def delaunay(cls, points: Sequence[Point], *,
context: Context) -> 'Triangulation':
"""
Constructs Delaunay triangulation of given points.
Based on divide-and-conquer algorithm by L. Guibas & J. Stolfi.
Time complexity:
``O(len(points) * log len(points))``
Memory complexity:
``O(len(points))``
Reference:
http://www.sccg.sk/~samuelcik/dgs/quad_edge.pdf
:param points: 3 or more points to triangulate.
:param context: geometric context.
:returns: triangulation of the points.
"""
points = sorted(to_distinct(points))
lengths = coin_change(len(points), base_cases)
result = [
cls._initialize_triangulation(points[start:stop], context)
for start, stop in pairwise(accumulate((0, ) + lengths))
]
for _ in repeat(None, ceil_log2(len(result))):
parts_to_merge_count = len(result) // 2 * 2
result = ([
merge(result[offset], result[offset + 1])
for offset in range(0, parts_to_merge_count, 2)
] + result[parts_to_merge_count:])
return result[0]
def from_points(cls, points: Iterable[Point]) -> 'Triangulation':
points = sorted(to_unique_objects(points))
lengths = coin_change(len(points), _initializers)
result = [
_initialize_triangulation(points[start:stop])
for start, stop in pairwise(accumulate(chain((0, ), lengths)))
]
for _ in repeat(None, ceil_log2(len(result))):
parts_to_merge_count = len(result) // 2 * 2
result = ([
result[offset]._merge_with(result[offset + 1])
for offset in range(0, parts_to_merge_count, 2)
] + result[parts_to_merge_count:])
return result[0]
def delaunay(cls, points: Sequence[Point],
context: Context) -> 'Triangulation':
"""Constructs Delaunay triangulation from given points."""
points = sorted(points)
result = [
cls._initialize_triangulation(points[start:stop], context)
for start, stop in pairwise(
accumulate(chain((
0, ), coin_change(len(points), _base_cases))))
]
for _ in repeat(None, ceil_log2(len(result))):
parts_to_merge_count = len(result) // 2 * 2
result = ([
result[offset]._merge(result[offset + 1])
for offset in range(0, parts_to_merge_count, 2)
] + result[parts_to_merge_count:])
return result[0]
def test_invalid_denominations(amount: int, denominations: List[int]) -> None:
with pytest.raises(ValueError):
coin_change(amount, denominations)
def test_properties(amount: int, denominations: List[int]) -> None:
result = coin_change(amount, denominations)
assert sum(result) >= amount
assert len(result) <= ceil_division(amount, min(denominations))
def test_elements(amount: int, denominations: List[int]) -> None:
result = coin_change(amount, denominations)
assert all(element in denominations for element in result)
def test_basic(amount: int, denominations: List[int]) -> None:
result = coin_change(amount, denominations)
assert isinstance(result, tuple)
assert all(isinstance(element, int) for element in result)