227 lines
7.3 KiB
Python
227 lines
7.3 KiB
Python
from bisect import bisect_left, bisect_right,insort
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import unittest
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from collections import namedtuple
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import math
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def find_intersections(horizontal_segments, vertical_segments, epsilon=0.0):
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horizontal_segments.sort(key=lambda h: h[0][1]) # sortiere nach y
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horizontal_ys = []
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horizontal_x_ranges = []
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for (x1, y), (x2, _) in horizontal_segments:
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if x1 > x2:
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x1, x2 = x2, x1
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horizontal_ys.append(y)
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horizontal_x_ranges.append((x1, x2))
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intersections = []
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for (x, y1), (_, y2) in vertical_segments:
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if y1 > y2:
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y1, y2 = y2, y1
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for idx, y in enumerate(horizontal_ys):
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if y1 - epsilon <= y <= y2 + epsilon:
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x_start, x_end = horizontal_x_ranges[idx]
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if x_start - epsilon <= x <= x_end + epsilon:
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intersections.append((x, y))
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return intersections
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Point = namedtuple('Point', ['x', 'y'])
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Segment = namedtuple('Segment', ['p1', 'p2'])
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def ccw(a, b, c):
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return (c.y - a.y) * (b.x - a.x) > (b.y - a.y) * (c.x - a.x)
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def intersect(s1, s2, tol=1e-8):
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"""Erweiterte Schnittprüfung mit Toleranz."""
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# Klassische Schnitttest
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a, b = s1.p1, s1.p2
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c, d = s2.p1, s2.p2
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if ccw(a, c, d) != ccw(b, c, d) and ccw(a, b, c) != ccw(a, b, d):
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return True
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# Zusätzliche Toleranzprüfung: Mindestabstand der Segmente
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return segment_distance(s1, s2) < tol
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def point_distance(p1, p2):
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return math.hypot(p1.x - p2.x, p1.y - p2.y)
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def point_segment_distance(p, seg):
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"""Abstand eines Punkts zu einem Segment."""
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x, y = p.x, p.y
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x1, y1 = seg.p1.x, seg.p1.y
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x2, y2 = seg.p2.x, seg.p2.y
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dx, dy = x2 - x1, y2 - y1
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if dx == dy == 0:
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return point_distance(p, seg.p1)
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t = max(0, min(1, ((x - x1) * dx + (y - y1) * dy) / (dx * dx + dy * dy)))
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nearest = Point(x1 + t * dx, y1 + t * dy)
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return point_distance(p, nearest)
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def segment_distance(s1, s2):
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"""Kleinster Abstand zweier Segmente."""
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return min(
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point_segment_distance(s1.p1, s2),
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point_segment_distance(s1.p2, s2),
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point_segment_distance(s2.p1, s1),
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point_segment_distance(s2.p2, s1),
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)
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def segment_cmp_x(segment, x):
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p1, p2 = segment.p1, segment.p2
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if p1.x == p2.x:
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return min(p1.y, p2.y)
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slope = (p2.y - p1.y) / (p2.x - p1.x)
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y = p1.y + slope * (x - p1.x)
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return y
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def schnittpunkttest(segments, tolerance=1e-8):
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events = []
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for seg in segments:
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left = seg.p1 if seg.p1.x < seg.p2.x else seg.p2
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right = seg.p2 if seg.p1.x < seg.p2.x else seg.p1
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events.append((left.x, True, seg))
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events.append((right.x, False, seg))
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events.sort()
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L = []
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for x, is_left, seg in events:
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key = lambda s: segment_cmp_x(s, x)
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idx = bisect_left(L, seg, key=key)
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if is_left:
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insort(L, seg, key=key)
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idx = bisect_left(L, seg, key=key)
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pred = L[idx - 1] if idx > 0 else None
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succ = L[idx + 1] if idx < len(L) - 1 else None
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if (pred and intersect(pred, seg, tolerance)) or (succ and intersect(succ, seg, tolerance)):
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#print("ja")
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return
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else:
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idx = bisect_left(L, seg, key=key)
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if idx < len(L) and L[idx] == seg:
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pred = L[idx - 1] if idx > 0 else None
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succ = L[idx + 1] if idx < len(L) - 1 else None
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L.pop(idx)
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if pred and succ and intersect(pred, succ, tolerance):
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#print("ja")
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return
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#print("nein")
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def sektionen(segmente, tolerance):
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laenge = len(segmente)
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lseg = list()
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for r1 in range(laenge):
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s1 = segmente[r1]
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p1 = Point(s1[0][0],s1[0][1])
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p2 = Point(s1[1][0],s1[1][1])
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seg1 = Segment( p1, p2 )
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lseg.append(seg1)
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schnittpunkttest(lseg, tolerance)
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# class TestSweepMethods(unittest.TestCase):
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# def test_sweep(self):
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# horizontal = [((1, 2), (5, 2)), ((3, 4), (7, 4))]
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# vertical = [((4, 1), (4, 5)), ((6, 3), (6, 6))]
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# a = find_intersections(horizontal, vertical)
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# self.assertEqual( [(4,2),(4,4),(6,4)], a)
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# def test_tol_hor(self):
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# """Testet die Anzahl der Schnittpunkte bei gegebener Toleranz
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# schnittpunkt zwischen gegebener horizontalen und zu kurzen vertikalen
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# """
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# horizontal = [((0, 0), (10, 0))]
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# vertical = [((4, 0.6), (4, 5)), ((6, 0.2), (6, 6)),((8,-0.2),(8, 4))]
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# b = find_intersections(horizontal, vertical, 0.5)
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# self.assertEqual( len(b), 2)
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# self.assertEqual( [(6,0),(8,0)], b)
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# def test_tol_ver(self):
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# """Testet die Anzahl der Schnittpunkte bei gegebener Toleranz
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# schnittpunkt zwischen gegebener vertikalen und zu kurzen horizontalen
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# """
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# horizontal = [((0.2, 0), (9.8, 0))]
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# vertical = [((0, 0), (0, 10)), ((10, 0), (10, 10))]
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# b = find_intersections(horizontal, vertical, 0.5)
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# self.assertEqual( len(b), 2)
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# self.assertEqual( [(6,0),(8,0)], b)
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# def test_tol_diag(self):
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# """Testet die Anzahl der Schnittpunkte bei gegebener Toleranz
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# Horizontale mit Diagonalen
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# """
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# horizontal = [((0, 0), (5, 0))]
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# diagonal = [((0, -5), (10, 5))]
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# b = find_intersections(horizontal, diagonal, 0.5)
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# self.assertEqual( len(b), 1)
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# self.assertEqual( [(0,0),(0,0)], b)
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class TestScanLineAllgMethods(unittest.TestCase):
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# def test_sweep(self):
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# seks = [((1, 2), (5, 2)), ((3, 4), (7, 4)), ((4, 1), (4, 5)), ((6, 3), (6, 6))]
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# a = sektionen(seks)
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# self.assertEqual( [(4,2),(4,4),(6,4)], a)
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# def test_tol_hor(self):
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# """Testet die Anzahl der Schnittpunkte bei gegebener Toleranz
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# schnittpunkt zwischen gegebener horizontalen und zu kurzen vertikalen
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# """
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# seks = [((0, 0), (10, 0)), ((4, 0.6), (4, 5)), ((6, 0.2), (6, 6)),((8,-0.2),(8, 4))]
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# b = sektionen(seks, 0.5)
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# self.assertEqual( len(b), 2)
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# self.assertEqual( [(6,0),(8,0)], b)
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# def test_tol_ver(self):
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# """Testet die Anzahl der Schnittpunkte bei gegebener Toleranz
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# schnittpunkt zwischen gegebener vertikalen und zu kurzen horizontalen
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# """
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# seks = [((0.2, 0), (9.8, 0)), ((0, 0), (0, 10)), ((10, 0), (10, 10))]
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# b = sektionen(seks, 0.5)
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# self.assertEqual( len(b), 2)
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# self.assertEqual( [(6,0),(8,0)], b)
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# def test_tol_diag(self):
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# """Testet die Anzahl der Schnittpunkte bei gegebener Toleranz
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# Horizontale mit Diagonalen
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# """
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# seks = [((0, 0), (5, 0)), ((0, -5), (10, 5))]
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# b = sektionen(seks, 0.5)
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# self.assertEqual( len(b), 1)
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# self.assertEqual( [(6,0),(8,0)], b)
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def test_chatgpt(self):
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s1 = Segment(Point(0, 0), Point(4, 4)) # Diagonale
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s2 = Segment(Point(0, 4), Point(4, 0)) # Kreuzt s1 → Schnitt
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s3 = Segment(Point(5, 5), Point(6, 6)) # Weit entfernt, kein Schnitt
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s4 = Segment(Point(1, 1), Point(1, 3)) # Schneidet s1 → weiterer Schnitt
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schnittpunkttest([s1, s2, s3, s4], tolerance=1e-8) # Ausgabe: ja
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if __name__ == '__main__':
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unittest.main() |