FA-97586 / Knitting and sewing pattern grading / Open access

Cutting layout fabric length: row height · case 01

A row with a tall piece first and a short piece last is measured as short.

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

ROOT CAUSE

Row height is the last piece placed, not the tallest.

VERIFIED REPAIR

Track the tallest piece in the row.

Unsuccessful approach: Tracking width mixes the axes.

Case contract

Pieces [w, h, qty] (cm; w across the fabric). A piece wider than the fabric is rotated if the fabric is not directional and its height fits, else "error: piece too wide". Expand qty, sort by (height, width) descending, then shelf-pack: start a new row when the row width plus the piece would exceed the fabric width; each row is as tall as its tallest piece. Return [length_cm, eighths_of_a_yard] with eighths = ceiling(length/91.44*8).

Why this case matters

Pattern envelopes and cutting planners estimate yardage from piece layouts and nap direction.

1 / The failure

Exit 1

"""Failure Map reference implementation. Python standard library only."""
import json
import math
from fractions import Fraction
N = 1
observations = []
def solve(pieces, width, directional):
    items = []
    for w, h, qty in pieces:
        for _ in range(qty):
            if w > width:
                if directional or h > width:
                    return 'error: piece too wide'
                w, h = h, w
            items.append((h, w))
    items.sort(reverse=True)
    length = 0
    row_w = 0
    row_h = 0
    for h, w in items:
        if row_w + w > width:
            length += row_h
            row_w, row_h = 0, 0
        row_w += w
        row_h = h
    length += row_h
    return [length, math.ceil(Fraction(length) / Fraction(9144, 100) * 8)]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['two pieces one row', [[[70, 60, 2]], 140, False], [60, 6]],
  ['rotate wide piece', [[[150, 60, 1]], 140, False], [150, 14]],
  ['directional wide piece', [[[150, 60, 1]], 140, True], 'error: piece too wide'],
  ['regression: row height', [[[70, 30, 3], [70, 80, 3], [150, 80, 1]], 140, False], [340, 30]],
  ['repair check: row height', [[[150, 100, 2], [35, 80, 3], [40, 80, 1]], 150, False], [280, 25]],
  ['generated control 1', [[[55, 45, 1], [40, 45, 3], [150, 45, 3]], 140, True], 'error: piece too wide'],
  ['generated control 2', [[[70, 30, 3]], 150, False], [60, 6]],
  ['generated control 3', [[[150, 30, 1], [110, 100, 1]], 150, True], [130, 12]]],
 [['rotate wide piece', [[[150, 60, 1]], 140, False], [150, 14]],
  ['directional wide piece', [[[150, 60, 1]], 140, True], 'error: piece too wide'],
  ['exact fit row', [[[55, 80, 2], [40, 45, 1]], 150, False], [80, 7]],
  ['regression: row height', [[[35, 60, 1], [70, 100, 1], [55, 80, 1], [35, 45, 1]], 150, True], [160, 14]],
  ['repair check: row height', [[[35, 80, 2], [150, 100, 1], [35, 80, 3]], 110, False], [310, 28]],
  ['generated control 1', [[[70, 60, 1], [35, 100, 2], [110, 60, 2]], 150, False], [280, 25]],
  ['generated control 2', [[[110, 45, 3], [35, 80, 1], [110, 60, 1]], 140, True], [275, 25]],
  ['generated control 3', [[[35, 80, 2], [150, 45, 2], [150, 45, 1]], 150, True], [215, 19]]],
 [['directional wide piece', [[[150, 60, 1]], 140, True], 'error: piece too wide'],
  ['exact fit row', [[[55, 80, 2], [40, 45, 1]], 150, False], [80, 7]],
  ['two pieces one row', [[[70, 60, 2]], 140, False], [60, 6]],
  ['regression: row height', [[[40, 80, 3], [20, 60, 1], [110, 100, 2], [40, 30, 1]], 110, True], [360, 32]],
  ['repair check: row height', [[[40, 45, 2], [55, 100, 3]], 150, False], [200, 18]],
  ['generated control 1', [[[150, 80, 1], [70, 45, 2], [40, 60, 2], [35, 100, 3]], 110, True],
   'error: piece too wide'],
  ['generated control 2', [[[20, 80, 3]], 150, True], [80, 7]],
  ['generated control 3', [[[110, 30, 3]], 140, False], [90, 8]]],
 [['exact fit row', [[[55, 80, 2], [40, 45, 1]], 150, False], [80, 7]],
  ['two pieces one row', [[[70, 60, 2]], 140, False], [60, 6]],
  ['rotate wide piece', [[[150, 60, 1]], 140, False], [150, 14]],
  ['regression: row height', [[[20, 100, 3], [70, 80, 2], [110, 100, 1], [35, 60, 2]], 150, False],
   [280, 25]],
  ['repair check: row height', [[[150, 30, 1]], 150, True], [30, 3]],
  ['generated control 1', [[[20, 30, 1], [110, 45, 1], [150, 30, 1]], 140, True], 'error: piece too wide'],
  ['generated control 2', [[[110, 30, 3], [55, 60, 3]], 150, False], [210, 19]],
  ['generated control 3', [[[70, 45, 1], [70, 45, 1], [70, 80, 3]], 110, True], [330, 29]]],
 [['two pieces one row', [[[70, 60, 2]], 140, False], [60, 6]],
  ['rotate wide piece', [[[150, 60, 1]], 140, False], [150, 14]],
  ['directional wide piece', [[[150, 60, 1]], 140, True], 'error: piece too wide'],
  ['regression: row height', [[[40, 100, 1], [40, 45, 3]], 150, False], [145, 13]],
  ['repair check: row height', [[[55, 80, 2], [70, 45, 3]], 150, True], [170, 15]],
  ['generated control 1', [[[40, 80, 3], [20, 45, 1], [40, 45, 3], [70, 100, 1]], 140, False], [225, 20]],
  ['generated control 2', [[[20, 60, 2], [150, 30, 3]], 140, False], [150, 14]],
  ['generated control 3', [[[110, 100, 1]], 150, True], [100, 9]]]]
for label, args, expected in fixtures[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 pieces one row	`[60, 6]`	`[60, 6]`	Passed
rotate wide piece	`[150, 14]`	`[150, 14]`	Passed
directional wide piece	`error: piece too wide`	`error: piece too wide`	Passed
regression: row height	`[290, 26]`	`[340, 30]`	Failed
repair check: row height	`[280, 25]`	`[280, 25]`	Passed
generated control 1	`error: piece too wide`	`error: piece too wide`	Passed
generated control 2	`[60, 6]`	`[60, 6]`	Passed
generated control 3	`[130, 12]`	`[130, 12]`	Passed

SHA-256 / d25808ded7730044b6ca51e300f8575ade9bfc5d5aad547be51956f577bdb9e5

2 / The unsuccessful fix

Exit 1

"""Failure Map reference implementation. Python standard library only."""
import json
import math
from fractions import Fraction
N = 1
observations = []
def solve(pieces, width, directional):
    items = []
    for w, h, qty in pieces:
        for _ in range(qty):
            if w > width:
                if directional or h > width:
                    return 'error: piece too wide'
                w, h = h, w
            items.append((h, w))
    items.sort(reverse=True)
    length = 0
    row_w = 0
    row_h = 0
    for h, w in items:
        if row_w + w > width:
            length += row_h
            row_w, row_h = 0, 0
        row_w += w
        row_h = max(row_h, w)
    length += row_h
    return [length, math.ceil(Fraction(length) / Fraction(9144, 100) * 8)]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['two pieces one row', [[[70, 60, 2]], 140, False], [60, 6]],
  ['rotate wide piece', [[[150, 60, 1]], 140, False], [150, 14]],
  ['directional wide piece', [[[150, 60, 1]], 140, True], 'error: piece too wide'],
  ['regression: row height', [[[70, 30, 3], [70, 80, 3], [150, 80, 1]], 140, False], [340, 30]],
  ['repair check: row height', [[[150, 100, 2], [35, 80, 3], [40, 80, 1]], 150, False], [280, 25]],
  ['generated control 1', [[[55, 45, 1], [40, 45, 3], [150, 45, 3]], 140, True], 'error: piece too wide'],
  ['generated control 2', [[[70, 30, 3]], 150, False], [60, 6]],
  ['generated control 3', [[[150, 30, 1], [110, 100, 1]], 150, True], [130, 12]]],
 [['rotate wide piece', [[[150, 60, 1]], 140, False], [150, 14]],
  ['directional wide piece', [[[150, 60, 1]], 140, True], 'error: piece too wide'],
  ['exact fit row', [[[55, 80, 2], [40, 45, 1]], 150, False], [80, 7]],
  ['regression: row height', [[[35, 60, 1], [70, 100, 1], [55, 80, 1], [35, 45, 1]], 150, True], [160, 14]],
  ['repair check: row height', [[[35, 80, 2], [150, 100, 1], [35, 80, 3]], 110, False], [310, 28]],
  ['generated control 1', [[[70, 60, 1], [35, 100, 2], [110, 60, 2]], 150, False], [280, 25]],
  ['generated control 2', [[[110, 45, 3], [35, 80, 1], [110, 60, 1]], 140, True], [275, 25]],
  ['generated control 3', [[[35, 80, 2], [150, 45, 2], [150, 45, 1]], 150, True], [215, 19]]],
 [['directional wide piece', [[[150, 60, 1]], 140, True], 'error: piece too wide'],
  ['exact fit row', [[[55, 80, 2], [40, 45, 1]], 150, False], [80, 7]],
  ['two pieces one row', [[[70, 60, 2]], 140, False], [60, 6]],
  ['regression: row height', [[[40, 80, 3], [20, 60, 1], [110, 100, 2], [40, 30, 1]], 110, True], [360, 32]],
  ['repair check: row height', [[[40, 45, 2], [55, 100, 3]], 150, False], [200, 18]],
  ['generated control 1', [[[150, 80, 1], [70, 45, 2], [40, 60, 2], [35, 100, 3]], 110, True],
   'error: piece too wide'],
  ['generated control 2', [[[20, 80, 3]], 150, True], [80, 7]],
  ['generated control 3', [[[110, 30, 3]], 140, False], [90, 8]]],
 [['exact fit row', [[[55, 80, 2], [40, 45, 1]], 150, False], [80, 7]],
  ['two pieces one row', [[[70, 60, 2]], 140, False], [60, 6]],
  ['rotate wide piece', [[[150, 60, 1]], 140, False], [150, 14]],
  ['regression: row height', [[[20, 100, 3], [70, 80, 2], [110, 100, 1], [35, 60, 2]], 150, False],
   [280, 25]],
  ['repair check: row height', [[[150, 30, 1]], 150, True], [30, 3]],
  ['generated control 1', [[[20, 30, 1], [110, 45, 1], [150, 30, 1]], 140, True], 'error: piece too wide'],
  ['generated control 2', [[[110, 30, 3], [55, 60, 3]], 150, False], [210, 19]],
  ['generated control 3', [[[70, 45, 1], [70, 45, 1], [70, 80, 3]], 110, True], [330, 29]]],
 [['two pieces one row', [[[70, 60, 2]], 140, False], [60, 6]],
  ['rotate wide piece', [[[150, 60, 1]], 140, False], [150, 14]],
  ['directional wide piece', [[[150, 60, 1]], 140, True], 'error: piece too wide'],
  ['regression: row height', [[[40, 100, 1], [40, 45, 3]], 150, False], [145, 13]],
  ['repair check: row height', [[[55, 80, 2], [70, 45, 3]], 150, True], [170, 15]],
  ['generated control 1', [[[40, 80, 3], [20, 45, 1], [40, 45, 3], [70, 100, 1]], 140, False], [225, 20]],
  ['generated control 2', [[[20, 60, 2], [150, 30, 3]], 140, False], [150, 14]],
  ['generated control 3', [[[110, 100, 1]], 150, True], [100, 9]]]]
for label, args, expected in fixtures[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 pieces one row	`[70, 7]`	`[60, 6]`	Failed
rotate wide piece	`[60, 6]`	`[150, 14]`	Failed
directional wide piece	`error: piece too wide`	`error: piece too wide`	Passed
regression: row height	`[290, 26]`	`[340, 30]`	Failed
repair check: row height	`[340, 30]`	`[280, 25]`	Failed
generated control 1	`error: piece too wide`	`error: piece too wide`	Passed
generated control 2	`[140, 13]`	`[60, 6]`	Failed
generated control 3	`[260, 23]`	`[130, 12]`	Failed

SHA-256 / f28b8804fe20313005353e4d1b7dcda16ce6f1d9cc8583485c4c242805f94a4d

3 / The verified repair

Exit 0

"""Failure Map reference implementation. Python standard library only."""
import json
import math
from fractions import Fraction
N = 1
observations = []
def solve(pieces, width, directional):
    items = []
    for w, h, qty in pieces:
        for _ in range(qty):
            if w > width:
                if directional or h > width:
                    return 'error: piece too wide'
                w, h = h, w
            items.append((h, w))
    items.sort(reverse=True)
    length = 0
    row_w = 0
    row_h = 0
    for h, w in items:
        if row_w + w > width:
            length += row_h
            row_w, row_h = 0, 0
        row_w += w
        row_h = max(row_h, h)
    length += row_h
    return [length, math.ceil(Fraction(length) / Fraction(9144, 100) * 8)]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['two pieces one row', [[[70, 60, 2]], 140, False], [60, 6]],
  ['rotate wide piece', [[[150, 60, 1]], 140, False], [150, 14]],
  ['directional wide piece', [[[150, 60, 1]], 140, True], 'error: piece too wide'],
  ['regression: row height', [[[70, 30, 3], [70, 80, 3], [150, 80, 1]], 140, False], [340, 30]],
  ['repair check: row height', [[[150, 100, 2], [35, 80, 3], [40, 80, 1]], 150, False], [280, 25]],
  ['generated control 1', [[[55, 45, 1], [40, 45, 3], [150, 45, 3]], 140, True], 'error: piece too wide'],
  ['generated control 2', [[[70, 30, 3]], 150, False], [60, 6]],
  ['generated control 3', [[[150, 30, 1], [110, 100, 1]], 150, True], [130, 12]]],
 [['rotate wide piece', [[[150, 60, 1]], 140, False], [150, 14]],
  ['directional wide piece', [[[150, 60, 1]], 140, True], 'error: piece too wide'],
  ['exact fit row', [[[55, 80, 2], [40, 45, 1]], 150, False], [80, 7]],
  ['regression: row height', [[[35, 60, 1], [70, 100, 1], [55, 80, 1], [35, 45, 1]], 150, True], [160, 14]],
  ['repair check: row height', [[[35, 80, 2], [150, 100, 1], [35, 80, 3]], 110, False], [310, 28]],
  ['generated control 1', [[[70, 60, 1], [35, 100, 2], [110, 60, 2]], 150, False], [280, 25]],
  ['generated control 2', [[[110, 45, 3], [35, 80, 1], [110, 60, 1]], 140, True], [275, 25]],
  ['generated control 3', [[[35, 80, 2], [150, 45, 2], [150, 45, 1]], 150, True], [215, 19]]],
 [['directional wide piece', [[[150, 60, 1]], 140, True], 'error: piece too wide'],
  ['exact fit row', [[[55, 80, 2], [40, 45, 1]], 150, False], [80, 7]],
  ['two pieces one row', [[[70, 60, 2]], 140, False], [60, 6]],
  ['regression: row height', [[[40, 80, 3], [20, 60, 1], [110, 100, 2], [40, 30, 1]], 110, True], [360, 32]],
  ['repair check: row height', [[[40, 45, 2], [55, 100, 3]], 150, False], [200, 18]],
  ['generated control 1', [[[150, 80, 1], [70, 45, 2], [40, 60, 2], [35, 100, 3]], 110, True],
   'error: piece too wide'],
  ['generated control 2', [[[20, 80, 3]], 150, True], [80, 7]],
  ['generated control 3', [[[110, 30, 3]], 140, False], [90, 8]]],
 [['exact fit row', [[[55, 80, 2], [40, 45, 1]], 150, False], [80, 7]],
  ['two pieces one row', [[[70, 60, 2]], 140, False], [60, 6]],
  ['rotate wide piece', [[[150, 60, 1]], 140, False], [150, 14]],
  ['regression: row height', [[[20, 100, 3], [70, 80, 2], [110, 100, 1], [35, 60, 2]], 150, False],
   [280, 25]],
  ['repair check: row height', [[[150, 30, 1]], 150, True], [30, 3]],
  ['generated control 1', [[[20, 30, 1], [110, 45, 1], [150, 30, 1]], 140, True], 'error: piece too wide'],
  ['generated control 2', [[[110, 30, 3], [55, 60, 3]], 150, False], [210, 19]],
  ['generated control 3', [[[70, 45, 1], [70, 45, 1], [70, 80, 3]], 110, True], [330, 29]]],
 [['two pieces one row', [[[70, 60, 2]], 140, False], [60, 6]],
  ['rotate wide piece', [[[150, 60, 1]], 140, False], [150, 14]],
  ['directional wide piece', [[[150, 60, 1]], 140, True], 'error: piece too wide'],
  ['regression: row height', [[[40, 100, 1], [40, 45, 3]], 150, False], [145, 13]],
  ['repair check: row height', [[[55, 80, 2], [70, 45, 3]], 150, True], [170, 15]],
  ['generated control 1', [[[40, 80, 3], [20, 45, 1], [40, 45, 3], [70, 100, 1]], 140, False], [225, 20]],
  ['generated control 2', [[[20, 60, 2], [150, 30, 3]], 140, False], [150, 14]],
  ['generated control 3', [[[110, 100, 1]], 150, True], [100, 9]]]]
for label, args, expected in fixtures[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 pieces one row	`[60, 6]`	`[60, 6]`	Passed
rotate wide piece	`[150, 14]`	`[150, 14]`	Passed
directional wide piece	`error: piece too wide`	`error: piece too wide`	Passed
regression: row height	`[340, 30]`	`[340, 30]`	Passed
repair check: row height	`[280, 25]`	`[280, 25]`	Passed
generated control 1	`error: piece too wide`	`error: piece too wide`	Passed
generated control 2	`[60, 6]`	`[60, 6]`	Passed
generated control 3	`[130, 12]`	`[130, 12]`	Passed

SHA-256 / 99b1413d79233a11fc77f1743551de6f92e1ef9e4f2eb7856e320d3fc8e2292f

Verification & scope

A deterministic toy contract stated in full here; it is a bounded teaching model, not an authoritative reference or standards implementation. 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 2026-09-29T14:52:33.686363+00:00.

Case digest / 47004fd92bc0addc2af2f279e3dbfcd2c40062baa004b10e88c9c365c1737d5d