '.#.', '...', '#.~', '~##', '...'], [0, 1], 3],
   [2, 0]),
  ('partial repair boundary #1',
   [['..#', '.#.', '#.#', '...', '..#'], ['#', '.', '#', '.'], [0, 0], 0],
   [0, 1]),
  ('partial repair boundary #2',
   [['.....#', '..#.#.', '.#..#.', '..###.', '#.#..#'], ['.#.~~#', '.#.##.', '~~#~..', '......'], [0, 3], 5],
   [2, 0]),
  ('water below #1', [['.'], ['~'], [0, 0], 0], None),
  ('distance exactly min #1', [['...'], ['...'], [0, 0], 2], [2, 0]),
  ('control #1',
   [['...', '.#.', '...', '..#', '###', '..#'], ['~.#.~', '##~~#', '~~#..', '.~.~.'], [2, 4], 5],
   [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 fixtureActualExpectedOutcome
first row candidate #1[0, 1][1, 0]Failed
regression scan order #1[1, 3][2, 0]Failed
regression scan order #2[2, 2][2, 0]Failed
partial repair boundary #1[0, 4][0, 2]Failed
partial repair boundary #2[0, 4][0, 1]Failed
water below #1NoneNonePassed
distance exactly min #1[2, 0][2, 0]Passed
control #1NoneNonePassed

SHA-256 / 5043bedb0220dedba35f9588cd41d452efa9c8985f0f1d37c9116ffa9b94ff63

3 / The verified repair

Exit 0
"""Failure Map reference implementation. Python standard library only."""
import json

N = 1
observations = []
def solve(floor_a, floor_b, entrance, min_dist):
    for y in range(len(floor_a)):
        for x in range(len(floor_a[0])):
            if floor_a[y][x] != '.':
                continue
            if y >= len(floor_b) or x >= len(floor_b[0]) or floor_b[y][x] != '.':
                continue
            if abs(x - entrance[0]) + abs(y - entrance[1]) < min_dist:
                continue
            return [x, y]
    return None
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
cases = [[('first row candidate #1', [['..', '..'], ['#.', '..'], [0, 0], 1], [1, 0]),
  ('regression scan order #1',
   [['#....', '..#..', '#...#', '#..#.', '.#.#.', '.#.#.'],
    ['#~..', '..~.', '..~.', '..#.', '##~~'],
    [1, 4],
    1],
   [2, 0]),
  ('regression scan order #2',
   [['.#..', '....', '....', '#...'], ['~#...', '~.~..', '#~.~.'], [3, 0], 0],
   [2, 0]),
  ('partial repair boundary #1',
   [['..###.', '.#.#..', '...##.', '###...', '.#..##'], ['#', '~', '.', '.', '.', '#'], [2, 2], 2],
   [0, 2]),
  ('partial repair boundary #2',
   [['#', '.', '.', '.', '.', '#'], ['..', '..', '..', '.~', '.~', '##'], [0, 3], 0],
   [0, 1]),
  ('water below #1', [['.'], ['~'], [0, 0], 0], None),
  ('distance exactly min #1', [['...'], ['...'], [0, 0], 2], [2, 0]),
  ('control #1', [['#.#.', '...#'], ['...#~', '.....'], [3, 1], 4], None)],
 [('first row candidate #1', [['..', '..'], ['#.', '..'], [0, 0], 1], [1, 0]),
  ('regression scan order #1',
   [['.#..', '....', '....', '#...'], ['~#...', '~.~..', '#~.~.'], [3, 0], 0],
   [2, 0]),
  ('regression scan order #2',
   [['..#..', '#..#.', '..#..', '.....', '.#...', '##.#.'],
    ['~~.', '##.', '~#~', '###', '.##', '...'],
    [2, 1],
    0],
   [2, 1]),
  ('partial repair boundary #1',
   [['..###.', '.#.#..', '...##.', '###...', '.#..##'], ['#', '~', '.', '.', '.', '#'], [2, 2], 2],
   [0, 2]),
  ('partial repair boundary #2',
   [['#', '.', '.', '.', '.', '#'], ['..', '..', '..', '.~', '.~', '##'], [0, 3], 0],
   [0, 1]),
  ('water below #1', [['.'], ['~'], [0, 0], 0], None),
  ('distance exactly min #1', [['...'], ['...'], [0, 0], 2], [2, 0]),
  ('control #1', [['#.#.', '...#'], ['...#~', '.....'], [3, 1], 4], None)],
 [('first row candidate #1', [['..', '..'], ['#.', '..'], [0, 0], 1], [1, 0]),
  ('regression scan order #1',
   [['###..', '.#.##', '.....', '.....', '#.##.'], ['~#..', '...#'], [0, 0], 3],
   [3, 0]),
  ('regression scan order #2',
   [['..#..', '#....', '##...', '...#.', '..#..'], ['~.~.', '.##.', '~.##', '....', '...~'], [4, 2], 0],
   [1, 0]),
  ('partial repair boundary #1',
   [['#', '.', '.', '.', '.', '#'], ['..', '..', '..', '.~', '.~', '##'], [0, 3], 0],
   [0, 1]),
  ('partial repair boundary #2',
   [['...#', '.##.', '#..#', '.#..', '.#.#', '....'], ['.....', '.#..~', '.#~.#', '.#~.#'], [2, 5], 1],
   [0, 0]),
  ('water below #1', [['.'], ['~'], [0, 0], 0], None),
  ('distance exactly min #1', [['...'], ['...'], [0, 0], 2], [2, 0]),
  ('control #1', [['#.#.', '...#'], ['...#~', '.....'], [3, 1], 4], None)],
 [('first row candidate #1', [['..', '..'], ['#.', '..'], [0, 0], 1], [1, 0]),
  ('regression scan order #1',
   [['...', '...', '###', '...', '###'], ['~.#', '.#~', '~..', '.#~', '.#.'], [1, 3], 2],
   [1, 0]),
  ('regression scan order #2',
   [['..', '..', '.#', '##', '..', '..'], ['~.', '.~', '..', '~.', '~#'], [1, 4], 4],
   [1, 0]),
  ('regression scan order #3',
   [['..#..', '#..#.', '..#..', '.....', '.#...', '##.#.'],
    ['~~.', '##.', '~#~', '###', '.##', '...'],
    [2, 1],
    0],
   [2, 1]),
  ('regression scan order #4',
   [['###..', '.#.##', '.....', '.....', '#.##.'], ['~#..', '...#'], [0, 0], 3],
   [3, 0]),
  ('water below #1', [['.'], ['~'], [0, 0], 0], None),
  ('distance exactly min #1', [['...'], ['...'], [0, 0], 2], [2, 0]),
  ('control #1', [['.', '#', '.', '#'], ['#.....'], [0, 1], 4], None)],
 [('first row candidate #1', [['..', '..'], ['#.', '..'], [0, 0], 1], [1, 0]),
  ('regression scan order #1',
   [['...#', '##..', '.##.', '....', '.#..', '..##'], ['~.', '#.', '##', '~.', '#.', '.#'], [3, 2], 2],
   [1, 0]),
  ('regression scan order #2',
   [['.#...', '.....', '.....', '..##.'], ['~~.', '.#.', '...', '#.~', '~##', '...'], [0, 1], 3],
   [2, 0]),
  ('partial repair boundary #1',
   [['..#', '.#.', '#.#', '...', '..#'], ['#', '.', '#', '.'], [0, 0], 0],
   [0, 1]),
  ('partial repair boundary #2',
   [['.....#', '..#.#.', '.#..#.', '..###.', '#.#..#'], ['.#.~~#', '.#.##.', '~~#~..', '......'], [0, 3], 5],
   [2, 0]),
  ('water below #1', [['.'], ['~'], [0, 0], 0], None),
  ('distance exactly min #1', [['...'], ['...'], [0, 0], 2], [2, 0]),
  ('control #1',
   [['...', '.#.', '...', '..#', '###', '..#'], ['~.#.~', '##~~#', '~~#..', '.~.~.'], [2, 4], 5],
   [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 fixtureActualExpectedOutcome
first row candidate #1[1, 0][1, 0]Passed
regression scan order #1[2, 0][2, 0]Passed
regression scan order #2[2, 0][2, 0]Passed
partial repair boundary #1[0, 2][0, 2]Passed
partial repair boundary #2[0, 1][0, 1]Passed
water below #1NoneNonePassed
distance exactly min #1[2, 0][2, 0]Passed
control #1NoneNonePassed

SHA-256 / f41668c6b88b6ac5893cc84b0d21df1ab015f13d7530400e6e13abc6f8cafc0e

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 2026-09-29T14:50:53.143519+00:00.

Case digest / 041a2d355ff503a42077fcb584889f3378780c8f4d616aa2ade85a38c9288a71