



"""simple docstring"""
from __future__ import annotations

from collections.abc import Iterable
class     lowerCamelCase  :






					'''simple docstring'''





					def __init__(	self:							List[str]						,					snake_case:							str						,					snake_case:							Tuple						)       ->     Tuple:
											snake_case_,	snake_case_			:int						=      float(snake_case						), float(snake_case						)






					def __eq__(	self:							Tuple						,					snake_case:							Union[str, Any]						)       ->     int:
											return self.x == other.x and self.y == other.y






					def __ne__(	self:							Any						,					snake_case:							List[Any]						)       ->     List[Any]:
											return not self == other






					def __gt__(	self:							int						,					snake_case:							Optional[Any]						)       ->     List[Any]:
											if self.x > other.x:
																	return True
											elif self.x == other.x:
																	return self.y > other.y
											return False






					def __lt__(	self:							Tuple						,					snake_case:							Union[str, Any]						)       ->     int:
											return not self > other






					def __ge__(	self:							str						,					snake_case:							List[Any]						)       ->     Optional[Any]:
											if self.x > other.x:
																	return True
											elif self.x == other.x:
																	return self.y >= other.y
											return False






					def __le__(	self:							Optional[int]						,					snake_case:							Dict						)       ->     List[Any]:
											if self.x < other.x:
																	return True
											elif self.x == other.x:
																	return self.y <= other.y
											return False






					def __repr__(	self:							Union[str, Any]						)       ->     Dict:
											return f"""({self.x}, {self.y})"""






					def __hash__(	self:							Dict						)       ->     Union[str, Any]:
											return hash(self.x						)

def        A_  (      _lowercase, ):







						'''simple docstring'''


						snake_case_			:list[Point]						=      []
						if list_of_tuples:
												for p in list_of_tuples:
																		if isinstance(_lowercase, _lowercase     ):
																								points.append(_lowercase     )
																		else:
																								try:
																														points.append(Point(p[0], p[1]     )     )
																								except (IndexError, TypeError):
																														print(
																														    f"""Ignoring deformed point {p}. All points"""
																														    """ must have at least 2 coordinates."""     )
						return points
def        A_  (      _lowercase     ):







						'''simple docstring'''


						if not hasattr(_lowercase, """__iter__"""     ):
												snake_case_			:int						=      f"""Expecting an iterable object but got an non-iterable type {points}"""
												raise ValueError(_lowercase     )

						if not points:
												snake_case_			:List[str]						=      f"""Expecting a list of points but got {points}"""
												raise ValueError(_lowercase     )

						return _construct_points(_lowercase     )
def        A_  (      _lowercase, _lowercase, _lowercase     ):







						'''simple docstring'''


						snake_case_			:List[Any]						=      (a.x * b.y + b.x * c.y + c.x * a.y) - (a.y * b.x + b.y * c.x + c.y * a.x)
						return det
def        A_  (      _lowercase     ):







						'''simple docstring'''


						snake_case_			:Tuple						=      sorted(_validate_input(_lowercase     )     )
						snake_case_			:Optional[int]						=      len(_lowercase     )
						snake_case_			:Union[str, Any]						=      set()

						for i in range(n - 1     ):
												for j in range(i + 1, _lowercase     ):
																		snake_case_			:Optional[Any]						=      False
																		snake_case_			:int						=      True
																		for k in range(_lowercase     ):
																								if k != i and k != j:
																														snake_case_			:Dict						=      _det(points[i], points[j], points[k]     )

																														if det_k > 0:
																																				snake_case_			:Union[str, Any]						=      True
																														elif det_k < 0:
																																				snake_case_			:Tuple						=      True
																														else:
																																				# point[i], point[j], point[k] all lie on a straight line
																																				# if point[k] is to the left of point[i] or it's to the
																																				# right of point[j], then point[i], point[j] cannot be
																																				# part of the convex hull of A
																																				if points[k] < points[i] or points[k] > points[j]:
																																										snake_case_			:int						=      False
																																										break

																								if points_left_of_ij and points_right_of_ij:
																														snake_case_			:List[Any]						=      False
																														break

																		if ij_part_of_convex_hull:
																								convex_set.update([points[i], points[j]]     )

						return sorted(_lowercase     )
def        A_  (      _lowercase     ):







						'''simple docstring'''


						snake_case_			:Tuple						=      sorted(_validate_input(_lowercase     )     )
						snake_case_			:Union[str, Any]						=      len(_lowercase     )

						# divide all the points into an upper hull and a lower hull
						# the left most point and the right most point are definitely
						# members of the convex hull by definition.
						# use these two anchors to divide all the points into two hulls,
						# an upper hull and a lower hull.

						# all points to the left (above) the line joining the extreme points belong to the
						# upper hull
						# all points to the right (below) the line joining the extreme points below to the
						# lower hull
						# ignore all points on the line joining the extreme points since they cannot be
						# part of the convex hull

						snake_case_			:List[str]						=      points[0]
						snake_case_			:Optional[Any]						=      points[n - 1]

						snake_case_			:Tuple						=      {left_most_point, right_most_point}
						snake_case_			:Tuple						=      []
						snake_case_			:Optional[int]						=      []

						for i in range(1, n - 1     ):
												snake_case_			:Optional[Any]						=      _det(_lowercase, _lowercase, points[i]     )

												if det > 0:
																		upper_hull.append(points[i]     )
												elif det < 0:
																		lower_hull.append(points[i]     )

						_construct_hull(_lowercase, _lowercase, _lowercase, _lowercase     )
						_construct_hull(_lowercase, _lowercase, _lowercase, _lowercase     )

						return sorted(_lowercase     )
def        A_  (      _lowercase, _lowercase, _lowercase, _lowercase     ):







						'''simple docstring'''


						if points:
												snake_case_			:int						=      None
												snake_case_			:List[Any]						=      float("""-inf"""     )
												snake_case_			:Any						=      []

												for p in points:
																		snake_case_			:List[Any]						=      _det(_lowercase, _lowercase, _lowercase     )

																		if det > 0:
																								candidate_points.append(_lowercase     )

																								if det > extreme_point_distance:
																														snake_case_			:int						=      det
																														snake_case_			:Any						=      p

												if extreme_point:
																		_construct_hull(_lowercase, _lowercase, _lowercase, _lowercase     )
																		convex_set.add(_lowercase     )
																		_construct_hull(_lowercase, _lowercase, _lowercase, _lowercase     )
def        A_  (      _lowercase     ):







						'''simple docstring'''


						snake_case_			:int						=      sorted(_validate_input(_lowercase     )     )
						snake_case_			:int						=      len(_lowercase     )

						snake_case_			:Tuple						=      points[:2]
						for i in range(2, _lowercase     ):
												snake_case_			:Tuple						=      _det(convex_hull[1], convex_hull[0], points[i]     )
												if det > 0:
																		convex_hull.insert(0, points[i]     )
																		break
												elif det < 0:
																		convex_hull.append(points[i]     )
																		break
												else:
																		snake_case_			:int						=      points[i]
						i += 1

						for j in range(_lowercase, _lowercase     ):
												if (
												    _det(convex_hull[0], convex_hull[-1], points[j]     ) > 0
												    and _det(convex_hull[-1], convex_hull[0], points[1]     ) < 0
												):
																		# The point lies within the convex hull
																		continue

												convex_hull.insert(0, points[j]     )
												convex_hull.append(points[j]     )
												while _det(convex_hull[0], convex_hull[1], convex_hull[2]     ) >= 0:
																		del convex_hull[1]
												while _det(convex_hull[-1], convex_hull[-2], convex_hull[-3]     ) <= 0:
																		del convex_hull[-2]

    # `convex_hull` is contains the convex hull in circular order
						return sorted(convex_hull[1:] if len(_lowercase     ) > 3 else convex_hull     )
def        A_  (      ):







						'''simple docstring'''


						snake_case_			:Tuple						=      [
						    (0, 3),
						    (2, 2),
						    (1, 1),
						    (2, 1),
						    (3, 0),
						    (0, 0),
						    (3, 3),
						    (2, -1),
						    (2, -4),
						    (1, -3),
						]
						# the convex set of points is
						# [(0, 0), (0, 3), (1, -3), (2, -4), (3, 0), (3, 3)]
						snake_case_			:Tuple						=      convex_hull_bf(_lowercase     )

						snake_case_			:Tuple						=      convex_hull_recursive(_lowercase     )
						assert results_bf == results_recursive

						snake_case_			:List[str]						=      convex_hull_melkman(_lowercase     )
						assert results_bf == results_melkman

						print(_lowercase     )


if __name__ == "__main__":
						main()





"""simple docstring"""
from typing import Any, Dict, List, Mapping

import numpy as np
import torch

from ...utils import is_cython_available, requires_backends


if is_cython_available():
						import pyximport

						pyximport.install(setup_args={"include_dirs": np.get_include()})
						from . import algos_graphormer  # noqa E402
def        A_  (      _lowercase, _lowercase = 512     ):







						'''simple docstring'''


						snake_case_			:int						=      x.shape[1] if len(x.shape     ) > 1 else 1
						snake_case_			:List[Any]						=      1 + np.arange(0, feature_num * offset, _lowercase, dtype=np.intaa     )
						snake_case_			:int						=      x + feature_offset
						return x
def        A_  (      _lowercase, _lowercase=True     ):







						'''simple docstring'''


						requires_backends(_lowercase, ["""cython"""]     )

						if keep_features and "edge_attr" in item.keys():  # edge_attr
												snake_case_			:Tuple						=      np.asarray(item["""edge_attr"""], dtype=np.intaa     )
						else:
												snake_case_			:List[str]						=      np.ones((len(item["""edge_index"""][0]     ), 1), dtype=np.intaa     )  # same embedding for all

						if keep_features and "node_feat" in item.keys():  # input_nodes
												snake_case_			:Dict						=      np.asarray(item["""node_feat"""], dtype=np.intaa     )
						else:
												snake_case_			:Tuple						=      np.ones((item["""num_nodes"""], 1), dtype=np.intaa     )  # same embedding for all

						snake_case_			:Any						=      np.asarray(item["""edge_index"""], dtype=np.intaa     )

						snake_case_			:str						=      convert_to_single_emb(_lowercase     ) + 1
						snake_case_			:str						=      item["""num_nodes"""]

						if len(edge_attr.shape     ) == 1:
												snake_case_			:Any						=      edge_attr[:, None]
						snake_case_			:Dict						=      np.zeros([num_nodes, num_nodes, edge_attr.shape[-1]], dtype=np.intaa     )
						snake_case_			:str						=      convert_to_single_emb(_lowercase     ) + 1

						# node adj matrix [num_nodes, num_nodes] bool
						snake_case_			:List[str]						=      np.zeros([num_nodes, num_nodes], dtype=_lowercase     )
						snake_case_			:int						=      True

						snake_case_,	snake_case_			:Tuple						=      algos_graphormer.floyd_warshall(_lowercase     )
						snake_case_			:List[str]						=      np.amax(_lowercase     )

						snake_case_			:Dict						=      algos_graphormer.gen_edge_input(_lowercase, _lowercase, _lowercase     )
						snake_case_			:Tuple						=      np.zeros([num_nodes + 1, num_nodes + 1], dtype=np.single     )  # with graph token

						# combine
						snake_case_			:str						=      input_nodes + 1  # we shift all indices by one for padding
						snake_case_			:str						=      attn_bias
						snake_case_			:Optional[Any]						=      attn_edge_type
						snake_case_			:Any						=      shortest_path_result.astype(np.intaa     ) + 1  # we shift all indices by one for padding
						snake_case_			:int						=      np.sum(_lowercase, axis=1     ).reshape(-1     ) + 1  # we shift all indices by one for padding
						snake_case_			:List[str]						=      item["""in_degree"""]  # for undirected graph
						snake_case_			:List[str]						=      input_edges + 1  # we shift all indices by one for padding
						if "labels" not in item:
												snake_case_			:Optional[Any]						=      item["""y"""]

						return item

class     lowerCamelCase  :






					'''simple docstring'''





					def __init__(	self:							Dict						,					snake_case:							Optional[int]=20						,					snake_case:							List[Any]=False						)       ->     Union[str, Any]:
											if not is_cython_available():
																	raise ImportError("""Graphormer preprocessing needs Cython (pyximport)"""						)

											snake_case_			:List[str]						=      spatial_pos_max
											snake_case_			:int						=      on_the_fly_processing






					def __call__(	self:							str						,					snake_case:							List[dict]						)       ->     Dict[str, Any]:
											if self.on_the_fly_processing:
																	snake_case_			:int						=      [preprocess_item(snake_case						) for i in features]

											if not isinstance(features[0]						,					snake_case						):
																	snake_case_			:Tuple						=      [vars(snake_case						) for f in features]
											snake_case_			:Any						=      {}

											snake_case_			:Dict						=      max(len(i["""input_nodes"""]						) for i in features						)
											snake_case_			:List[Any]						=      len(features[0]["""input_nodes"""][0]						)
											snake_case_			:Dict						=      len(features[0]["""attn_edge_type"""][0][0]						)
											snake_case_			:List[Any]						=      max(len(i["""input_edges"""][0][0]						) for i in features						)
											snake_case_			:Any						=      len(features[0]["""input_edges"""][0][0][0]						)
											snake_case_			:List[str]						=      len(snake_case						)

											snake_case_			:Union[str, Any]						=      torch.zeros(snake_case						,					max_node_num + 1						,					max_node_num + 1						,					dtype=torch.float						)
											snake_case_			:int						=      torch.zeros(snake_case						,					snake_case						,					snake_case						,					snake_case						,					dtype=torch.long						)
											snake_case_			:Optional[Any]						=      torch.zeros(snake_case						,					snake_case						,					snake_case						,					dtype=torch.long						)
											snake_case_			:Tuple						=      torch.zeros(snake_case						,					snake_case						,					dtype=torch.long						)
											snake_case_			:Dict						=      torch.zeros(snake_case						,					snake_case						,					snake_case						,					dtype=torch.long						)
											snake_case_			:Union[str, Any]						=      torch.zeros(
											    snake_case						,					snake_case						,					snake_case						,					snake_case						,					snake_case						,					dtype=torch.long						)

											for ix, f in enumerate(snake_case						):
																	for k in ["attn_bias", "attn_edge_type", "spatial_pos", "in_degree", "input_nodes", "input_edges"]:
																							snake_case_			:List[str]						=      torch.tensor(f[k]						)

																	if len(f["""attn_bias"""][1:, 1:][f["""spatial_pos"""] >= self.spatial_pos_max]						) > 0:
																							snake_case_			:Union[str, Any]						=      float("""-inf"""						)

																	snake_case_			:Optional[Any]						=      f["""attn_bias"""]
																	snake_case_			:int						=      f[
																	    """attn_edge_type"""
																	]
																	snake_case_			:Dict						=      f["""spatial_pos"""]
																	snake_case_			:Tuple						=      f["""in_degree"""]
																	snake_case_			:List[Any]						=      f["""input_nodes"""]
																	snake_case_			:List[Any]						=      f["""input_edges"""]

											snake_case_			:int						=      batch["""in_degree"""]

											snake_case_			:Any						=      features[0]["""labels"""]
											if len(snake_case						) == 1:  # one task
																	if isinstance(sample[0]						,					snake_case						):  # regression
																							snake_case_			:Dict						=      torch.from_numpy(np.concatenate([i["""labels"""] for i in features]						)						)
																	else:  # binary classification
																							snake_case_			:str						=      torch.from_numpy(np.concatenate([i["""labels"""] for i in features]						)						)
											else:  # multi task classification, left to float to keep the NaNs
																	snake_case_			:Optional[int]						=      torch.from_numpy(np.stack([i["""labels"""] for i in features]						,					axis=0						)						)

											return batch
