broken_source:
"""Failure Map reference implementation. Python standard library only."""
import json
import math
N = 1
observations = []
def solve(x):
    ring = x
    if len(ring) < 4:
        return 'too_few_points'
    if ring[0] != ring[-1]:
        return 'not_closed'
    pts = ring[:-1]
    n = len(pts)
    for i in range(n):
        if pts[i] == pts[(i + 1) % n]:
            return 'repeated_point'
    for i in range(1, n - 1):
        a, b, c = pts[i - 1], pts[i], pts[(i + 1) % n]
        cross = (b[0] - a[0]) * (c[1] - b[1]) - (b[1] - a[1]) * (c[0] - b[0])
        dot = (b[0] - a[0]) * (c[0] - b[0]) + (b[1] - a[1]) * (c[1] - b[1])
        if cross == 0 and dot < 0:
            return 'spike'
    def orient(p, q, r):
        v = (q[0] - p[0]) * (r[1] - p[1]) - (q[1] - p[1]) * (r[0] - p[0])
        return (v > 0) - (v < 0)
    def within(p, q, r):
        return min(p[0], r[0]) <= q[0] <= max(p[0], r[0]) and min(p[1], r[1]) <= q[1] <= max(p[1], r[1])
    def hit(p1, p2, p3, p4):
        o1, o2, o3, o4 = orient(p1, p2, p3), orient(p1, p2, p4), orient(p3, p4, p1), orient(p3, p4, p2)
        if o1 * o2 < 0 and o3 * o4 < 0:
            return True
        return (o1 == 0 and within(p1, p3, p2)) or (o2 == 0 and within(p1, p4, p2)) or (o3 == 0 and within(p3, p1, p4)) or (o4 == 0 and within(p3, p2, p4))
    for i in range(n):
        for j in range(i + 1, n):
            if j == i + 1 or (i == 0 and j == n - 1):
                continue
            if hit(pts[i], pts[(i + 1) % n], pts[j], pts[(j + 1) % n]):
                return 'self_intersection'
    return 'valid'
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('control #0', [[0, 0], [10, 0], [10, 10], [0, 10], [0, 0]], 'valid'), ('control #1', [[0, 0], [10, 0], [5, 8], [0, 0]], 'valid'), ('control #2', [[0, 0], [5, 0], [10, 0], [10, 10], [0, 10], [0, 0]], 'valid'), ('regression #3', [[0, 0], [10, 10], [10, 0], [0, 10], [0, 0]], 'self_intersection'), ('regression #4', [[0, 0], [10, 0], [10, 10], [10, 5], [0, 5], [0, 0]], 'spike'), ('regression #5', [[5, 0], [10, 0], [10, 10], [0, 10], [0, 0], [5, 0], [0, 0]], 'not_closed'), ('regression #12', [[0, 5], [0, 0], [10, 0], [10, 10], [0, 10], [0, 12], [0, 5]], 'spike'), ('regression #23', [[10, 0], [7, 0], [7, 5], [0, 5], [0, 0], [5, 0], [10, 0]], 'spike')], [('regression #3', [[0, 0], [10, 10], [10, 0], [0, 10], [0, 0]], 'self_intersection'), ('regression #4', [[0, 0], [10, 0], [10, 10], [10, 5], [0, 5], [0, 0]], 'spike'), ('regression #5', [[5, 0], [10, 0], [10, 10], [0, 10], [0, 0], [5, 0], [0, 0]], 'not_closed'), ('boundary #6', [[0, 0], [10, 0], [10, 10], [0, 0]], 'valid'), ('boundary #7', [[0, 0], [10, 0], [10, 10]], 'too_few_points'), ('boundary #8', [[0, 0], [10, 0], [10, 10], [0, 10], [0, 1]], 'not_closed'), ('boundary #9', [[0, 0], [10, 0], [10, 0], [10, 10], [0, 0]], 'repeated_point'), ('regression #23', [[10, 0], [7, 0], [7, 5], [0, 5], [0, 0], [5, 0], [10, 0]], 'spike')], [('boundary #6', [[0, 0], [10, 0], [10, 10], [0, 0]], 'valid'), ('boundary #7', [[0, 0], [10, 0], [10, 10]], 'too_few_points'), ('boundary #8', [[0, 0], [10, 0], [10, 10], [0, 10], [0, 1]], 'not_closed'), ('boundary #9', [[0, 0], [10, 0], [10, 0], [10, 10], [0, 0]], 'repeated_point'), ('regression #10', [[0, 0], [10, 0], [10, 10], [0, 10], [0, 0], [0, 0]], 'repeated_point'), ('regression #11', [[0, 0], [10, 0], [10, 10], [0, 10], [0, 5], [0, 12], [0, 0]], 'spike'), ('regression #12', [[0, 5], [0, 0], [10, 0], [10, 10], [0, 10], [0, 12], [0, 5]], 'spike'), ('regression #23', [[10, 0], [7, 0], [7, 5], [0, 5], [0, 0], [5, 0], [10, 0]], 'spike')], [('boundary #9', [[0, 0], [10, 0], [10, 0], [10, 10], [0, 0]], 'repeated_point'), ('regression #10', [[0, 0], [10, 0], [10, 10], [0, 10], [0, 0], [0, 0]], 'repeated_point'), ('regression #11', [[0, 0], [10, 0], [10, 10], [0, 10], [0, 5], [0, 12], [0, 0]], 'spike'), ('regression #12', [[0, 5], [0, 0], [10, 0], [10, 10], [0, 10], [0, 12], [0, 5]], 'spike'), ('regression #13', [[0, 0], [4, 0], [4, 4], [8, 4], [8, 8], [4, 8], [4, 4], [0, 4], [0, 0]], 'self_intersection'), ('regression #14', [[0, 0], [10, 0], [10, 10], [5, 0], [0, 10], [0, 0]], 'self_intersection'), ('regression #15', [[0, 0], [10, 0], [10, 5], [2, 5], [6, 5], [6, 8], [0, 8], [0, 0]], 'spike'), ('regression #23', [[10, 0], [7, 0], [7, 5], [0, 5], [0, 0], [5, 0], [10, 0]], 'spike')], [('regression #12', [[0, 5], [0, 0], [10, 0], [10, 10], [0, 10], [0, 12], [0, 5]], 'spike'), ('regression #13', [[0, 0], [4, 0], [4, 4], [8, 4], [8, 8], [4, 8], [4, 4], [0, 4], [0, 0]], 'self_intersection'), ('regression #14', [[0, 0], [10, 0], [10, 10], [5, 0], [0, 10], [0, 0]], 'self_intersection'), ('regression #15', [[0, 0], [10, 0], [10, 5], [2, 5], [6, 5], [6, 8], [0, 8], [0, 0]], 'spike'), ('control #16', [[0, 0], [6, 0], [6, 6], [3, 3], [0, 6], [0, 0]], 'valid'), ('regression #17', [[0, 0], [10, 0], [10, 10], [0, 10], [4, 10], [0, 0]], 'spike'), ('control #18', [[1, 1], [9, 2], [8, 9], [2, 7], [1, 1]], 'valid'), ('regression #23', [[10, 0], [7, 0], [7, 5], [0, 5], [0, 0], [5, 0], [10, 0]], 'spike')]]
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)

source:
"""Failure Map reference implementation. Python standard library only."""
import json
import math
N = 1
observations = []
def solve(x):
    ring = x
    if len(ring) < 4:
        return 'too_few_points'
    if ring[0] != ring[-1]:
        return 'not_closed'
    pts = ring[:-1]
    n = len(pts)
    for i in range(n):
        if pts[i] == pts[(i + 1) % n]:
            return 'repeated_point'
    for i in range(1, n):
        a, b, c = pts[i - 1], pts[i], pts[(i + 1) % n]
        cross = (b[0] - a[0]) * (c[1] - b[1]) - (b[1] - a[1]) * (c[0] - b[0])
        dot = (b[0] - a[0]) * (c[0] - b[0]) + (b[1] - a[1]) * (c[1] - b[1])
        if cross == 0 and dot < 0:
            return 'spike'
    def orient(p, q, r):
        v = (q[0] - p[0]) * (r[1] - p[1]) - (q[1] - p[1]) * (r[0] - p[0])
        return (v > 0) - (v < 0)
    def within(p, q, r):
        return min(p[0], r[0]) <= q[0] <= max(p[0], r[0]) and min(p[1], r[1]) <= q[1] <= max(p[1], r[1])
    def hit(p1, p2, p3, p4):
        o1, o2, o3, o4 = orient(p1, p2, p3), orient(p1, p2, p4), orient(p3, p4, p1), orient(p3, p4, p2)
        if o1 * o2 < 0 and o3 * o4 < 0:
            return True
        return (o1 == 0 and within(p1, p3, p2)) or (o2 == 0 and within(p1, p4, p2)) or (o3 == 0 and within(p3, p1, p4)) or (o4 == 0 and within(p3, p2, p4))
    for i in range(n):
        for j in range(i + 1, n):
            if j == i + 1 or (i == 0 and j == n - 1):
                continue
            if hit(pts[i], pts[(i + 1) % n], pts[j], pts[(j + 1) % n]):
                return 'self_intersection'
    return 'valid'
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('control #0', [[0, 0], [10, 0], [10, 10], [0, 10], [0, 0]], 'valid'), ('control #1', [[0, 0], [10, 0], [5, 8], [0, 0]], 'valid'), ('control #2', [[0, 0], [5, 0], [10, 0], [10, 10], [0, 10], [0, 0]], 'valid'), ('regression #3', [[0, 0], [10, 10], [10, 0], [0, 10], [0, 0]], 'self_intersection'), ('regression #4', [[0, 0], [10, 0], [10, 10], [10, 5], [0, 5], [0, 0]], 'spike'), ('regression #5', [[5, 0], [10, 0], [10, 10], [0, 10], [0, 0], [5, 0], [0, 0]], 'not_closed'), ('regression #12', [[0, 5], [0, 0], [10, 0], [10, 10], [0, 10], [0, 12], [0, 5]], 'spike'), ('regression #23', [[10, 0], [7, 0], [7, 5], [0, 5], [0, 0], [5, 0], [10, 0]], 'spike')], [('regression #3', [[0, 0], [10, 10], [10, 0], [0, 10], [0, 0]], 'self_intersection'), ('regression #4', [[0, 0], [10, 0], [10, 10], [10, 5], [0, 5], [0, 0]], 'spike'), ('regression #5', [[5, 0], [10, 0], [10, 10], [0, 10], [0, 0], [5, 0], [0, 0]], 'not_closed'), ('boundary #6', [[0, 0], [10, 0], [10, 10], [0, 0]], 'valid'), ('boundary #7', [[0, 0], [10, 0], [10, 10]], 'too_few_points'), ('boundary #8', [[0, 0], [10, 0], [10, 10], [0, 10], [0, 1]], 'not_closed'), ('boundary #9', [[0, 0], [10, 0], [10, 0], [10, 10], [0, 0]], 'repeated_point'), ('regression #23', [[10, 0], [7, 0], [7, 5], [0, 5], [0, 0], [5, 0], [10, 0]], 'spike')], [('boundary #6', [[0, 0], [10, 0], [10, 10], [0, 0]], 'valid'), ('boundary #7', [[0, 0], [10, 0], [10, 10]], 'too_few_points'), ('boundary #8', [[0, 0], [10, 0], [10, 10], [0, 10], [0, 1]], 'not_closed'), ('boundary #9', [[0, 0], [10, 0], [10, 0], [10, 10], [0, 0]], 'repeated_point'), ('regression #10', [[0, 0], [10, 0], [10, 10], [0, 10], [0, 0], [0, 0]], 'repeated_point'), ('regression #11', [[0, 0], [10, 0], [10, 10], [0, 10], [0, 5], [0, 12], [0, 0]], 'spike'), ('regression #12', [[0, 5], [0, 0], [10, 0], [10, 10], [0, 10], [0, 12], [0, 5]], 'spike'), ('regression #23', [[10, 0], [7, 0], [7, 5], [0, 5], [0, 0], [5, 0], [10, 0]], 'spike')], [('boundary #9', [[0, 0], [10, 0], [10, 0], [10, 10], [0, 0]], 'repeated_point'), ('regression #10', [[0, 0], [10, 0], [10, 10], [0, 10], [0, 0], [0, 0]], 'repeated_point'), ('regression #11', [[0, 0], [10, 0], [10, 10], [0, 10], [0, 5], [0, 12], [0, 0]], 'spike'), ('regression #12', [[0, 5], [0, 0], [10, 0], [10, 10], [0, 10], [0, 12], [0, 5]], 'spike'), ('regression #13', [[0, 0], [4, 0], [4, 4], [8, 4], [8, 8], [4, 8], [4, 4], [0, 4], [0, 0]], 'self_intersection'), ('regression #14', [[0, 0], [10, 0], [10, 10], [5, 0], [0, 10], [0, 0]], 'self_intersection'), ('regression #15', [[0, 0], [10, 0], [10, 5], [2, 5], [6, 5], [6, 8], [0, 8], [0, 0]], 'spike'), ('regression #23', [[10, 0], [7, 0], [7, 5], [0, 5], [0, 0], [5, 0], [10, 0]], 'spike')], [('regression #12', [[0, 5], [0, 0], [10, 0], [10, 10], [0, 10], [0, 12], [0, 5]], 'spike'), ('regression #13', [[0, 0], [4, 0], [4, 4], [8, 4], [8, 8], [4, 8], [4, 4], [0, 4], [0, 0]], 'self_intersection'), ('regression #14', [[0, 0], [10, 0], [10, 10], [5, 0], [0, 10], [0, 0]], 'self_intersection'), ('regression #15', [[0, 0], [10, 0], [10, 5], [2, 5], [6, 5], [6, 8], [0, 8], [0, 0]], 'spike'), ('control #16', [[0, 0], [6, 0], [6, 6], [3, 3], [0, 6], [0, 0]], 'valid'), ('regression #17', [[0, 0], [10, 0], [10, 10], [0, 10], [4, 10], [0, 0]], 'spike'), ('control #18', [[1, 1], [9, 2], [8, 9], [2, 7], [1, 1]], 'valid'), ('regression #23', [[10, 0], [7, 0], [7, 5], [0, 5], [0, 0], [5, 0], [10, 0]], 'spike')]]
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)

prompt:
Spikes located at the ring start vertex are reported as self-intersections.

Input: one ring as a list of integer [x, y]. Report the first failing check in this order: fewer than 4 positions "too_few_points"; first != last "not_closed"; two cyclically consecutive equal vertices "repeated_point"; a vertex where the boundary reverses direction along a line (collinear with a negative dot product of the incoming and outgoing edge, checked cyclically) "spike"; any two non-adjacent edges sharing a point (crossing, touching or collinear overlap) "self_intersection"; otherwise "valid".

split: open-access


broken_source:
"""Failure Map reference implementation. Python standard library only."""
import json
import math
N = 1
observations = []
def solve(x):
    ring = x
    if len(ring) < 4:
        return 'too_few_points'
    if ring[0] != ring[-1]:
        return 'not_closed'
    pts = ring[:-1]
    n = len(pts)
    for i in range(n):
        if pts[i] == pts[(i + 1) % n]:
            return 'repeated_point'
    for i in range(n):
        a, b, c = pts[i - 1], pts[i], pts[(i + 1) % n]
        cross = (b[0] - a[0]) * (c[1] - b[1]) - (b[1] - a[1]) * (c[0] - b[0])
        dot = (b[0] - a[0]) * (c[0] - b[0]) + (b[1] - a[1]) * (c[1] - b[1])
        if cross == 0:
            return 'spike'
    def orient(p, q, r):
        v = (q[0] - p[0]) * (r[1] - p[1]) - (q[1] - p[1]) * (r[0] - p[0])
        return (v > 0) - (v < 0)
    def within(p, q, r):
        return min(p[0], r[0]) <= q[0] <= max(p[0], r[0]) and min(p[1], r[1]) <= q[1] <= max(p[1], r[1])
    def hit(p1, p2, p3, p4):
        o1, o2, o3, o4 = orient(p1, p2, p3), orient(p1, p2, p4), orient(p3, p4, p1), orient(p3, p4, p2)
        if o1 * o2 < 0 and o3 * o4 < 0:
            return True
        return (o1 == 0 and within(p1, p3, p2)) or (o2 == 0 and within(p1, p4, p2)) or (o3 == 0 and within(p3, p1, p4)) or (o4 == 0 and within(p3, p2, p4))
    for i in range(n):
        for j in range(i + 1, n):
            if j == i + 1 or (i == 0 and j == n - 1):
                continue
            if hit(pts[i], pts[(i + 1) % n], pts[j], pts[(j + 1) % n]):
                return 'self_intersection'
    return 'valid'
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('control #0', [[0, 0], [10, 0], [10, 10], [0, 10], [0, 0]], 'valid'), ('control #1', [[0, 0], [10, 0], [5, 8], [0, 0]], 'valid'), ('control #2', [[0, 0], [5, 0], [10, 0], [10, 10], [0, 10], [0, 0]], 'valid'), ('regression #3', [[0, 0], [10, 10], [10, 0], [0, 10], [0, 0]], 'self_intersection'), ('regression #4', [[0, 0], [10, 0], [10, 10], [10, 5], [0, 5], [0, 0]], 'spike'), ('regression #5', [[5, 0], [10, 0], [10, 10], [0, 10], [0, 0], [5, 0], [0, 0]], 'not_closed'), ('boundary #6', [[0, 0], [10, 0], [10, 10], [0, 0]], 'valid'), ('boundary #7', [[0, 0], [10, 0], [10, 10]], 'too_few_points')], [('control #2', [[0, 0], [5, 0], [10, 0], [10, 10], [0, 10], [0, 0]], 'valid'), ('regression #4', [[0, 0], [10, 0], [10, 10], [10, 5], [0, 5], [0, 0]], 'spike'), ('regression #5', [[5, 0], [10, 0], [10, 10], [0, 10], [0, 0], [5, 0], [0, 0]], 'not_closed'), ('boundary #6', [[0, 0], [10, 0], [10, 10], [0, 0]], 'valid'), ('boundary #7', [[0, 0], [10, 0], [10, 10]], 'too_few_points'), ('boundary #8', [[0, 0], [10, 0], [10, 10], [0, 10], [0, 1]], 'not_closed'), ('boundary #9', [[0, 0], [10, 0], [10, 0], [10, 10], [0, 0]], 'repeated_point'), ('regression #11', [[0, 0], [10, 0], [10, 10], [0, 10], [0, 5], [0, 12], [0, 0]], 'spike')], [('control #2', [[0, 0], [5, 0], [10, 0], [10, 10], [0, 10], [0, 0]], 'valid'), ('boundary #7', [[0, 0], [10, 0], [10, 10]], 'too_few_points'), ('boundary #8', [[0, 0], [10, 0], [10, 10], [0, 10], [0, 1]], 'not_closed'), ('boundary #9', [[0, 0], [10, 0], [10, 0], [10, 10], [0, 0]], 'repeated_point'), ('regression #10', [[0, 0], [10, 0], [10, 10], [0, 10], [0, 0], [0, 0]], 'repeated_point'), ('regression #11', [[0, 0], [10, 0], [10, 10], [0, 10], [0, 5], [0, 12], [0, 0]], 'spike'), ('regression #12', [[0, 5], [0, 0], [10, 0], [10, 10], [0, 10], [0, 12], [0, 5]], 'spike'), ('regression #15', [[0, 0], [10, 0], [10, 5], [2, 5], [6, 5], [6, 8], [0, 8], [0, 0]], 'spike')], [('control #2', [[0, 0], [5, 0], [10, 0], [10, 10], [0, 10], [0, 0]], 'valid'), ('regression #10', [[0, 0], [10, 0], [10, 10], [0, 10], [0, 0], [0, 0]], 'repeated_point'), ('regression #11', [[0, 0], [10, 0], [10, 10], [0, 10], [0, 5], [0, 12], [0, 0]], 'spike'), ('regression #12', [[0, 5], [0, 0], [10, 0], [10, 10], [0, 10], [0, 12], [0, 5]], 'spike'), ('regression #13', [[0, 0], [4, 0], [4, 4], [8, 4], [8, 8], [4, 8], [4, 4], [0, 4], [0, 0]], 'self_intersection'), ('regression #14', [[0, 0], [10, 0], [10, 10], [5, 0], [0, 10], [0, 0]], 'self_intersection'), ('regression #15', [[0, 0], [10, 0], [10, 5], [2, 5], [6, 5], [6, 8], [0, 8], [0, 0]], 'spike'), ('regression #17', [[0, 0], [10, 0], [10, 10], [0, 10], [4, 10], [0, 0]], 'spike')], [('control #2', [[0, 0], [5, 0], [10, 0], [10, 10], [0, 10], [0, 0]], 'valid'), ('regression #13', [[0, 0], [4, 0], [4, 4], [8, 4], [8, 8], [4, 8], [4, 4], [0, 4], [0, 0]], 'self_intersection'), ('regression #14', [[0, 0], [10, 0], [10, 10], [5, 0], [0, 10], [0, 0]], 'self_intersection'), ('regression #15', [[0, 0], [10, 0], [10, 5], [2, 5], [6, 5], [6, 8], [0, 8], [0, 0]], 'spike'), ('control #16', [[0, 0], [6, 0], [6, 6], [3, 3], [0, 6], [0, 0]], 'valid'), ('regression #17', [[0, 0], [10, 0], [10, 10], [0, 10], [4, 10], [0, 0]], 'spike'), ('control #18', [[1, 1], [9, 2], [8, 9], [2, 7], [1, 1]], 'valid'), ('regression #26', [[0, 0], [6, 0], [6, 6], [0, 6], [3, 6], [3, 9], [0, 9], [0, 0]], 'spike')]]
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)

meaning: Fixture-count band, not measured model difficulty

deps: stdlib

source:
"""Failure Map reference implementation. Python standard library only."""
import json
import math
N = 1
observations = []
def solve(x):
    ring = x
    if len(ring) < 4:
        return 'too_few_points'
    if ring[0] != ring[-1]:
        return 'not_closed'
    pts = ring[:-1]
    n = len(pts)
    for i in range(n):
        if pts[i] == pts[(i + 1) % n]:
            return 'repeated_point'
    for i in range(n):
        a, b, c = pts[i - 1], pts[i], pts[(i + 1) % n]
        cross = (b[0] - a[0]) * (c[1] - b[1]) - (b[1] - a[1]) * (c[0] - b[0])
        dot = (b[0] - a[0]) * (c[0] - b[0]) + (b[1] - a[1]) * (c[1] - b[1])
        if cross == 0 and dot > 0:
            return 'spike'
    def orient(p, q, r):
        v = (q[0] - p[0]) * (r[1] - p[1]) - (q[1] - p[1]) * (r[0] - p[0])
        return (v > 0) - (v < 0)
    def within(p, q, r):
        return min(p[0], r[0]) <= q[0] <= max(p[0], r[0]) and min(p[1], r[1]) <= q[1] <= max(p[1], r[1])
    def hit(p1, p2, p3, p4):
        o1, o2, o3, o4 = orient(p1, p2, p3), orient(p1, p2, p4), orient(p3, p4, p1), orient(p3, p4, p2)
        if o1 * o2 < 0 and o3 * o4 < 0:
            return True
        return (o1 == 0 and within(p1, p3, p2)) or (o2 == 0 and within(p1, p4, p2)) or (o3 == 0 and within(p3, p1, p4)) or (o4 == 0 and within(p3, p2, p4))
    for i in range(n):
        for j in range(i + 1, n):
            if j == i + 1 or (i == 0 and j == n - 1):
                continue
            if hit(pts[i], pts[(i + 1) % n], pts[j], pts[(j + 1) % n]):
                return 'self_intersection'
    return 'valid'
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('control #0', [[0, 0], [10, 0], [10, 10], [0, 10], [0, 0]], 'valid'), ('control #1', [[0, 0], [10, 0], [5, 8], [0, 0]], 'valid'), ('control #2', [[0, 0], [5, 0], [10, 0], [10, 10], [0, 10], [0, 0]], 'valid'), ('regression #3', [[0, 0], [10, 10], [10, 0], [0, 10], [0, 0]], 'self_intersection'), ('regression #4', [[0, 0], [10, 0], [10, 10], [10, 5], [0, 5], [0, 0]], 'spike'), ('regression #5', [[5, 0], [10, 0], [10, 10], [0, 10], [0, 0], [5, 0], [0, 0]], 'not_closed'), ('boundary #6', [[0, 0], [10, 0], [10, 10], [0, 0]], 'valid'), ('boundary #7', [[0, 0], [10, 0], [10, 10]], 'too_few_points')], [('control #2', [[0, 0], [5, 0], [10, 0], [10, 10], [0, 10], [0, 0]], 'valid'), ('regression #4', [[0, 0], [10, 0], [10, 10], [10, 5], [0, 5], [0, 0]], 'spike'), ('regression #5', [[5, 0], [10, 0], [10, 10], [0, 10], [0, 0], [5, 0], [0, 0]], 'not_closed'), ('boundary #6', [[0, 0], [10, 0], [10, 10], [0, 0]], 'valid'), ('boundary #7', [[0, 0], [10, 0], [10, 10]], 'too_few_points'), ('boundary #8', [[0, 0], [10, 0], [10, 10], [0, 10], [0, 1]], 'not_closed'), ('boundary #9', [[0, 0], [10, 0], [10, 0], [10, 10], [0, 0]], 'repeated_point'), ('regression #11', [[0, 0], [10, 0], [10, 10], [0, 10], [0, 5], [0, 12], [0, 0]], 'spike')], [('control #2', [[0, 0], [5, 0], [10, 0], [10, 10], [0, 10], [0, 0]], 'valid'), ('boundary #7', [[0, 0], [10, 0], [10, 10]], 'too_few_points'), ('boundary #8', [[0, 0], [10, 0], [10, 10], [0, 10], [0, 1]], 'not_closed'), ('boundary #9', [[0, 0], [10, 0], [10, 0], [10, 10], [0, 0]], 'repeated_point'), ('regression #10', [[0, 0], [10, 0], [10, 10], [0, 10], [0, 0], [0, 0]], 'repeated_point'), ('regression #11', [[0, 0], [10, 0], [10, 10], [0, 10], [0, 5], [0, 12], [0, 0]], 'spike'), ('regression #12', [[0, 5], [0, 0], [10, 0], [10, 10], [0, 10], [0, 12], [0, 5]], 'spike'), ('regression #15', [[0, 0], [10, 0], [10, 5], [2, 5], [6, 5], [6, 8], [0, 8], [0, 0]], 'spike')], [('control #2', [[0, 0], [5, 0], [10, 0], [10, 10], [0, 10], [0, 0]], 'valid'), ('regression #10', [[0, 0], [10, 0], [10, 10], [0, 10], [0, 0], [0, 0]], 'repeated_point'), ('regression #11', [[0, 0], [10, 0], [10, 10], [0, 10], [0, 5], [0, 12], [0, 0]], 'spike'), ('regression #12', [[0, 5], [0, 0], [10, 0], [10, 10], [0, 10], [0, 12], [0, 5]], 'spike'), ('regression #13', [[0, 0], [4, 0], [4, 4], [8, 4], [8, 8], [4, 8], [4, 4], [0, 4], [0, 0]], 'self_intersection'), ('regression #14', [[0, 0], [10, 0], [10, 10], [5, 0], [0, 10], [0, 0]], 'self_intersection'), ('regression #15', [[0, 0], [10, 0], [10, 5], [2, 5], [6, 5], [6, 8], [0, 8], [0, 0]], 'spike'), ('regression #17', [[0, 0], [10, 0], [10, 10], [0, 10], [4, 10], [0, 0]], 'spike')], [('control #2', [[0, 0], [5, 0], [10, 0], [10, 10], [0, 10], [0, 0]], 'valid'), ('regression #13', [[0, 0], [4, 0], [4, 4], [8, 4], [8, 8], [4, 8], [4, 4], [0, 4], [0, 0]], 'self_intersection'), ('regression #14', [[0, 0], [10, 0], [10, 10], [5, 0], [0, 10], [0, 0]], 'self_intersection'), ('regression #15', [[0, 0], [10, 0], [10, 5], [2, 5], [6, 5], [6, 8], [0, 8], [0, 0]], 'spike'), ('control #16', [[0, 0], [6, 0], [6, 6], [3, 3], [0, 6], [0, 0]], 'valid'), ('regression #17', [[0, 0], [10, 0], [10, 10], [0, 10], [4, 10], [0, 0]], 'spike'), ('control #18', [[1, 1], [9, 2], [8, 9], [2, 7], [1, 1]], 'valid'), ('regression #26', [[0, 0], [6, 0], [6, 6], [0, 6], [3, 6], [3, 9], [0, 9], [0, 0]], 'spike')]]
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)

prompt:
Rings with a redundant collinear vertex are rejected as spiky.

Input: one ring as a list of integer [x, y]. Report the first failing check in this order: fewer than 4 positions "too_few_points"; first != last "not_closed"; two cyclically consecutive equal vertices "repeated_point"; a vertex where the boundary reverses direction along a line (collinear with a negative dot product of the incoming and outgoing edge, checked cyclically) "spike"; any two non-adjacent edges sharing a point (crossing, touching or collinear overlap) "self_intersection"; otherwise "valid".

split: open-access


broken_source:
"""Failure Map reference implementation. Python standard library only."""
import json
import math
N = 1
observations = []
def solve(x):
    ring = x
    if len(ring) < 4:
        return 'too_few_points'
    if ring[0] != ring[-1]:
        return 'not_closed'
    pts = ring[:-1]
    n = len(pts)
    for i in range(n - 1):
        if pts[i] == pts[i + 1]:
            return 'repeated_point'
    for i in range(n):
        a, b, c = pts[i - 1], pts[i], pts[(i + 1) % n]
        cross = (b[0] - a[0]) * (c[1] - b[1]) - (b[1] - a[1]) * (c[0] - b[0])
        dot = (b[0] - a[0]) * (c[0] - b[0]) + (b[1] - a[1]) * (c[1] - b[1])
        if cross == 0 and dot < 0:
            return 'spike'
    def orient(p, q, r):
        v = (q[0] - p[0]) * (r[1] - p[1]) - (q[1] - p[1]) * (r[0] - p[0])
        return (v > 0) - (v < 0)
    def within(p, q, r):
        return min(p[0], r[0]) <= q[0] <= max(p[0], r[0]) and min(p[1], r[1]) <= q[1] <= max(p[1], r[1])
    def hit(p1, p2, p3, p4):
        o1, o2, o3, o4 = orient(p1, p2, p3), orient(p1, p2, p4), orient(p3, p4, p1), orient(p3, p4, p2)
        if o1 * o2 < 0 and o3 * o4 < 0:
            return True
        return (o1 == 0 and within(p1, p3, p2)) or (o2 == 0 and within(p1, p4, p2)) or (o3 == 0 and within(p3, p1, p4)) or (o4 == 0 and within(p3, p2, p4))
    for i in range(n):
        for j in range(i + 1, n):
            if j == i + 1 or (i == 0 and j == n - 1):
                continue
            if hit(pts[i], pts[(i + 1) % n], pts[j], pts[(j + 1) % n]):
                return 'self_intersection'
    return 'valid'
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('control #0', [[0, 0], [10, 0], [10, 10], [0, 10], [0, 0]], 'valid'), ('control #1', [[0, 0], [10, 0], [5, 8], [0, 0]], 'valid'), ('control #2', [[0, 0], [5, 0], [10, 0], [10, 10], [0, 10], [0, 0]], 'valid'), ('regression #3', [[0, 0], [10, 10], [10, 0], [0, 10], [0, 0]], 'self_intersection'), ('regression #4', [[0, 0], [10, 0], [10, 10], [10, 5], [0, 5], [0, 0]], 'spike'), ('regression #5', [[5, 0], [10, 0], [10, 10], [0, 10], [0, 0], [5, 0], [0, 0]], 'not_closed'), ('regression #10', [[0, 0], [10, 0], [10, 10], [0, 10], [0, 0], [0, 0]], 'repeated_point'), ('regression #13', [[0, 0], [4, 0], [4, 4], [8, 4], [8, 8], [4, 8], [4, 4], [0, 4], [0, 0]], 'self_intersection')], [('regression #3', [[0, 0], [10, 10], [10, 0], [0, 10], [0, 0]], 'self_intersection'), ('regression #4', [[0, 0], [10, 0], [10, 10], [10, 5], [0, 5], [0, 0]], 'spike'), ('regression #5', [[5, 0], [10, 0], [10, 10], [0, 10], [0, 0], [5, 0], [0, 0]], 'not_closed'), ('boundary #6', [[0, 0], [10, 0], [10, 10], [0, 0]], 'valid'), ('boundary #7', [[0, 0], [10, 0], [10, 10]], 'too_few_points'), ('boundary #8', [[0, 0], [10, 0], [10, 10], [0, 10], [0, 1]], 'not_closed'), ('regression #10', [[0, 0], [10, 0], [10, 10], [0, 10], [0, 0], [0, 0]], 'repeated_point'), ('regression #13', [[0, 0], [4, 0], [4, 4], [8, 4], [8, 8], [4, 8], [4, 4], [0, 4], [0, 0]], 'self_intersection')], [('boundary #6', [[0, 0], [10, 0], [10, 10], [0, 0]], 'valid'), ('boundary #7', [[0, 0], [10, 0], [10, 10]], 'too_few_points'), ('boundary #8', [[0, 0], [10, 0], [10, 10], [0, 10], [0, 1]], 'not_closed'), ('boundary #9', [[0, 0], [10, 0], [10, 0], [10, 10], [0, 0]], 'repeated_point'), ('regression #10', [[0, 0], [10, 0], [10, 10], [0, 10], [0, 0], [0, 0]], 'repeated_point'), ('regression #11', [[0, 0], [10, 0], [10, 10], [0, 10], [0, 5], [0, 12], [0, 0]], 'spike'), ('regression #12', [[0, 5], [0, 0], [10, 0], [10, 10], [0, 10], [0, 12], [0, 5]], 'spike'), ('regression #13', [[0, 0], [4, 0], [4, 4], [8, 4], [8, 8], [4, 8], [4, 4], [0, 4], [0, 0]], 'self_intersection')], [('boundary #9', [[0, 0], [10, 0], [10, 0], [10, 10], [0, 0]], 'repeated_point'), ('regression #10', [[0, 0], [10, 0], [10, 10], [0, 10], [0, 0], [0, 0]], 'repeated_point'), ('regression #11', [[0, 0], [10, 0], [10, 10], [0, 10], [0, 5], [0, 12], [0, 0]], 'spike'), ('regression #12', [[0, 5], [0, 0], [10, 0], [10, 10], [0, 10], [0, 12], [0, 5]], 'spike'), ('regression #13', [[0, 0], [4, 0], [4, 4], [8, 4], [8, 8], [4, 8], [4, 4], [0, 4], [0, 0]], 'self_intersection'), ('regression #14', [[0, 0], [10, 0], [10, 10], [5, 0], [0, 10], [0, 0]], 'self_intersection'), ('regression #15', [[0, 0], [10, 0], [10, 5], [2, 5], [6, 5], [6, 8], [0, 8], [0, 0]], 'spike'), ('control #16', [[0, 0], [6, 0], [6, 6], [3, 3], [0, 6], [0, 0]], 'valid')], [('regression #10', [[0, 0], [10, 0], [10, 10], [0, 10], [0, 0], [0, 0]], 'repeated_point'), ('regression #13', [[0, 0], [4, 0], [4, 4], [8, 4], [8, 8], [4, 8], [4, 4], [0, 4], [0, 0]], 'self_intersection'), ('regression #14', [[0, 0], [10, 0], [10, 10], [5, 0], [0, 10], [0, 0]], 'self_intersection'), ('regression #15', [[0, 0], [10, 0], [10, 5], [2, 5], [6, 5], [6, 8], [0, 8], [0, 0]], 'spike'), ('control #16', [[0, 0], [6, 0], [6, 6], [3, 3], [0, 6], [0, 0]], 'valid'), ('regression #17', [[0, 0], [10, 0], [10, 10], [0, 10], [4, 10], [0, 0]], 'spike'), ('control #18', [[1, 1], [9, 2], [8, 9], [2, 7], [1, 1]], 'valid'), ('regression #19', [[0, 0], [8, 0], [8, 8], [0, 8], [0, 4], [8, 4], [0, 0]], 'self_intersection')]]
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)

source:
"""Failure Map reference implementation. Python standard library only."""
import json
import math
N = 1
observations = []
def solve(x):
    ring = x
    if len(ring) < 4:
        return 'too_few_points'
    if ring[0] != ring[-1]:
        return 'not_closed'
    pts = ring[:-1]
    n = len(pts)
    for i in range(n):
        if pts[i] in pts[i + 1:]:
            return 'repeated_point'
    for i in range(n):
        a, b, c = pts[i - 1], pts[i], pts[(i + 1) % n]
        cross = (b[0] - a[0]) * (c[1] - b[1]) - (b[1] - a[1]) * (c[0] - b[0])
        dot = (b[0] - a[0]) * (c[0] - b[0]) + (b[1] - a[1]) * (c[1] - b[1])
        if cross == 0 and dot < 0:
            return 'spike'
    def orient(p, q, r):
        v = (q[0] - p[0]) * (r[1] - p[1]) - (q[1] - p[1]) * (r[0] - p[0])
        return (v > 0) - (v < 0)
    def within(p, q, r):
        return min(p[0], r[0]) <= q[0] <= max(p[0], r[0]) and min(p[1], r[1]) <= q[1] <= max(p[1], r[1])
    def hit(p1, p2, p3, p4):
        o1, o2, o3, o4 = orient(p1, p2, p3), orient(p1, p2, p4), orient(p3, p4, p1), orient(p3, p4, p2)
        if o1 * o2 < 0 and o3 * o4 < 0:
            return True
        return (o1 == 0 and within(p1, p3, p2)) or (o2 == 0 and within(p1, p4, p2)) or (o3 == 0 and within(p3, p1, p4)) or (o4 == 0 and within(p3, p2, p4))
    for i in range(n):
        for j in range(i + 1, n):
            if j == i + 1 or (i == 0 and j == n - 1):
                continue
            if hit(pts[i], pts[(i + 1) % n], pts[j], pts[(j + 1) % n]):
                return 'self_intersection'
    return 'valid'
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('control #0', [[0, 0], [10, 0], [10, 10], [0, 10], [0, 0]], 'valid'), ('control #1', [[0, 0], [10, 0], [5, 8], [0, 0]], 'valid'), ('control #2', [[0, 0], [5, 0], [10, 0], [10, 10], [0, 10], [0, 0]], 'valid'), ('regression #3', [[0, 0], [10, 10], [10, 0], [0, 10], [0, 0]], 'self_intersection'), ('regression #4', [[0, 0], [10, 0], [10, 10], [10, 5], [0, 5], [0, 0]], 'spike'), ('regression #5', [[5, 0], [10, 0], [10, 10], [0, 10], [0, 0], [5, 0], [0, 0]], 'not_closed'), ('regression #10', [[0, 0], [10, 0], [10, 10], [0, 10], [0, 0], [0, 0]], 'repeated_point'), ('regression #13', [[0, 0], [4, 0], [4, 4], [8, 4], [8, 8], [4, 8], [4, 4], [0, 4], [0, 0]], 'self_intersection')], [('regression #3', [[0, 0], [10, 10], [10, 0], [0, 10], [0, 0]], 'self_intersection'), ('regression #4', [[0, 0], [10, 0], [10, 10], [10, 5], [0, 5], [0, 0]], 'spike'), ('regression #5', [[5, 0], [10, 0], [10, 10], [0, 10], [0, 0], [5, 0], [0, 0]], 'not_closed'), ('boundary #6', [[0, 0], [10, 0], [10, 10], [0, 0]], 'valid'), ('boundary #7', [[0, 0], [10, 0], [10, 10]], 'too_few_points'), ('boundary #8', [[0, 0], [10, 0], [10, 10], [0, 10], [0, 1]], 'not_closed'), ('regression #10', [[0, 0], [10, 0], [10, 10], [0, 10], [0, 0], [0, 0]], 'repeated_point'), ('regression #13', [[0, 0], [4, 0], [4, 4], [8, 4], [8, 8], [4, 8], [4, 4], [0, 4], [0, 0]], 'self_intersection')], [('boundary #6', [[0, 0], [10, 0], [10, 10], [0, 0]], 'valid'), ('boundary #7', [[0, 0], [10, 0], [10, 10]], 'too_few_points'), ('boundary #8', [[0, 0], [10, 0], [10, 10], [0, 10], [0, 1]], 'not_closed'), ('boundary #9', [[0, 0], [10, 0], [10, 0], [10, 10], [0, 0]], 'repeated_point'), ('regression #10', [[0, 0], [10, 0], [10, 10], [0, 10], [0, 0], [0, 0]], 'repeated_point'), ('regression #11', [[0, 0], [10, 0], [10, 10], [0, 10], [0, 5], [0, 12], [0, 0]], 'spike'), ('regression #12', [[0, 5], [0, 0], [10, 0], [10, 10], [0, 10], [0, 12], [0, 5]], 'spike'), ('regression #13', [[0, 0], [4, 0], [4, 4], [8, 4], [8, 8], [4, 8], [4, 4], [0, 4], [0, 0]], 'self_intersection')], [('boundary #9', [[0, 0], [10, 0], [10, 0], [10, 10], [0, 0]], 'repeated_point'), ('regression #10', [[0, 0], [10, 0], [10, 10], [0, 10], [0, 0], [0, 0]], 'repeated_point'), ('regression #11', [[0, 0], [10, 0], [10, 10], [0, 10], [0, 5], [0, 12], [0, 0]], 'spike'), ('regression #12', [[0, 5], [0, 0], [10, 0], [10, 10], [0, 10], [0, 12], [0, 5]], 'spike'), ('regression #13', [[0, 0], [4, 0], [4, 4], [8, 4], [8, 8], [4, 8], [4, 4], [0, 4], [0, 0]], 'self_intersection'), ('regression #14', [[0, 0], [10, 0], [10, 10], [5, 0], [0, 10], [0, 0]], 'self_intersection'), ('regression #15', [[0, 0], [10, 0], [10, 5], [2, 5], [6, 5], [6, 8], [0, 8], [0, 0]], 'spike'), ('control #16', [[0, 0], [6, 0], [6, 6], [3, 3], [0, 6], [0, 0]], 'valid')], [('regression #10', [[0, 0], [10, 0], [10, 10], [0, 10], [0, 0], [0, 0]], 'repeated_point'), ('regression #13', [[0, 0], [4, 0], [4, 4], [8, 4], [8, 8], [4, 8], [4, 4], [0, 4], [0, 0]], 'self_intersection'), ('regression #14', [[0, 0], [10, 0], [10, 10], [5, 0], [0, 10], [0, 0]], 'self_intersection'), ('regression #15', [[0, 0], [10, 0], [10, 5], [2, 5], [6, 5], [6, 8], [0, 8], [0, 0]], 'spike'), ('control #16', [[0, 0], [6, 0], [6, 6], [3, 3], [0, 6], [0, 0]], 'valid'), ('regression #17', [[0, 0], [10, 0], [10, 10], [0, 10], [4, 10], [0, 0]], 'spike'), ('control #18', [[1, 1], [9, 2], [8, 9], [2, 7], [1, 1]], 'valid'), ('regression #19', [[0, 0], [8, 0], [8, 8], [0, 8], [0, 4], [8, 4], [0, 0]], 'self_intersection')]]
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)

prompt:
A ring whose closing position is doubled is diagnosed as a spike instead of a repeated point.

Input: one ring as a list of integer [x, y]. Report the first failing check in this order: fewer than 4 positions "too_few_points"; first != last "not_closed"; two cyclically consecutive equal vertices "repeated_point"; a vertex where the boundary reverses direction along a line (collinear with a negative dot product of the incoming and outgoing edge, checked cyclically) "spike"; any two non-adjacent edges sharing a point (crossing, touching or collinear overlap) "self_intersection"; otherwise "valid".

split: open-access


broken_source:
"""Failure Map reference implementation. Python standard library only."""
import json
import math
N = 1
observations = []
def solve(x):
    ring = x
    if len(ring) < 4:
        return 'too_few_points'
    if ring[0] != ring[-1]:
        return 'not_closed'
    pts = ring[:-1]
    n = len(pts)
    for i in range(n):
        if pts[i] == pts[(i + 1) % n]:
            return 'repeated_point'
    for i in range(n):
        a, b, c = pts[i - 1], pts[i], pts[(i + 1) % n]
        cross = (b[0] - a[0]) * (c[1] - b[1]) - (b[1] - a[1]) * (c[0] - b[0])
        dot = (b[0] - a[0]) * (c[0] - b[0]) + (b[1] - a[1]) * (c[1] - b[1])
        if cross == 0 and dot < 0:
            return 'spike'
    def orient(p, q, r):
        v = (q[0] - p[0]) * (r[1] - p[1]) - (q[1] - p[1]) * (r[0] - p[0])
        return (v > 0) - (v < 0)
    def within(p, q, r):
        return min(p[0], r[0]) <= q[0] <= max(p[0], r[0]) and min(p[1], r[1]) <= q[1] <= max(p[1], r[1])
    def hit(p1, p2, p3, p4):
        o1, o2, o3, o4 = orient(p1, p2, p3), orient(p1, p2, p4), orient(p3, p4, p1), orient(p3, p4, p2)
        if o1 * o2 < 0 and o3 * o4 < 0:
            return True
        return False
    for i in range(n):
        for j in range(i + 1, n):
            if j == i + 1 or (i == 0 and j == n - 1):
                continue
            if hit(pts[i], pts[(i + 1) % n], pts[j], pts[(j + 1) % n]):
                return 'self_intersection'
    return 'valid'
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('control #0', [[0, 0], [10, 0], [10, 10], [0, 10], [0, 0]], 'valid'), ('control #1', [[0, 0], [10, 0], [5, 8], [0, 0]], 'valid'), ('control #2', [[0, 0], [5, 0], [10, 0], [10, 10], [0, 10], [0, 0]], 'valid'), ('regression #3', [[0, 0], [10, 10], [10, 0], [0, 10], [0, 0]], 'self_intersection'), ('regression #4', [[0, 0], [10, 0], [10, 10], [10, 5], [0, 5], [0, 0]], 'spike'), ('regression #5', [[5, 0], [10, 0], [10, 10], [0, 10], [0, 0], [5, 0], [0, 0]], 'not_closed'), ('regression #13', [[0, 0], [4, 0], [4, 4], [8, 4], [8, 8], [4, 8], [4, 4], [0, 4], [0, 0]], 'self_intersection'), ('regression #27', [[4, 4], [2, 1], [2, 2], [1, 0], [4, 3], [4, 4]], 'self_intersection')], [('regression #3', [[0, 0], [10, 10], [10, 0], [0, 10], [0, 0]], 'self_intersection'), ('regression #4', [[0, 0], [10, 0], [10, 10], [10, 5], [0, 5], [0, 0]], 'spike'), ('regression #5', [[5, 0], [10, 0], [10, 10], [0, 10], [0, 0], [5, 0], [0, 0]], 'not_closed'), ('boundary #6', [[0, 0], [10, 0], [10, 10], [0, 0]], 'valid'), ('boundary #7', [[0, 0], [10, 0], [10, 10]], 'too_few_points'), ('boundary #8', [[0, 0], [10, 0], [10, 10], [0, 10], [0, 1]], 'not_closed'), ('regression #14', [[0, 0], [10, 0], [10, 10], [5, 0], [0, 10], [0, 0]], 'self_intersection'), ('regression #28', [[2, 0], [1, 0], [0, 3], [2, 1], [4, 1], [2, 2], [2, 0]], 'self_intersection')], [('boundary #6', [[0, 0], [10, 0], [10, 10], [0, 0]], 'valid'), ('boundary #7', [[0, 0], [10, 0], [10, 10]], 'too_few_points'), ('boundary #8', [[0, 0], [10, 0], [10, 10], [0, 10], [0, 1]], 'not_closed'), ('boundary #9', [[0, 0], [10, 0], [10, 0], [10, 10], [0, 0]], 'repeated_point'), ('regression #10', [[0, 0], [10, 0], [10, 10], [0, 10], [0, 0], [0, 0]], 'repeated_point'), ('regression #11', [[0, 0], [10, 0], [10, 10], [0, 10], [0, 5], [0, 12], [0, 0]], 'spike'), ('regression #19', [[0, 0], [8, 0], [8, 8], [0, 8], [0, 4], [8, 4], [0, 0]], 'self_intersection'), ('regression #29', [[0, 2], [2, 2], [4, 3], [4, 0], [0, 4], [0, 2]], 'self_intersection')], [('boundary #9', [[0, 0], [10, 0], [10, 0], [10, 10], [0, 0]], 'repeated_point'), ('regression #10', [[0, 0], [10, 0], [10, 10], [0, 10], [0, 0], [0, 0]], 'repeated_point'), ('regression #11', [[0, 0], [10, 0], [10, 10], [0, 10], [0, 5], [0, 12], [0, 0]], 'spike'), ('regression #12', [[0, 5], [0, 0], [10, 0], [10, 10], [0, 10], [0, 12], [0, 5]], 'spike'), ('regression #13', [[0, 0], [4, 0], [4, 4], [8, 4], [8, 8], [4, 8], [4, 4], [0, 4], [0, 0]], 'self_intersection'), ('regression #14', [[0, 0], [10, 0], [10, 10], [5, 0], [0, 10], [0, 0]], 'self_intersection'), ('regression #24', [[0, 0], [10, 0], [10, 4], [5, 0], [0, 4], [0, 0]], 'self_intersection'), ('regression #27', [[4, 4], [2, 1], [2, 2], [1, 0], [4, 3], [4, 4]], 'self_intersection')], [('regression #12', [[0, 5], [0, 0], [10, 0], [10, 10], [0, 10], [0, 12], [0, 5]], 'spike'), ('regression #13', [[0, 0], [4, 0], [4, 4], [8, 4], [8, 8], [4, 8], [4, 4], [0, 4], [0, 0]], 'self_intersection'), ('regression #14', [[0, 0], [10, 0], [10, 10], [5, 0], [0, 10], [0, 0]], 'self_intersection'), ('regression #15', [[0, 0], [10, 0], [10, 5], [2, 5], [6, 5], [6, 8], [0, 8], [0, 0]], 'spike'), ('control #16', [[0, 0], [6, 0], [6, 6], [3, 3], [0, 6], [0, 0]], 'valid'), ('regression #17', [[0, 0], [10, 0], [10, 10], [0, 10], [4, 10], [0, 0]], 'spike'), ('regression #25', [[0, 0], [10, 0], [10, 10], [4, 10], [4, 0], [0, 10], [0, 0]], 'self_intersection'), ('regression #28', [[2, 0], [1, 0], [0, 3], [2, 1], [4, 1], [2, 2], [2, 0]], 'self_intersection')]]
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)

source:
"""Failure Map reference implementation. Python standard library only."""
import json
import math
N = 1
observations = []
def solve(x):
    ring = x
    if len(ring) < 4:
        return 'too_few_points'
    if ring[0] != ring[-1]:
        return 'not_closed'
    pts = ring[:-1]
    n = len(pts)
    for i in range(n):
        if pts[i] == pts[(i + 1) % n]:
            return 'repeated_point'
    for i in range(n):
        a, b, c = pts[i - 1], pts[i], pts[(i + 1) % n]
        cross = (b[0] - a[0]) * (c[1] - b[1]) - (b[1] - a[1]) * (c[0] - b[0])
        dot = (b[0] - a[0]) * (c[0] - b[0]) + (b[1] - a[1]) * (c[1] - b[1])
        if cross == 0 and dot < 0:
            return 'spike'
    def orient(p, q, r):
        v = (q[0] - p[0]) * (r[1] - p[1]) - (q[1] - p[1]) * (r[0] - p[0])
        return (v > 0) - (v < 0)
    def within(p, q, r):
        return min(p[0], r[0]) <= q[0] <= max(p[0], r[0]) and min(p[1], r[1]) <= q[1] <= max(p[1], r[1])
    def hit(p1, p2, p3, p4):
        o1, o2, o3, o4 = orient(p1, p2, p3), orient(p1, p2, p4), orient(p3, p4, p1), orient(p3, p4, p2)
        if o1 * o2 < 0 and o3 * o4 < 0:
            return True
        return (o1 == 0 and within(p1, p3, p2)) or (o2 == 0 and within(p1, p4, p2))
    for i in range(n):
        for j in range(i + 1, n):
            if j == i + 1 or (i == 0 and j == n - 1):
                continue
            if hit(pts[i], pts[(i + 1) % n], pts[j], pts[(j + 1) % n]):
                return 'self_intersection'
    return 'valid'
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('control #0', [[0, 0], [10, 0], [10, 10], [0, 10], [0, 0]], 'valid'), ('control #1', [[0, 0], [10, 0], [5, 8], [0, 0]], 'valid'), ('control #2', [[0, 0], [5, 0], [10, 0], [10, 10], [0, 10], [0, 0]], 'valid'), ('regression #3', [[0, 0], [10, 10], [10, 0], [0, 10], [0, 0]], 'self_intersection'), ('regression #4', [[0, 0], [10, 0], [10, 10], [10, 5], [0, 5], [0, 0]], 'spike'), ('regression #5', [[5, 0], [10, 0], [10, 10], [0, 10], [0, 0], [5, 0], [0, 0]], 'not_closed'), ('regression #13', [[0, 0], [4, 0], [4, 4], [8, 4], [8, 8], [4, 8], [4, 4], [0, 4], [0, 0]], 'self_intersection'), ('regression #27', [[4, 4], [2, 1], [2, 2], [1, 0], [4, 3], [4, 4]], 'self_intersection')], [('regression #3', [[0, 0], [10, 10], [10, 0], [0, 10], [0, 0]], 'self_intersection'), ('regression #4', [[0, 0], [10, 0], [10, 10], [10, 5], [0, 5], [0, 0]], 'spike'), ('regression #5', [[5, 0], [10, 0], [10, 10], [0, 10], [0, 0], [5, 0], [0, 0]], 'not_closed'), ('boundary #6', [[0, 0], [10, 0], [10, 10], [0, 0]], 'valid'), ('boundary #7', [[0, 0], [10, 0], [10, 10]], 'too_few_points'), ('boundary #8', [[0, 0], [10, 0], [10, 10], [0, 10], [0, 1]], 'not_closed'), ('regression #14', [[0, 0], [10, 0], [10, 10], [5, 0], [0, 10], [0, 0]], 'self_intersection'), ('regression #28', [[2, 0], [1, 0], [0, 3], [2, 1], [4, 1], [2, 2], [2, 0]], 'self_intersection')], [('boundary #6', [[0, 0], [10, 0], [10, 10], [0, 0]], 'valid'), ('boundary #7', [[0, 0], [10, 0], [10, 10]], 'too_few_points'), ('boundary #8', [[0, 0], [10, 0], [10, 10], [0, 10], [0, 1]], 'not_closed'), ('boundary #9', [[0, 0], [10, 0], [10, 0], [10, 10], [0, 0]], 'repeated_point'), ('regression #10', [[0, 0], [10, 0], [10, 10], [0, 10], [0, 0], [0, 0]], 'repeated_point'), ('regression #11', [[0, 0], [10, 0], [10, 10], [0, 10], [0, 5], [0, 12], [0, 0]], 'spike'), ('regression #19', [[0, 0], [8, 0], [8, 8], [0, 8], [0, 4], [8, 4], [0, 0]], 'self_intersection'), ('regression #29', [[0, 2], [2, 2], [4, 3], [4, 0], [0, 4], [0, 2]], 'self_intersection')], [('boundary #9', [[0, 0], [10, 0], [10, 0], [10, 10], [0, 0]], 'repeated_point'), ('regression #10', [[0, 0], [10, 0], [10, 10], [0, 10], [0, 0], [0, 0]], 'repeated_point'), ('regression #11', [[0, 0], [10, 0], [10, 10], [0, 10], [0, 5], [0, 12], [0, 0]], 'spike'), ('regression #12', [[0, 5], [0, 0], [10, 0], [10, 10], [0, 10], [0, 12], [0, 5]], 'spike'), ('regression #13', [[0, 0], [4, 0], [4, 4], [8, 4], [8, 8], [4, 8], [4, 4], [0, 4], [0, 0]], 'self_intersection'), ('regression #14', [[0, 0], [10, 0], [10, 10], [5, 0], [0, 10], [0, 0]], 'self_intersection'), ('regression #24', [[0, 0], [10, 0], [10, 4], [5, 0], [0, 4], [0, 0]], 'self_intersection'), ('regression #27', [[4, 4], [2, 1], [2, 2], [1, 0], [4, 3], [4, 4]], 'self_intersection')], [('regression #12', [[0, 5], [0, 0], [10, 0], [10, 10], [0, 10], [0, 12], [0, 5]], 'spike'), ('regression #13', [[0, 0], [4, 0], [4, 4], [8, 4], [8, 8], [4, 8], [4, 4], [0, 4], [0, 0]], 'self_intersection'), ('regression #14', [[0, 0], [10, 0], [10, 10], [5, 0], [0, 10], [0, 0]], 'self_intersection'), ('regression #15', [[0, 0], [10, 0], [10, 5], [2, 5], [6, 5], [6, 8], [0, 8], [0, 0]], 'spike'), ('control #16', [[0, 0], [6, 0], [6, 6], [3, 3], [0, 6], [0, 0]], 'valid'), ('regression #17', [[0, 0], [10, 0], [10, 10], [0, 10], [4, 10], [0, 0]], 'spike'), ('regression #25', [[0, 0], [10, 0], [10, 10], [4, 10], [4, 0], [0, 10], [0, 0]], 'self_intersection'), ('regression #28', [[2, 0], [1, 0], [0, 3], [2, 1], [4, 1], [2, 2], [2, 0]], 'self_intersection')]]
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)

prompt:
Rings that touch themselves at a vertex or fold back along an edge are reported valid.

Input: one ring as a list of integer [x, y]. Report the first failing check in this order: fewer than 4 positions "too_few_points"; first != last "not_closed"; two cyclically consecutive equal vertices "repeated_point"; a vertex where the boundary reverses direction along a line (collinear with a negative dot product of the incoming and outgoing edge, checked cyclically) "spike"; any two non-adjacent edges sharing a point (crossing, touching or collinear overlap) "self_intersection"; otherwise "valid".

split: open-access


prompt:
Holes that touch the shell at a vertex are rejected as outside.

Input [shell, holes], closed integer rings. Point classification against a ring: on an edge = 0, inside by half-open crossing number = 1, else -1. For each hole in order: "outside" if any hole vertex is strictly outside the shell; else "coincident" if every hole vertex lies on the shell boundary; else "nested" if for some OTHER hole all its vertices are inside-or-on that hole and at least one is strictly inside; else "ok". Return one label per hole.

split: open-access


prompt:
Holes that start inside the shell but cross out of it are accepted.

Input [shell, holes], closed integer rings. Point classification against a ring: on an edge = 0, inside by half-open crossing number = 1, else -1. For each hole in order: "outside" if any hole vertex is strictly outside the shell; else "coincident" if every hole vertex lies on the shell boundary; else "nested" if for some OTHER hole all its vertices are inside-or-on that hole and at least one is strictly inside; else "ok". Return one label per hole.

split: open-access


prompt:
Duplicate or edge-sharing holes are reported as nested.

Input [shell, holes], closed integer rings. Point classification against a ring: on an edge = 0, inside by half-open crossing number = 1, else -1. For each hole in order: "outside" if any hole vertex is strictly outside the shell; else "coincident" if every hole vertex lies on the shell boundary; else "nested" if for some OTHER hole all its vertices are inside-or-on that hole and at least one is strictly inside; else "ok". Return one label per hole.

split: open-access


prompt:
Holes touching the shell at their first vertex are labelled coincident.

Input [shell, holes], closed integer rings. Point classification against a ring: on an edge = 0, inside by half-open crossing number = 1, else -1. For each hole in order: "outside" if any hole vertex is strictly outside the shell; else "coincident" if every hole vertex lies on the shell boundary; else "nested" if for some OTHER hole all its vertices are inside-or-on that hole and at least one is strictly inside; else "ok". Return one label per hole.

split: open-access


prompt:
Hole reports have more labels than holes.

Input [shell, holes], closed integer rings. Point classification against a ring: on an edge = 0, inside by half-open crossing number = 1, else -1. For each hole in order: "outside" if any hole vertex is strictly outside the shell; else "coincident" if every hole vertex lies on the shell boundary; else "nested" if for some OTHER hole all its vertices are inside-or-on that hole and at least one is strictly inside; else "ok". Return one label per hole.

split: open-access


prompt:
Coordinates exactly half-way between grid lines snap inconsistently.

Input [rings, g]: polygon rings (exterior first), closed, numeric coordinates; grid size g > 0 anchored at 0. Each coordinate snaps to floor(v/g + 0.5)*g (halves round toward +infinity). Consecutive identical snapped positions are merged. A ring left with fewer than 4 positions has collapsed: if it is the exterior return None, otherwise drop that hole. Return the snapped rings.

split: open-access


prompt:
Snapped rings contain zero-length edges and collapsed rings survive.

Input [rings, g]: polygon rings (exterior first), closed, numeric coordinates; grid size g > 0 anchored at 0. Each coordinate snaps to floor(v/g + 0.5)*g (halves round toward +infinity). Consecutive identical snapped positions are merged. A ring left with fewer than 4 positions has collapsed: if it is the exterior return None, otherwise drop that hole. Return the snapped rings.

split: open-access


prompt:
Rings collapsed to a doubled segment are kept.

Input [rings, g]: polygon rings (exterior first), closed, numeric coordinates; grid size g > 0 anchored at 0. Each coordinate snaps to floor(v/g + 0.5)*g (halves round toward +infinity). Consecutive identical snapped positions are merged. A ring left with fewer than 4 positions has collapsed: if it is the exterior return None, otherwise drop that hole. Return the snapped rings.

split: open-access


prompt:
A polygon disappears because one tiny hole collapsed.

Input [rings, g]: polygon rings (exterior first), closed, numeric coordinates; grid size g > 0 anchored at 0. Each coordinate snaps to floor(v/g + 0.5)*g (halves round toward +infinity). Consecutive identical snapped positions are merged. A ring left with fewer than 4 positions has collapsed: if it is the exterior return None, otherwise drop that hole. Return the snapped rings.

split: open-access


prompt:
Vertices that overshoot the end of the base segment are dropped as if they lay on it.

Input [points, tol]: an arc as integer [x, y] positions (possibly closed, first == last). Keep both endpoints; recursively (explicit stack) find the interior vertex farthest from the SEGMENT between the current endpoints (projection clamped to the segment; distance to the point itself if the endpoints coincide), taking the first maximum; keep it and split when that distance is strictly greater than tol. Return kept positions in order.

split: open-access


prompt:
Closed arcs collapse to a single point.

Input [points, tol]: an arc as integer [x, y] positions (possibly closed, first == last). Keep both endpoints; recursively (explicit stack) find the interior vertex farthest from the SEGMENT between the current endpoints (projection clamped to the segment; distance to the point itself if the endpoints coincide), taking the first maximum; keep it and split when that distance is strictly greater than tol. Return kept positions in order.

split: open-access


prompt:
Vertices exactly at the tolerance are retained.

Input [points, tol]: an arc as integer [x, y] positions (possibly closed, first == last). Keep both endpoints; recursively (explicit stack) find the interior vertex farthest from the SEGMENT between the current endpoints (projection clamped to the segment; distance to the point itself if the endpoints coincide), taking the first maximum; keep it and split when that distance is strictly greater than tol. Return kept positions in order.

split: open-access


prompt:
Vertices right after a kept vertex are judged against the wrong base segment.

Input [points, tol]: an arc as integer [x, y] positions (possibly closed, first == last). Keep both endpoints; recursively (explicit stack) find the interior vertex farthest from the SEGMENT between the current endpoints (projection clamped to the segment; distance to the point itself if the endpoints coincide), taking the first maximum; keep it and split when that distance is strictly greater than tol. Return kept positions in order.

split: open-access


prompt:
Among equally distant vertices the last one is kept, changing the simplified shape.

Input [points, tol]: an arc as integer [x, y] positions (possibly closed, first == last). Keep both endpoints; recursively (explicit stack) find the interior vertex farthest from the SEGMENT between the current endpoints (projection clamped to the segment; distance to the point itself if the endpoints coincide), taking the first maximum; keep it and split when that distance is strictly greater than tol. Return kept positions in order.

split: open-access


prompt:
Donut-shaped slivers look compact because hole area is added.

Input [rings, threshold]: exterior then holes, closed rings in any orientation. Area = |exterior area| minus the sum of |hole areas|; perimeter = total length of all rings. If area <= 0 or perimeter == 0 return ["degenerate", 0.0]. Thinness t = 4*pi*area/perimeter**2; return ["sliver" if t < threshold else "ok", t rounded to 6 decimals].

split: open-access


prompt:
Thin rims around large holes are not flagged.

Input [rings, threshold]: exterior then holes, closed rings in any orientation. Area = |exterior area| minus the sum of |hole areas|; perimeter = total length of all rings. If area <= 0 or perimeter == 0 return ["degenerate", 0.0]. Thinness t = 4*pi*area/perimeter**2; return ["sliver" if t < threshold else "ok", t rounded to 6 decimals].

split: open-access


prompt:
Clockwise polygons are always reported as degenerate.

Input [rings, threshold]: exterior then holes, closed rings in any orientation. Area = |exterior area| minus the sum of |hole areas|; perimeter = total length of all rings. If area <= 0 or perimeter == 0 return ["degenerate", 0.0]. Thinness t = 4*pi*area/perimeter**2; return ["sliver" if t < threshold else "ok", t rounded to 6 decimals].

split: open-access


prompt:
Polygons exactly at the threshold are flagged as slivers.

Input [rings, threshold]: exterior then holes, closed rings in any orientation. Area = |exterior area| minus the sum of |hole areas|; perimeter = total length of all rings. If area <= 0 or perimeter == 0 return ["degenerate", 0.0]. Thinness t = 4*pi*area/perimeter**2; return ["sliver" if t < threshold else "ok", t rounded to 6 decimals].

split: open-access


prompt:
Collapsed or fully-holed polygons get a negative or zero thinness and are reported as slivers.

Input [rings, threshold]: exterior then holes, closed rings in any orientation. Area = |exterior area| minus the sum of |hole areas|; perimeter = total length of all rings. If area <= 0 or perimeter == 0 return ["degenerate", 0.0]. Thinness t = 4*pi*area/perimeter**2; return ["sliver" if t < threshold else "ok", t rounded to 6 decimals].

split: open-access


prompt:
Centroids of polygons with holes move toward the hole.

Input: a multipolygon as a list of polygons, each a list of closed rings (exterior first). Ring orientation is arbitrary: every ring contributes its absolute area and matching first moments, exteriors positively and holes negatively. Moments use the shoelace terms (xi + xi+1)*cross/6. If the total area is 0 return None, else the centroid [cx, cy] rounded to 6 decimals.

split: open-access


prompt:
Clockwise parts pull the centroid away instead of toward themselves.

Input: a multipolygon as a list of polygons, each a list of closed rings (exterior first). Ring orientation is arbitrary: every ring contributes its absolute area and matching first moments, exteriors positively and holes negatively. Moments use the shoelace terms (xi + xi+1)*cross/6. If the total area is 0 return None, else the centroid [cx, cy] rounded to 6 decimals.

split: open-access


prompt:
The centroid of a multipolygon equals the centroid of its last part.

Input: a multipolygon as a list of polygons, each a list of closed rings (exterior first). Ring orientation is arbitrary: every ring contributes its absolute area and matching first moments, exteriors positively and holes negatively. Moments use the shoelace terms (xi + xi+1)*cross/6. If the total area is 0 return None, else the centroid [cx, cy] rounded to 6 decimals.

split: open-access


prompt:
Centroid x coordinates drift along the edge direction.

Input: a multipolygon as a list of polygons, each a list of closed rings (exterior first). Ring orientation is arbitrary: every ring contributes its absolute area and matching first moments, exteriors positively and holes negatively. Moments use the shoelace terms (xi + xi+1)*cross/6. If the total area is 0 return None, else the centroid [cx, cy] rounded to 6 decimals.

split: open-access


prompt:
Rectangles that merely share an edge are reported as overlapping.

Input [rects, extent]: axis-aligned integer rectangles [x0, y0, x1, y1] forming a coverage and an extent box. Split the plane on all rectangle and extent edges; for each cell inside the extent count the rectangles whose OPEN interior contains the cell centre. Gap area sums cells with count 0, overlap area sums (once) cells with count >= 2. Parts outside the extent are ignored. Return [gap, overlap].

split: open-access


prompt:
Triple overlaps are counted twice.

Input [rects, extent]: axis-aligned integer rectangles [x0, y0, x1, y1] forming a coverage and an extent box. Split the plane on all rectangle and extent edges; for each cell inside the extent count the rectangles whose OPEN interior contains the cell centre. Gap area sums cells with count 0, overlap area sums (once) cells with count >= 2. Parts outside the extent are ignored. Return [gap, overlap].

split: open-access


prompt:
Gaps and overlaps outside the study area are reported.

Input [rects, extent]: axis-aligned integer rectangles [x0, y0, x1, y1] forming a coverage and an extent box. Split the plane on all rectangle and extent edges; for each cell inside the extent count the rectangles whose OPEN interior contains the cell centre. Gap area sums cells with count 0, overlap area sums (once) cells with count >= 2. Parts outside the extent are ignored. Return [gap, overlap].

split: open-access


prompt:
Uncovered strips along the extent edge are missing from the gap total.

Input [rects, extent]: axis-aligned integer rectangles [x0, y0, x1, y1] forming a coverage and an extent box. Split the plane on all rectangle and extent edges; for each cell inside the extent count the rectangles whose OPEN interior contains the cell centre. Gap area sums cells with count 0, overlap area sums (once) cells with count >= 2. Parts outside the extent are ignored. Return [gap, overlap].

split: open-access


prompt:
Every shapefile polygon comes out inside-out.

Input: a list of closed integer rings from one shapefile record. Clockwise rings (negative shoelace sum) are exteriors, counter-clockwise rings are holes, zero-area rings are ignored. Each hole joins the SMALLEST-area exterior whose interior contains the hole first vertex (crossing-number test). A hole contained by no exterior is promoted to an exterior of its own. Return [[exterior_index, sorted hole indexes], ...] sorted by exterior index.

split: open-access


prompt:
Holes in islands inside lakes are attached to the outer mainland ring.

Input: a list of closed integer rings from one shapefile record. Clockwise rings (negative shoelace sum) are exteriors, counter-clockwise rings are holes, zero-area rings are ignored. Each hole joins the SMALLEST-area exterior whose interior contains the hole first vertex (crossing-number test). A hole contained by no exterior is promoted to an exterior of its own. Return [[exterior_index, sorted hole indexes], ...] sorted by exterior index.

split: open-access


prompt:
Holes with no enclosing exterior vanish from the output.

Input: a list of closed integer rings from one shapefile record. Clockwise rings (negative shoelace sum) are exteriors, counter-clockwise rings are holes, zero-area rings are ignored. Each hole joins the SMALLEST-area exterior whose interior contains the hole first vertex (crossing-number test). A hole contained by no exterior is promoted to an exterior of its own. Return [[exterior_index, sorted hole indexes], ...] sorted by exterior index.

split: open-access


prompt:
Holes in the notch of an L-shaped parcel are attached to that parcel.

Input: a list of closed integer rings from one shapefile record. Clockwise rings (negative shoelace sum) are exteriors, counter-clockwise rings are holes, zero-area rings are ignored. Each hole joins the SMALLEST-area exterior whose interior contains the hole first vertex (crossing-number test). A hole contained by no exterior is promoted to an exterior of its own. Return [[exterior_index, sorted hole indexes], ...] sorted by exterior index.

split: open-access


prompt:
Promoted orphan rings appear after all regular exteriors regardless of their index.

Input: a list of closed integer rings from one shapefile record. Clockwise rings (negative shoelace sum) are exteriors, counter-clockwise rings are holes, zero-area rings are ignored. Each hole joins the SMALLEST-area exterior whose interior contains the hole first vertex (crossing-number test). A hole contained by no exterior is promoted to an exterior of its own. Return [[exterior_index, sorted hole indexes], ...] sorted by exterior index.

split: open-access


broken_source:
"""Failure Map reference implementation. Python standard library only."""
import json
import math
N = 1
observations = []
def solve(x):
    s = x.strip()
    up = s.upper()
    words = up.replace('(', ' ( ').split()
    if not words or words[0] not in ('POLYGON', 'MULTIPOLYGON'):
        return None
    if len(words) == 2 and words[1] == 'EMPTY':
        return []
    if '(' not in s:
        return None
    body = s[s.index('('):]
    stack = [[]]
    cur = ''
    for ch in body:
        if ch == '(':
            stack.append([])
        elif ch in '),':
            if cur.strip():
                nums = [float(t) for t in cur.split()]
                stack[-1].append(nums)
            cur = ''
            if ch == ')':
                done = stack.pop()
                stack[-1].append(done)
        else:
            cur += ch
    tree = stack[0][0]
    polys = [tree] if words[0] == 'POLYGON' else tree
    for poly in polys:
        for ring in poly:
            if len(ring) < 4 or ring[0] != ring[-1]:
                return None
    return polys
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('control #0', 'POLYGON ((0 0, 4 0, 4 4, 0 4, 0 0))', [[[[0.0, 0.0], [4.0, 0.0], [4.0, 4.0], [0.0, 4.0], [0.0, 0.0]]]]), ('control #1', 'POLYGON ((0 0, 10 0, 10 10, 0 10, 0 0), (2 2, 2 4, 4 4, 2 2))', [[[[0.0, 0.0], [10.0, 0.0], [10.0, 10.0], [0.0, 10.0], [0.0, 0.0]], [[2.0, 2.0], [2.0, 4.0], [4.0, 4.0], [2.0, 2.0]]]]), ('regression #2', 'POLYGON Z ((0 0 5, 4 0 5, 4 4 6, 0 0 5))', [[[[0.0, 0.0], [4.0, 0.0], [4.0, 4.0], [0.0, 0.0]]]]), ('regression #3', 'POLYGON ZM ((0 0 5 1, 4 0 5 2, 4 4 6 3, 0 0 5 1))', [[[[0.0, 0.0], [4.0, 0.0], [4.0, 4.0], [0.0, 0.0]]]]), ('regression #4', 'POLYGON M ((0 0 7, 4 0 8, 4 4 9, 0 0 7))', [[[[0.0, 0.0], [4.0, 0.0], [4.0, 4.0], [0.0, 0.0]]]]), ('boundary #5', 'POLYGON EMPTY', []), ('boundary #6', 'polygon empty', []), ('regression #7', 'MULTIPOLYGON (((0 0, 1 0, 1 1, 0 0)), ((5 5, 6 5, 6 6, 5 5), (5.2 5.1, 5.8 5.8, 5.8 5.1, 5.2 5.1)))', [[[[0.0, 0.0], [1.0, 0.0], [1.0, 1.0], [0.0, 0.0]]], [[[5.0, 5.0], [6.0, 5.0], [6.0, 6.0], [5.0, 5.0]], [[5.2, 5.1], [5.8, 5.8], [5.8, 5.1], [5.2, 5.1]]]])], [('regression #3', 'POLYGON ZM ((0 0 5 1, 4 0 5 2, 4 4 6 3, 0 0 5 1))', [[[[0.0, 0.0], [4.0, 0.0], [4.0, 4.0], [0.0, 0.0]]]]), ('regression #4', 'POLYGON M ((0 0 7, 4 0 8, 4 4 9, 0 0 7))', [[[[0.0, 0.0], [4.0, 0.0], [4.0, 4.0], [0.0, 0.0]]]]), ('boundary #5', 'POLYGON EMPTY', []), ('boundary #6', 'polygon empty', []), ('regression #7', 'MULTIPOLYGON (((0 0, 1 0, 1 1, 0 0)), ((5 5, 6 5, 6 6, 5 5), (5.2 5.1, 5.8 5.8, 5.8 5.1, 5.2 5.1)))', [[[[0.0, 0.0], [1.0, 0.0], [1.0, 1.0], [0.0, 0.0]]], [[[5.0, 5.0], [6.0, 5.0], [6.0, 6.0], [5.0, 5.0]], [[5.2, 5.1], [5.8, 5.8], [5.8, 5.1], [5.2, 5.1]]]]), ('regression #8', 'MULTIPOLYGON (((0 0, 1 0, 1 1, 0 0)))', [[[[0.0, 0.0], [1.0, 0.0], [1.0, 1.0], [0.0, 0.0]]]]), ('regression #9', 'multipolygon (((-1.5 -2, 3e2 0, 0 1e1, -1.5 -2)))', [[[[-1.5, -2.0], [300.0, 0.0], [0.0, 10.0], [-1.5, -2.0]]]]), ('boundary #10', 'POLYGON ((0 0, 4 0, 4 4, 0 1))', None)], [('regression #3', 'POLYGON ZM ((0 0 5 1, 4 0 5 2, 4 4 6 3, 0 0 5 1))', [[[[0.0, 0.0], [4.0, 0.0], [4.0, 4.0], [0.0, 0.0]]]]), ('regression #4', 'POLYGON M ((0 0 7, 4 0 8, 4 4 9, 0 0 7))', [[[[0.0, 0.0], [4.0, 0.0], [4.0, 4.0], [0.0, 0.0]]]]), ('regression #8', 'MULTIPOLYGON (((0 0, 1 0, 1 1, 0 0)))', [[[[0.0, 0.0], [1.0, 0.0], [1.0, 1.0], [0.0, 0.0]]]]), ('regression #9', 'multipolygon (((-1.5 -2, 3e2 0, 0 1e1, -1.5 -2)))', [[[[-1.5, -2.0], [300.0, 0.0], [0.0, 10.0], [-1.5, -2.0]]]]), ('boundary #10', 'POLYGON ((0 0, 4 0, 4 4, 0 1))', None), ('boundary #11', 'POLYGON ((0 0, 4 0, 0 0))', None), ('control #12', 'Polygon((1 1,5 1,5 5,1 1))', [[[[1.0, 1.0], [5.0, 1.0], [5.0, 5.0], [1.0, 1.0]]]]), ('boundary #13', 'LINESTRING (0 0, 1 1)', None)], [('regression #3', 'POLYGON ZM ((0 0 5 1, 4 0 5 2, 4 4 6 3, 0 0 5 1))', [[[[0.0, 0.0], [4.0, 0.0], [4.0, 4.0], [0.0, 0.0]]]]), ('boundary #10', 'POLYGON ((0 0, 4 0, 4 4, 0 1))', None), ('boundary #11', 'POLYGON ((0 0, 4 0, 0 0))', None), ('control #12', 'Polygon((1 1,5 1,5 5,1 1))', [[[[1.0, 1.0], [5.0, 1.0], [5.0, 5.0], [1.0, 1.0]]]]), ('boundary #13', 'LINESTRING (0 0, 1 1)', None), ('boundary #14', 'MULTIPOLYGON EMPTY', []), ('control #15', '  POLYGON ((0 0, -3 0, -3 -3, 0 0))  ', [[[[0.0, 0.0], [-3.0, 0.0], [-3.0, -3.0], [0.0, 0.0]]]]), ('regression #16', 'MULTIPOLYGON Z (((0 0 1, 2 0 1, 2 2 1, 0 0 1)), ((9 9 0, 8 9 0, 8 8 0, 9 9 0)))', [[[[0.0, 0.0], [2.0, 0.0], [2.0, 2.0], [0.0, 0.0]]], [[[9.0, 9.0], [8.0, 9.0], [8.0, 8.0], [9.0, 9.0]]]])], [('control #0', 'POLYGON ((0 0, 4 0, 4 4, 0 4, 0 0))', [[[[0.0, 0.0], [4.0, 0.0], [4.0, 4.0], [0.0, 4.0], [0.0, 0.0]]]]), ('control #1', 'POLYGON ((0 0, 10 0, 10 10, 0 10, 0 0), (2 2, 2 4, 4 4, 2 2))', [[[[0.0, 0.0], [10.0, 0.0], [10.0, 10.0], [0.0, 10.0], [0.0, 0.0]], [[2.0, 2.0], [2.0, 4.0], [4.0, 4.0], [2.0, 2.0]]]]), ('regression #3', 'POLYGON ZM ((0 0 5 1, 4 0 5 2, 4 4 6 3, 0 0 5 1))', [[[[0.0, 0.0], [4.0, 0.0], [4.0, 4.0], [0.0, 0.0]]]]), ('boundary #13', 'LINESTRING (0 0, 1 1)', None), ('boundary #14', 'MULTIPOLYGON EMPTY', []), ('control #15', '  POLYGON ((0 0, -3 0, -3 -3, 0 0))  ', [[[[0.0, 0.0], [-3.0, 0.0], [-3.0, -3.0], [0.0, 0.0]]]]), ('regression #16', 'MULTIPOLYGON Z (((0 0 1, 2 0 1, 2 2 1, 0 0 1)), ((9 9 0, 8 9 0, 8 8 0, 9 9 0)))', [[[[0.0, 0.0], [2.0, 0.0], [2.0, 2.0], [0.0, 0.0]]], [[[9.0, 9.0], [8.0, 9.0], [8.0, 8.0], [9.0, 9.0]]]]), ('boundary #17', 'POLYGON ((0 0 1, 4 0 1, 4 4 1, 0 0 2))', [[[[0.0, 0.0], [4.0, 0.0], [4.0, 4.0], [0.0, 0.0]]]])]]
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)

source:
"""Failure Map reference implementation. Python standard library only."""
import json
import math
N = 1
observations = []
def solve(x):
    s = x.strip()
    up = s.upper()
    words = up.replace('(', ' ( ').split()
    if not words or words[0] not in ('POLYGON', 'MULTIPOLYGON'):
        return None
    if len(words) == 2 and words[1] == 'EMPTY':
        return []
    if '(' not in s:
        return None
    body = s[s.index('('):]
    stack = [[]]
    cur = ''
    for ch in body:
        if ch == '(':
            stack.append([])
        elif ch in '),':
            if cur.strip():
                nums = [float(t) for t in cur.split()]
                stack[-1].append(nums[:2] if len(nums) == 3 else nums)
            cur = ''
            if ch == ')':
                done = stack.pop()
                stack[-1].append(done)
        else:
            cur += ch
    tree = stack[0][0]
    polys = [tree] if words[0] == 'POLYGON' else tree
    for poly in polys:
        for ring in poly:
            if len(ring) < 4 or ring[0] != ring[-1]:
                return None
    return polys
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('control #0', 'POLYGON ((0 0, 4 0, 4 4, 0 4, 0 0))', [[[[0.0, 0.0], [4.0, 0.0], [4.0, 4.0], [0.0, 4.0], [0.0, 0.0]]]]), ('control #1', 'POLYGON ((0 0, 10 0, 10 10, 0 10, 0 0), (2 2, 2 4, 4 4, 2 2))', [[[[0.0, 0.0], [10.0, 0.0], [10.0, 10.0], [0.0, 10.0], [0.0, 0.0]], [[2.0, 2.0], [2.0, 4.0], [4.0, 4.0], [2.0, 2.0]]]]), ('regression #2', 'POLYGON Z ((0 0 5, 4 0 5, 4 4 6, 0 0 5))', [[[[0.0, 0.0], [4.0, 0.0], [4.0, 4.0], [0.0, 0.0]]]]), ('regression #3', 'POLYGON ZM ((0 0 5 1, 4 0 5 2, 4 4 6 3, 0 0 5 1))', [[[[0.0, 0.0], [4.0, 0.0], [4.0, 4.0], [0.0, 0.0]]]]), ('regression #4', 'POLYGON M ((0 0 7, 4 0 8, 4 4 9, 0 0 7))', [[[[0.0, 0.0], [4.0, 0.0], [4.0, 4.0], [0.0, 0.0]]]]), ('boundary #5', 'POLYGON EMPTY', []), ('boundary #6', 'polygon empty', []), ('regression #7', 'MULTIPOLYGON (((0 0, 1 0, 1 1, 0 0)), ((5 5, 6 5, 6 6, 5 5), (5.2 5.1, 5.8 5.8, 5.8 5.1, 5.2 5.1)))', [[[[0.0, 0.0], [1.0, 0.0], [1.0, 1.0], [0.0, 0.0]]], [[[5.0, 5.0], [6.0, 5.0], [6.0, 6.0], [5.0, 5.0]], [[5.2, 5.1], [5.8, 5.8], [5.8, 5.1], [5.2, 5.1]]]])], [('regression #3', 'POLYGON ZM ((0 0 5 1, 4 0 5 2, 4 4 6 3, 0 0 5 1))', [[[[0.0, 0.0], [4.0, 0.0], [4.0, 4.0], [0.0, 0.0]]]]), ('regression #4', 'POLYGON M ((0 0 7, 4 0 8, 4 4 9, 0 0 7))', [[[[0.0, 0.0], [4.0, 0.0], [4.0, 4.0], [0.0, 0.0]]]]), ('boundary #5', 'POLYGON EMPTY', []), ('boundary #6', 'polygon empty', []), ('regression #7', 'MULTIPOLYGON (((0 0, 1 0, 1 1, 0 0)), ((5 5, 6 5, 6 6, 5 5), (5.2 5.1, 5.8 5.8, 5.8 5.1, 5.2 5.1)))', [[[[0.0, 0.0], [1.0, 0.0], [1.0, 1.0], [0.0, 0.0]]], [[[5.0, 5.0], [6.0, 5.0], [6.0, 6.0], [5.0, 5.0]], [[5.2, 5.1], [5.8, 5.8], [5.8, 5.1], [5.2, 5.1]]]]), ('regression #8', 'MULTIPOLYGON (((0 0, 1 0, 1 1, 0 0)))', [[[[0.0, 0.0], [1.0, 0.0], [1.0, 1.0], [0.0, 0.0]]]]), ('regression #9', 'multipolygon (((-1.5 -2, 3e2 0, 0 1e1, -1.5 -2)))', [[[[-1.5, -2.0], [300.0, 0.0], [0.0, 10.0], [-1.5, -2.0]]]]), ('boundary #10', 'POLYGON ((0 0, 4 0, 4 4, 0 1))', None)], [('regression #3', 'POLYGON ZM ((0 0 5 1, 4 0 5 2, 4 4 6 3, 0 0 5 1))', [[[[0.0, 0.0], [4.0, 0.0], [4.0, 4.0], [0.0, 0.0]]]]), ('regression #4', 'POLYGON M ((0 0 7, 4 0 8, 4 4 9, 0 0 7))', [[[[0.0, 0.0], [4.0, 0.0], [4.0, 4.0], [0.0, 0.0]]]]), ('regression #8', 'MULTIPOLYGON (((0 0, 1 0, 1 1, 0 0)))', [[[[0.0, 0.0], [1.0, 0.0], [1.0, 1.0], [0.0, 0.0]]]]), ('regression #9', 'multipolygon (((-1.5 -2, 3e2 0, 0 1e1, -1.5 -2)))', [[[[-1.5, -2.0], [300.0, 0.0], [0.0, 10.0], [-1.5, -2.0]]]]), ('boundary #10', 'POLYGON ((0 0, 4 0, 4 4, 0 1))', None), ('boundary #11', 'POLYGON ((0 0, 4 0, 0 0))', None), ('control #12', 'Polygon((1 1,5 1,5 5,1 1))', [[[[1.0, 1.0], [5.0, 1.0], [5.0, 5.0], [1.0, 1.0]]]]), ('boundary #13', 'LINESTRING (0 0, 1 1)', None)], [('regression #3', 'POLYGON ZM ((0 0 5 1, 4 0 5 2, 4 4 6 3, 0 0 5 1))', [[[[0.0, 0.0], [4.0, 0.0], [4.0, 4.0], [0.0, 0.0]]]]), ('boundary #10', 'POLYGON ((0 0, 4 0, 4 4, 0 1))', None), ('boundary #11', 'POLYGON ((0 0, 4 0, 0 0))', None), ('control #12', 'Polygon((1 1,5 1,5 5,1 1))', [[[[1.0, 1.0], [5.0, 1.0], [5.0, 5.0], [1.0, 1.0]]]]), ('boundary #13', 'LINESTRING (0 0, 1 1)', None), ('boundary #14', 'MULTIPOLYGON EMPTY', []), ('control #15', '  POLYGON ((0 0, -3 0, -3 -3, 0 0))  ', [[[[0.0, 0.0], [-3.0, 0.0], [-3.0, -3.0], [0.0, 0.0]]]]), ('regression #16', 'MULTIPOLYGON Z (((0 0 1, 2 0 1, 2 2 1, 0 0 1)), ((9 9 0, 8 9 0, 8 8 0, 9 9 0)))', [[[[0.0, 0.0], [2.0, 0.0], [2.0, 2.0], [0.0, 0.0]]], [[[9.0, 9.0], [8.0, 9.0], [8.0, 8.0], [9.0, 9.0]]]])], [('control #0', 'POLYGON ((0 0, 4 0, 4 4, 0 4, 0 0))', [[[[0.0, 0.0], [4.0, 0.0], [4.0, 4.0], [0.0, 4.0], [0.0, 0.0]]]]), ('control #1', 'POLYGON ((0 0, 10 0, 10 10, 0 10, 0 0), (2 2, 2 4, 4 4, 2 2))', [[[[0.0, 0.0], [10.0, 0.0], [10.0, 10.0], [0.0, 10.0], [0.0, 0.0]], [[2.0, 2.0], [2.0, 4.0], [4.0, 4.0], [2.0, 2.0]]]]), ('regression #3', 'POLYGON ZM ((0 0 5 1, 4 0 5 2, 4 4 6 3, 0 0 5 1))', [[[[0.0, 0.0], [4.0, 0.0], [4.0, 4.0], [0.0, 0.0]]]]), ('boundary #13', 'LINESTRING (0 0, 1 1)', None), ('boundary #14', 'MULTIPOLYGON EMPTY', []), ('control #15', '  POLYGON ((0 0, -3 0, -3 -3, 0 0))  ', [[[[0.0, 0.0], [-3.0, 0.0], [-3.0, -3.0], [0.0, 0.0]]]]), ('regression #16', 'MULTIPOLYGON Z (((0 0 1, 2 0 1, 2 2 1, 0 0 1)), ((9 9 0, 8 9 0, 8 8 0, 9 9 0)))', [[[[0.0, 0.0], [2.0, 0.0], [2.0, 2.0], [0.0, 0.0]]], [[[9.0, 9.0], [8.0, 9.0], [8.0, 8.0], [9.0, 9.0]]]]), ('boundary #17', 'POLYGON ((0 0 1, 4 0 1, 4 4 1, 0 0 2))', [[[[0.0, 0.0], [4.0, 0.0], [4.0, 4.0], [0.0, 0.0]]]])]]
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)

prompt:
Rings from 3D sources carry elevations and fail closure when only z differs.

Input: a WKT string. The keyword (case-insensitive) must be POLYGON or MULTIPOLYGON, else None; "<keyword> EMPTY" returns []. Otherwise parse the parenthesised body into polygons -> rings -> positions, keeping only x and y of every position (Z/M ordinates are dropped). Every ring must have at least 4 positions and be closed in x/y, else None. Return a list of polygons (a POLYGON gives a one-element list).

split: open-access


broken_source:
"""Failure Map reference implementation. Python standard library only."""
import json
import math
N = 1
observations = []
def solve(x):
    s = x.strip()
    up = s.upper()
    words = up.replace('(', ' ( ').split()
    if not words or words[0] not in ('POLYGON', 'MULTIPOLYGON'):
        return None
    if len(words) == 2 and words[1] == 'EMPTY':
        return None
    if '(' not in s:
        return None
    body = s[s.index('('):]
    stack = [[]]
    cur = ''
    for ch in body:
        if ch == '(':
            stack.append([])
        elif ch in '),':
            if cur.strip():
                nums = [float(t) for t in cur.split()]
                stack[-1].append(nums[:2])
            cur = ''
            if ch == ')':
                done = stack.pop()
                stack[-1].append(done)
        else:
            cur += ch
    tree = stack[0][0]
    polys = [tree] if words[0] == 'POLYGON' else tree
    for poly in polys:
        for ring in poly:
            if len(ring) < 4 or ring[0] != ring[-1]:
                return None
    return polys
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('control #0', 'POLYGON ((0 0, 4 0, 4 4, 0 4, 0 0))', [[[[0.0, 0.0], [4.0, 0.0], [4.0, 4.0], [0.0, 4.0], [0.0, 0.0]]]]), ('control #1', 'POLYGON ((0 0, 10 0, 10 10, 0 10, 0 0), (2 2, 2 4, 4 4, 2 2))', [[[[0.0, 0.0], [10.0, 0.0], [10.0, 10.0], [0.0, 10.0], [0.0, 0.0]], [[2.0, 2.0], [2.0, 4.0], [4.0, 4.0], [2.0, 2.0]]]]), ('regression #2', 'POLYGON Z ((0 0 5, 4 0 5, 4 4 6, 0 0 5))', [[[[0.0, 0.0], [4.0, 0.0], [4.0, 4.0], [0.0, 0.0]]]]), ('regression #3', 'POLYGON ZM ((0 0 5 1, 4 0 5 2, 4 4 6 3, 0 0 5 1))', [[[[0.0, 0.0], [4.0, 0.0], [4.0, 4.0], [0.0, 0.0]]]]), ('regression #4', 'POLYGON M ((0 0 7, 4 0 8, 4 4 9, 0 0 7))', [[[[0.0, 0.0], [4.0, 0.0], [4.0, 4.0], [0.0, 0.0]]]]), ('boundary #5', 'POLYGON EMPTY', []), ('boundary #6', 'polygon empty', []), ('regression #7', 'MULTIPOLYGON (((0 0, 1 0, 1 1, 0 0)), ((5 5, 6 5, 6 6, 5 5), (5.2 5.1, 5.8 5.8, 5.8 5.1, 5.2 5.1)))', [[[[0.0, 0.0], [1.0, 0.0], [1.0, 1.0], [0.0, 0.0]]], [[[5.0, 5.0], [6.0, 5.0], [6.0, 6.0], [5.0, 5.0]], [[5.2, 5.1], [5.8, 5.8], [5.8, 5.1], [5.2, 5.1]]]])], [('regression #3', 'POLYGON ZM ((0 0 5 1, 4 0 5 2, 4 4 6 3, 0 0 5 1))', [[[[0.0, 0.0], [4.0, 0.0], [4.0, 4.0], [0.0, 0.0]]]]), ('regression #4', 'POLYGON M ((0 0 7, 4 0 8, 4 4 9, 0 0 7))', [[[[0.0, 0.0], [4.0, 0.0], [4.0, 4.0], [0.0, 0.0]]]]), ('boundary #5', 'POLYGON EMPTY', []), ('boundary #6', 'polygon empty', []), ('regression #7', 'MULTIPOLYGON (((0 0, 1 0, 1 1, 0 0)), ((5 5, 6 5, 6 6, 5 5), (5.2 5.1, 5.8 5.8, 5.8 5.1, 5.2 5.1)))', [[[[0.0, 0.0], [1.0, 0.0], [1.0, 1.0], [0.0, 0.0]]], [[[5.0, 5.0], [6.0, 5.0], [6.0, 6.0], [5.0, 5.0]], [[5.2, 5.1], [5.8, 5.8], [5.8, 5.1], [5.2, 5.1]]]]), ('regression #8', 'MULTIPOLYGON (((0 0, 1 0, 1 1, 0 0)))', [[[[0.0, 0.0], [1.0, 0.0], [1.0, 1.0], [0.0, 0.0]]]]), ('regression #9', 'multipolygon (((-1.5 -2, 3e2 0, 0 1e1, -1.5 -2)))', [[[[-1.5, -2.0], [300.0, 0.0], [0.0, 10.0], [-1.5, -2.0]]]]), ('boundary #14', 'MULTIPOLYGON EMPTY', [])], [('boundary #5', 'POLYGON EMPTY', []), ('regression #7', 'MULTIPOLYGON (((0 0, 1 0, 1 1, 0 0)), ((5 5, 6 5, 6 6, 5 5), (5.2 5.1, 5.8 5.8, 5.8 5.1, 5.2 5.1)))', [[[[0.0, 0.0], [1.0, 0.0], [1.0, 1.0], [0.0, 0.0]]], [[[5.0, 5.0], [6.0, 5.0], [6.0, 6.0], [5.0, 5.0]], [[5.2, 5.1], [5.8, 5.8], [5.8, 5.1], [5.2, 5.1]]]]), ('regression #8', 'MULTIPOLYGON (((0 0, 1 0, 1 1, 0 0)))', [[[[0.0, 0.0], [1.0, 0.0], [1.0, 1.0], [0.0, 0.0]]]]), ('regression #9', 'multipolygon (((-1.5 -2, 3e2 0, 0 1e1, -1.5 -2)))', [[[[-1.5, -2.0], [300.0, 0.0], [0.0, 10.0], [-1.5, -2.0]]]]), ('boundary #10', 'POLYGON ((0 0, 4 0, 4 4, 0 1))', None), ('boundary #11', 'POLYGON ((0 0, 4 0, 0 0))', None), ('control #12', 'Polygon((1 1,5 1,5 5,1 1))', [[[[1.0, 1.0], [5.0, 1.0], [5.0, 5.0], [1.0, 1.0]]]]), ('boundary #14', 'MULTIPOLYGON EMPTY', [])], [('boundary #5', 'POLYGON EMPTY', []), ('boundary #10', 'POLYGON ((0 0, 4 0, 4 4, 0 1))', None), ('boundary #11', 'POLYGON ((0 0, 4 0, 0 0))', None), ('control #12', 'Polygon((1 1,5 1,5 5,1 1))', [[[[1.0, 1.0], [5.0, 1.0], [5.0, 5.0], [1.0, 1.0]]]]), ('boundary #13', 'LINESTRING (0 0, 1 1)', None), ('boundary #14', 'MULTIPOLYGON EMPTY', []), ('control #15', '  POLYGON ((0 0, -3 0, -3 -3, 0 0))  ', [[[[0.0, 0.0], [-3.0, 0.0], [-3.0, -3.0], [0.0, 0.0]]]]), ('regression #16', 'MULTIPOLYGON Z (((0 0 1, 2 0 1, 2 2 1, 0 0 1)), ((9 9 0, 8 9 0, 8 8 0, 9 9 0)))', [[[[0.0, 0.0], [2.0, 0.0], [2.0, 2.0], [0.0, 0.0]]], [[[9.0, 9.0], [8.0, 9.0], [8.0, 8.0], [9.0, 9.0]]]])], [('control #0', 'POLYGON ((0 0, 4 0, 4 4, 0 4, 0 0))', [[[[0.0, 0.0], [4.0, 0.0], [4.0, 4.0], [0.0, 4.0], [0.0, 0.0]]]]), ('control #1', 'POLYGON ((0 0, 10 0, 10 10, 0 10, 0 0), (2 2, 2 4, 4 4, 2 2))', [[[[0.0, 0.0], [10.0, 0.0], [10.0, 10.0], [0.0, 10.0], [0.0, 0.0]], [[2.0, 2.0], [2.0, 4.0], [4.0, 4.0], [2.0, 2.0]]]]), ('boundary #5', 'POLYGON EMPTY', []), ('boundary #6', 'polygon empty', []), ('boundary #14', 'MULTIPOLYGON EMPTY', []), ('control #15', '  POLYGON ((0 0, -3 0, -3 -3, 0 0))  ', [[[[0.0, 0.0], [-3.0, 0.0], [-3.0, -3.0], [0.0, 0.0]]]]), ('regression #16', 'MULTIPOLYGON Z (((0 0 1, 2 0 1, 2 2 1, 0 0 1)), ((9 9 0, 8 9 0, 8 8 0, 9 9 0)))', [[[[0.0, 0.0], [2.0, 0.0], [2.0, 2.0], [0.0, 0.0]]], [[[9.0, 9.0], [8.0, 9.0], [8.0, 8.0], [9.0, 9.0]]]]), ('boundary #17', 'POLYGON ((0 0 1, 4 0 1, 4 4 1, 0 0 2))', [[[[0.0, 0.0], [4.0, 0.0], [4.0, 4.0], [0.0, 0.0]]]])]]
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)

source:
"""Failure Map reference implementation. Python standard library only."""
import json
import math
N = 1
observations = []
def solve(x):
    s = x.strip()
    up = s.upper()
    words = up.replace('(', ' ( ').split()
    if not words or words[0] not in ('POLYGON', 'MULTIPOLYGON'):
        return None
    if len(words) == 2 and words[1] == 'EMPTY':
        return [[]]
    if '(' not in s:
        return None
    body = s[s.index('('):]
    stack = [[]]
    cur = ''
    for ch in body:
        if ch == '(':
            stack.append([])
        elif ch in '),':
            if cur.strip():
                nums = [float(t) for t in cur.split()]
                stack[-1].append(nums[:2])
            cur = ''
            if ch == ')':
                done = stack.pop()
                stack[-1].append(done)
        else:
            cur += ch
    tree = stack[0][0]
    polys = [tree] if words[0] == 'POLYGON' else tree
    for poly in polys:
        for ring in poly:
            if len(ring) < 4 or ring[0] != ring[-1]:
                return None
    return polys
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('control #0', 'POLYGON ((0 0, 4 0, 4 4, 0 4, 0 0))', [[[[0.0, 0.0], [4.0, 0.0], [4.0, 4.0], [0.0, 4.0], [0.0, 0.0]]]]), ('control #1', 'POLYGON ((0 0, 10 0, 10 10, 0 10, 0 0), (2 2, 2 4, 4 4, 2 2))', [[[[0.0, 0.0], [10.0, 0.0], [10.0, 10.0], [0.0, 10.0], [0.0, 0.0]], [[2.0, 2.0], [2.0, 4.0], [4.0, 4.0], [2.0, 2.0]]]]), ('regression #2', 'POLYGON Z ((0 0 5, 4 0 5, 4 4 6, 0 0 5))', [[[[0.0, 0.0], [4.0, 0.0], [4.0, 4.0], [0.0, 0.0]]]]), ('regression #3', 'POLYGON ZM ((0 0 5 1, 4 0 5 2, 4 4 6 3, 0 0 5 1))', [[[[0.0, 0.0], [4.0, 0.0], [4.0, 4.0], [0.0, 0.0]]]]), ('regression #4', 'POLYGON M ((0 0 7, 4 0 8, 4 4 9, 0 0 7))', [[[[0.0, 0.0], [4.0, 0.0], [4.0, 4.0], [0.0, 0.0]]]]), ('boundary #5', 'POLYGON EMPTY', []), ('boundary #6', 'polygon empty', []), ('regression #7', 'MULTIPOLYGON (((0 0, 1 0, 1 1, 0 0)), ((5 5, 6 5, 6 6, 5 5), (5.2 5.1, 5.8 5.8, 5.8 5.1, 5.2 5.1)))', [[[[0.0, 0.0], [1.0, 0.0], [1.0, 1.0], [0.0, 0.0]]], [[[5.0, 5.0], [6.0, 5.0], [6.0, 6.0], [5.0, 5.0]], [[5.2, 5.1], [5.8, 5.8], [5.8, 5.1], [5.2, 5.1]]]])], [('regression #3', 'POLYGON ZM ((0 0 5 1, 4 0 5 2, 4 4 6 3, 0 0 5 1))', [[[[0.0, 0.0], [4.0, 0.0], [4.0, 4.0], [0.0, 0.0]]]]), ('regression #4', 'POLYGON M ((0 0 7, 4 0 8, 4 4 9, 0 0 7))', [[[[0.0, 0.0], [4.0, 0.0], [4.0, 4.0], [0.0, 0.0]]]]), ('boundary #5', 'POLYGON EMPTY', []), ('boundary #6', 'polygon empty', []), ('regression #7', 'MULTIPOLYGON (((0 0, 1 0, 1 1, 0 0)), ((5 5, 6 5, 6 6, 5 5), (5.2 5.1, 5.8 5.8, 5.8 5.1, 5.2 5.1)))', [[[[0.0, 0.0], [1.0, 0.0], [1.0, 1.0], [0.0, 0.0]]], [[[5.0, 5.0], [6.0, 5.0], [6.0, 6.0], [5.0, 5.0]], [[5.2, 5.1], [5.8, 5.8], [5.8, 5.1], [5.2, 5.1]]]]), ('regression #8', 'MULTIPOLYGON (((0 0, 1 0, 1 1, 0 0)))', [[[[0.0, 0.0], [1.0, 0.0], [1.0, 1.0], [0.0, 0.0]]]]), ('regression #9', 'multipolygon (((-1.5 -2, 3e2 0, 0 1e1, -1.5 -2)))', [[[[-1.5, -2.0], [300.0, 0.0], [0.0, 10.0], [-1.5, -2.0]]]]), ('boundary #14', 'MULTIPOLYGON EMPTY', [])], [('boundary #5', 'POLYGON EMPTY', []), ('regression #7', 'MULTIPOLYGON (((0 0, 1 0, 1 1, 0 0)), ((5 5, 6 5, 6 6, 5 5), (5.2 5.1, 5.8 5.8, 5.8 5.1, 5.2 5.1)))', [[[[0.0, 0.0], [1.0, 0.0], [1.0, 1.0], [0.0, 0.0]]], [[[5.0, 5.0], [6.0, 5.0], [6.0, 6.0], [5.0, 5.0]], [[5.2, 5.1], [5.8, 5.8], [5.8, 5.1], [5.2, 5.1]]]]), ('regression #8', 'MULTIPOLYGON (((0 0, 1 0, 1 1, 0 0)))', [[[[0.0, 0.0], [1.0, 0.0], [1.0, 1.0], [0.0, 0.0]]]]), ('regression #9', 'multipolygon (((-1.5 -2, 3e2 0, 0 1e1, -1.5 -2)))', [[[[-1.5, -2.0], [300.0, 0.0], [0.0, 10.0], [-1.5, -2.0]]]]), ('boundary #10', 'POLYGON ((0 0, 4 0, 4 4, 0 1))', None), ('boundary #11', 'POLYGON ((0 0, 4 0, 0 0))', None), ('control #12', 'Polygon((1 1,5 1,5 5,1 1))', [[[[1.0, 1.0], [5.0, 1.0], [5.0, 5.0], [1.0, 1.0]]]]), ('boundary #14', 'MULTIPOLYGON EMPTY', [])], [('boundary #5', 'POLYGON EMPTY', []), ('boundary #10', 'POLYGON ((0 0, 4 0, 4 4, 0 1))', None), ('boundary #11', 'POLYGON ((0 0, 4 0, 0 0))', None), ('control #12', 'Polygon((1 1,5 1,5 5,1 1))', [[[[1.0, 1.0], [5.0, 1.0], [5.0, 5.0], [1.0, 1.0]]]]), ('boundary #13', 'LINESTRING (0 0, 1 1)', None), ('boundary #14', 'MULTIPOLYGON EMPTY', []), ('control #15', '  POLYGON ((0 0, -3 0, -3 -3, 0 0))  ', [[[[0.0, 0.0], [-3.0, 0.0], [-3.0, -3.0], [0.0, 0.0]]]]), ('regression #16', 'MULTIPOLYGON Z (((0 0 1, 2 0 1, 2 2 1, 0 0 1)), ((9 9 0, 8 9 0, 8 8 0, 9 9 0)))', [[[[0.0, 0.0], [2.0, 0.0], [2.0, 2.0], [0.0, 0.0]]], [[[9.0, 9.0], [8.0, 9.0], [8.0, 8.0], [9.0, 9.0]]]])], [('control #0', 'POLYGON ((0 0, 4 0, 4 4, 0 4, 0 0))', [[[[0.0, 0.0], [4.0, 0.0], [4.0, 4.0], [0.0, 4.0], [0.0, 0.0]]]]), ('control #1', 'POLYGON ((0 0, 10 0, 10 10, 0 10, 0 0), (2 2, 2 4, 4 4, 2 2))', [[[[0.0, 0.0], [10.0, 0.0], [10.0, 10.0], [0.0, 10.0], [0.0, 0.0]], [[2.0, 2.0], [2.0, 4.0], [4.0, 4.0], [2.0, 2.0]]]]), ('boundary #5', 'POLYGON EMPTY', []), ('boundary #6', 'polygon empty', []), ('boundary #14', 'MULTIPOLYGON EMPTY', []), ('control #15', '  POLYGON ((0 0, -3 0, -3 -3, 0 0))  ', [[[[0.0, 0.0], [-3.0, 0.0], [-3.0, -3.0], [0.0, 0.0]]]]), ('regression #16', 'MULTIPOLYGON Z (((0 0 1, 2 0 1, 2 2 1, 0 0 1)), ((9 9 0, 8 9 0, 8 8 0, 9 9 0)))', [[[[0.0, 0.0], [2.0, 0.0], [2.0, 2.0], [0.0, 0.0]]], [[[9.0, 9.0], [8.0, 9.0], [8.0, 8.0], [9.0, 9.0]]]]), ('boundary #17', 'POLYGON ((0 0 1, 4 0 1, 4 4 1, 0 0 2))', [[[[0.0, 0.0], [4.0, 0.0], [4.0, 4.0], [0.0, 0.0]]]])]]
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)

prompt:
Empty polygons are rejected as malformed.

Input: a WKT string. The keyword (case-insensitive) must be POLYGON or MULTIPOLYGON, else None; "<keyword> EMPTY" returns []. Otherwise parse the parenthesised body into polygons -> rings -> positions, keeping only x and y of every position (Z/M ordinates are dropped). Every ring must have at least 4 positions and be closed in x/y, else None. Return a list of polygons (a POLYGON gives a one-element list).

split: open-access


source:
"""Failure Map reference implementation. Python standard library only."""
import json
import math
N = 1
observations = []
def solve(x):
    s = x.strip()
    up = s.upper()
    words = up.replace('(', ' ( ').split()
    if not words or words[0] not in ('POLYGON', 'MULTIPOLYGON'):
        return None
    if len(words) == 2 and words[1] == 'EMPTY':
        return []
    if '(' not in s:
        return None
    body = s[s.index('('):]
    stack = [[]]
    cur = ''
    for ch in body:
        if ch == '(':
            stack.append([])
        elif ch in '),':
            if cur.strip():
                nums = [float(t) for t in cur.split()]
                stack[-1].append(nums[:2])
            cur = ''
            if ch == ')':
                done = stack.pop()
                stack[-1].append(done)
        else:
            cur += ch
    tree = stack[0][0]
    polys = tree if words[0] == 'MULTIPOLYGON' and len(tree) > 1 else [tree]
    for poly in polys:
        for ring in poly:
            if len(ring) < 4 or ring[0] != ring[-1]:
                return None
    return polys
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('control #0', 'POLYGON ((0 0, 4 0, 4 4, 0 4, 0 0))', [[[[0.0, 0.0], [4.0, 0.0], [4.0, 4.0], [0.0, 4.0], [0.0, 0.0]]]]), ('control #1', 'POLYGON ((0 0, 10 0, 10 10, 0 10, 0 0), (2 2, 2 4, 4 4, 2 2))', [[[[0.0, 0.0], [10.0, 0.0], [10.0, 10.0], [0.0, 10.0], [0.0, 0.0]], [[2.0, 2.0], [2.0, 4.0], [4.0, 4.0], [2.0, 2.0]]]]), ('regression #2', 'POLYGON Z ((0 0 5, 4 0 5, 4 4 6, 0 0 5))', [[[[0.0, 0.0], [4.0, 0.0], [4.0, 4.0], [0.0, 0.0]]]]), ('regression #3', 'POLYGON ZM ((0 0 5 1, 4 0 5 2, 4 4 6 3, 0 0 5 1))', [[[[0.0, 0.0], [4.0, 0.0], [4.0, 4.0], [0.0, 0.0]]]]), ('regression #4', 'POLYGON M ((0 0 7, 4 0 8, 4 4 9, 0 0 7))', [[[[0.0, 0.0], [4.0, 0.0], [4.0, 4.0], [0.0, 0.0]]]]), ('boundary #5', 'POLYGON EMPTY', []), ('regression #7', 'MULTIPOLYGON (((0 0, 1 0, 1 1, 0 0)), ((5 5, 6 5, 6 6, 5 5), (5.2 5.1, 5.8 5.8, 5.8 5.1, 5.2 5.1)))', [[[[0.0, 0.0], [1.0, 0.0], [1.0, 1.0], [0.0, 0.0]]], [[[5.0, 5.0], [6.0, 5.0], [6.0, 6.0], [5.0, 5.0]], [[5.2, 5.1], [5.8, 5.8], [5.8, 5.1], [5.2, 5.1]]]]), ('regression #8', 'MULTIPOLYGON (((0 0, 1 0, 1 1, 0 0)))', [[[[0.0, 0.0], [1.0, 0.0], [1.0, 1.0], [0.0, 0.0]]]])], [('regression #3', 'POLYGON ZM ((0 0 5 1, 4 0 5 2, 4 4 6 3, 0 0 5 1))', [[[[0.0, 0.0], [4.0, 0.0], [4.0, 4.0], [0.0, 0.0]]]]), ('regression #4', 'POLYGON M ((0 0 7, 4 0 8, 4 4 9, 0 0 7))', [[[[0.0, 0.0], [4.0, 0.0], [4.0, 4.0], [0.0, 0.0]]]]), ('boundary #5', 'POLYGON EMPTY', []), ('boundary #6', 'polygon empty', []), ('regression #7', 'MULTIPOLYGON (((0 0, 1 0, 1 1, 0 0)), ((5 5, 6 5, 6 6, 5 5), (5.2 5.1, 5.8 5.8, 5.8 5.1, 5.2 5.1)))', [[[[0.0, 0.0], [1.0, 0.0], [1.0, 1.0], [0.0, 0.0]]], [[[5.0, 5.0], [6.0, 5.0], [6.0, 6.0], [5.0, 5.0]], [[5.2, 5.1], [5.8, 5.8], [5.8, 5.1], [5.2, 5.1]]]]), ('regression #8', 'MULTIPOLYGON (((0 0, 1 0, 1 1, 0 0)))', [[[[0.0, 0.0], [1.0, 0.0], [1.0, 1.0], [0.0, 0.0]]]]), ('regression #9', 'multipolygon (((-1.5 -2, 3e2 0, 0 1e1, -1.5 -2)))', [[[[-1.5, -2.0], [300.0, 0.0], [0.0, 10.0], [-1.5, -2.0]]]]), ('boundary #10', 'POLYGON ((0 0, 4 0, 4 4, 0 1))', None)], [('boundary #6', 'polygon empty', []), ('regression #7', 'MULTIPOLYGON (((0 0, 1 0, 1 1, 0 0)), ((5 5, 6 5, 6 6, 5 5), (5.2 5.1, 5.8 5.8, 5.8 5.1, 5.2 5.1)))', [[[[0.0, 0.0], [1.0, 0.0], [1.0, 1.0], [0.0, 0.0]]], [[[5.0, 5.0], [6.0, 5.0], [6.0, 6.0], [5.0, 5.0]], [[5.2, 5.1], [5.8, 5.8], [5.8, 5.1], [5.2, 5.1]]]]), ('regression #8', 'MULTIPOLYGON (((0 0, 1 0, 1 1, 0 0)))', [[[[0.0, 0.0], [1.0, 0.0], [1.0, 1.0], [0.0, 0.0]]]]), ('regression #9', 'multipolygon (((-1.5 -2, 3e2 0, 0 1e1, -1.5 -2)))', [[[[-1.5, -2.0], [300.0, 0.0], [0.0, 10.0], [-1.5, -2.0]]]]), ('boundary #10', 'POLYGON ((0 0, 4 0, 4 4, 0 1))', None), ('boundary #11', 'POLYGON ((0 0, 4 0, 0 0))', None), ('control #12', 'Polygon((1 1,5 1,5 5,1 1))', [[[[1.0, 1.0], [5.0, 1.0], [5.0, 5.0], [1.0, 1.0]]]]), ('boundary #13', 'LINESTRING (0 0, 1 1)', None)], [('regression #9', 'multipolygon (((-1.5 -2, 3e2 0, 0 1e1, -1.5 -2)))', [[[[-1.5, -2.0], [300.0, 0.0], [0.0, 10.0], [-1.5, -2.0]]]]), ('boundary #10', 'POLYGON ((0 0, 4 0, 4 4, 0 1))', None), ('boundary #11', 'POLYGON ((0 0, 4 0, 0 0))', None), ('control #12', 'Polygon((1 1,5 1,5 5,1 1))', [[[[1.0, 1.0], [5.0, 1.0], [5.0, 5.0], [1.0, 1.0]]]]), ('boundary #13', 'LINESTRING (0 0, 1 1)', None), ('boundary #14', 'MULTIPOLYGON EMPTY', []), ('control #15', '  POLYGON ((0 0, -3 0, -3 -3, 0 0))  ', [[[[0.0, 0.0], [-3.0, 0.0], [-3.0, -3.0], [0.0, 0.0]]]]), ('regression #16', 'MULTIPOLYGON Z (((0 0 1, 2 0 1, 2 2 1, 0 0 1)), ((9 9 0, 8 9 0, 8 8 0, 9 9 0)))', [[[[0.0, 0.0], [2.0, 0.0], [2.0, 2.0], [0.0, 0.0]]], [[[9.0, 9.0], [8.0, 9.0], [8.0, 8.0], [9.0, 9.0]]]])], [('control #0', 'POLYGON ((0 0, 4 0, 4 4, 0 4, 0 0))', [[[[0.0, 0.0], [4.0, 0.0], [4.0, 4.0], [0.0, 4.0], [0.0, 0.0]]]]), ('control #1', 'POLYGON ((0 0, 10 0, 10 10, 0 10, 0 0), (2 2, 2 4, 4 4, 2 2))', [[[[0.0, 0.0], [10.0, 0.0], [10.0, 10.0], [0.0, 10.0], [0.0, 0.0]], [[2.0, 2.0], [2.0, 4.0], [4.0, 4.0], [2.0, 2.0]]]]), ('regression #7', 'MULTIPOLYGON (((0 0, 1 0, 1 1, 0 0)), ((5 5, 6 5, 6 6, 5 5), (5.2 5.1, 5.8 5.8, 5.8 5.1, 5.2 5.1)))', [[[[0.0, 0.0], [1.0, 0.0], [1.0, 1.0], [0.0, 0.0]]], [[[5.0, 5.0], [6.0, 5.0], [6.0, 6.0], [5.0, 5.0]], [[5.2, 5.1], [5.8, 5.8], [5.8, 5.1], [5.2, 5.1]]]]), ('regression #8', 'MULTIPOLYGON (((0 0, 1 0, 1 1, 0 0)))', [[[[0.0, 0.0], [1.0, 0.0], [1.0, 1.0], [0.0, 0.0]]]]), ('boundary #14', 'MULTIPOLYGON EMPTY', []), ('control #15', '  POLYGON ((0 0, -3 0, -3 -3, 0 0))  ', [[[[0.0, 0.0], [-3.0, 0.0], [-3.0, -3.0], [0.0, 0.0]]]]), ('regression #16', 'MULTIPOLYGON Z (((0 0 1, 2 0 1, 2 2 1, 0 0 1)), ((9 9 0, 8 9 0, 8 8 0, 9 9 0)))', [[[[0.0, 0.0], [2.0, 0.0], [2.0, 2.0], [0.0, 0.0]]], [[[9.0, 9.0], [8.0, 9.0], [8.0, 8.0], [9.0, 9.0]]]]), ('boundary #17', 'POLYGON ((0 0 1, 4 0 1, 4 4 1, 0 0 2))', [[[[0.0, 0.0], [4.0, 0.0], [4.0, 4.0], [0.0, 0.0]]]])]]
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)

prompt:
Multipolygons are read as one polygon whose rings are polygons.

Input: a WKT string. The keyword (case-insensitive) must be POLYGON or MULTIPOLYGON, else None; "<keyword> EMPTY" returns []. Otherwise parse the parenthesised body into polygons -> rings -> positions, keeping only x and y of every position (Z/M ordinates are dropped). Every ring must have at least 4 positions and be closed in x/y, else None. Return a list of polygons (a POLYGON gives a one-element list).

split: open-access