from __future__ import annotations

from random import random
from typing import Generic, TypeVar

lowerCamelCase_    :		List[str]							=	TypeVar("""KT""")
lowerCamelCase_    :		Optional[Any]							=	TypeVar("""VT""")


class 						a__							(       Generic[KT, VT]		):



			def __init__(						self				,						UpperCAmelCase = "root"				,						UpperCAmelCase = None   )			->   Optional[Any]:
								__a		 =       key
								__a		 =       value
								__a		 =       []



			def __repr__(						self   )			->   str:
								return f'''Node({self.key}: {self.value})'''







			@property
			def __SCREAMING_SNAKE_CASE							(						self   )			->   int:
								return len(self.forward   )






class 						a__							(       Generic[KT, VT]		):



			def __init__(						self				,						UpperCAmelCase = 0.5				,						UpperCAmelCase = 1_6   )			->   Any:
								__a		 =       Node[KT, VT]()
								__a		 =       0
								__a		 =       p
								__a		 =       max_level



			def __str__(						self   )			->   str:
								__a		 =       list(self   )

								if len(UpperCAmelCase   ) == 0:
													return f'''SkipList(level={self.level})'''

								__a		 =       max((len(str(UpperCAmelCase   )   ) for item in items)				,						default=4   )
								__a		 =       max(UpperCAmelCase				,						4   ) + 4

								__a		 =       self.head
								__a		 =       []

								__a		 =       node.forward.copy()
								lines.append(f'''[{node.key}]'''.ljust(UpperCAmelCase				,						'-'   ) + '* ' * len(UpperCAmelCase   )   )
								lines.append(' ' * label_size + '| ' * len(UpperCAmelCase   )   )

								while len(node.forward   ) != 0:
													__a		 =       node.forward[0]

													lines.append(
													    f'''[{node.key}]'''.ljust(UpperCAmelCase				,						'-'   )
													    + ' '.join(str(n.key   ) if n.key == node.key else '|' for n in forwards   )   )
													lines.append(' ' * label_size + '| ' * len(UpperCAmelCase   )   )
													__a		 =       node.forward

								lines.append('None'.ljust(UpperCAmelCase   ) + '* ' * len(UpperCAmelCase   )   )
								return f'''SkipList(level={self.level})\n''' + "\n".join(UpperCAmelCase   )



			def __iter__(						self   )			->   str:
								__a		 =       self.head

								while len(node.forward   ) != 0:
													yield node.forward[0].key
													__a		 =       node.forward[0]



			def __SCREAMING_SNAKE_CASE							(						self   )			->   int:
								__a		 =       1
								while random() < self.p and level < self.max_level:
													level += 1

								return level



			def __SCREAMING_SNAKE_CASE							(						self				,						UpperCAmelCase   )			->   tuple[Node[KT, VT] | None, list[Node[KT, VT]]]:
								__a		 =       []

								__a		 =       self.head

								for i in reversed(range(self.level   )   ):
													# i < node.level - When node level is lesser than `i` decrement `i`.
													# node.forward[i].key < key - Jumping to node with key value higher
													#                             or equal to searched key would result
													#                             in skipping searched key.
													while i < node.level and node.forward[i].key < key:
																		__a		 =       node.forward[i]
													# Each leftmost node (relative to searched node) will potentially have to
													# be updated.
													update_vector.append(UpperCAmelCase   )

								update_vector.reverse()  # Note that we were inserting values in reverse order.

								# len(node.forward) != 0 - If current node doesn't contain any further
								#                          references then searched key is not present.
								# node.forward[0].key == key - Next node key should be equal to search key
								#                              if key is present.
								if len(node.forward   ) != 0 and node.forward[0].key == key:
													return node.forward[0], update_vector
								else:
													return None, update_vector



			def __SCREAMING_SNAKE_CASE							(						self				,						UpperCAmelCase   )			->   Optional[int]:
								__a ,				__a		 =       self._locate_node(UpperCAmelCase   )

								if node is not None:
													for i, update_node in enumerate(UpperCAmelCase   ):
																		# Remove or replace all references to removed node.
																		if update_node.level > i and update_node.forward[i].key == key:
																							if node.level > i:
																												__a		 =       node.forward[i]
																							else:
																												__a		 =       update_node.forward[:i]



			def __SCREAMING_SNAKE_CASE							(						self				,						UpperCAmelCase				,						UpperCAmelCase   )			->   List[Any]:
								__a ,				__a		 =       self._locate_node(UpperCAmelCase   )
								if node is not None:
													__a		 =       value
								else:
													__a		 =       self.random_level()

													if level > self.level:
																		# After level increase we have to add additional nodes to head.
																		for _ in range(self.level - 1				,						UpperCAmelCase   ):
																							update_vector.append(self.head   )
																		__a		 =       level

													__a		 =       Node(UpperCAmelCase				,						UpperCAmelCase   )

													for i, update_node in enumerate(update_vector[:level]   ):
																		# Change references to pass through new node.
																		if update_node.level > i:
																							new_node.forward.append(update_node.forward[i]   )

																		if update_node.level < i + 1:
																							update_node.forward.append(UpperCAmelCase   )
																		else:
																							__a		 =       new_node







			def __SCREAMING_SNAKE_CASE							(						self				,						UpperCAmelCase   )			->   VT | None:
								__a ,				__a		 =       self._locate_node(UpperCAmelCase   )

								if node is not None:
													return node.value

								return None






def 							lowerCAmelCase(     ):
					__a		 =       SkipList()
					skip_list.insert('Key1'				,    3						)
					skip_list.insert('Key2'				,    12						)
					skip_list.insert('Key3'				,    41						)
					skip_list.insert('Key4'				,    -19						)

					__a		 =       skip_list.head
					__a		 =       {}
					while node.level != 0:
										__a		 =       node.forward[0]
										__a		 =       node.value

					assert len(__lowerCamelCase						) == 4
					assert all_values["Key1"] == 3
					assert all_values["Key2"] == 12
					assert all_values["Key3"] == 41
					assert all_values["Key4"] == -19
def 							lowerCAmelCase(     ):
					__a		 =       SkipList()
					skip_list.insert('Key1'				,    10						)
					skip_list.insert('Key1'				,    12						)

					skip_list.insert('Key5'				,    7						)
					skip_list.insert('Key7'				,    10						)
					skip_list.insert('Key10'				,    5						)

					skip_list.insert('Key7'				,    7						)
					skip_list.insert('Key5'				,    5						)
					skip_list.insert('Key10'				,    10						)

					__a		 =       skip_list.head
					__a		 =       {}
					while node.level != 0:
										__a		 =       node.forward[0]
										__a		 =       node.value

					if len(__lowerCamelCase						) != 4:
										print()
					assert len(__lowerCamelCase						) == 4
					assert all_values["Key1"] == 12
					assert all_values["Key7"] == 7
					assert all_values["Key5"] == 5
					assert all_values["Key10"] == 10
def 							lowerCAmelCase(     ):
					__a		 =       SkipList()
					assert skip_list.find('Some key'						) is None
def 							lowerCAmelCase(     ):
					__a		 =       SkipList()

					skip_list.insert('Key2'				,    20						)
					assert skip_list.find('Key2'						) == 20

					skip_list.insert('Some Key'				,    10						)
					skip_list.insert('Key2'				,    8						)
					skip_list.insert('V'				,    13						)

					assert skip_list.find('Y'						) is None
					assert skip_list.find('Key2'						) == 8
					assert skip_list.find('Some Key'						) == 10
					assert skip_list.find('V'						) == 13
def 							lowerCAmelCase(     ):
					__a		 =       SkipList()
					skip_list.delete('Some key'						)

					assert len(skip_list.head.forward						) == 0
def 							lowerCAmelCase(     ):
					__a		 =       SkipList()

					skip_list.insert('Key1'				,    12						)
					skip_list.insert('V'				,    13						)
					skip_list.insert('X'				,    14						)
					skip_list.insert('Key2'				,    15						)

					skip_list.delete('V'						)
					skip_list.delete('Key2'						)

					assert skip_list.find('V'						) is None
					assert skip_list.find('Key2'						) is None
def 							lowerCAmelCase(     ):
					__a		 =       SkipList()

					skip_list.insert('Key1'				,    12						)
					skip_list.insert('V'				,    13						)
					skip_list.insert('X'				,    14						)
					skip_list.insert('Key2'				,    15						)

					skip_list.delete('V'						)
					assert skip_list.find('V'						) is None
					assert skip_list.find('X'						) == 14
					assert skip_list.find('Key1'						) == 12
					assert skip_list.find('Key2'						) == 15

					skip_list.delete('X'						)
					assert skip_list.find('V'						) is None
					assert skip_list.find('X'						) is None
					assert skip_list.find('Key1'						) == 12
					assert skip_list.find('Key2'						) == 15

					skip_list.delete('Key1'						)
					assert skip_list.find('V'						) is None
					assert skip_list.find('X'						) is None
					assert skip_list.find('Key1'						) is None
					assert skip_list.find('Key2'						) == 15

					skip_list.delete('Key2'						)
					assert skip_list.find('V'						) is None
					assert skip_list.find('X'						) is None
					assert skip_list.find('Key1'						) is None
					assert skip_list.find('Key2'						) is None
def 							lowerCAmelCase(     ):
					__a		 =       SkipList()

					skip_list.insert('Key1'				,    12						)
					skip_list.insert('V'				,    13						)
					skip_list.insert('X'				,    142						)
					skip_list.insert('Key2'				,    15						)

					skip_list.delete('X'						)

					def traverse_keys(__lowerCamelCase						):
										yield node.key
										for forward_node in node.forward:
															yield from traverse_keys(__lowerCamelCase						)

					assert len(set(traverse_keys(skip_list.head						)						)						) == 4
def 							lowerCAmelCase(     ):
					def is_sorted(__lowerCamelCase						):
										return all(next_item >= item for item, next_item in zip(__lowerCamelCase				,    lst[1:]						)						)

					__a		 =       SkipList()
					for i in range(10						):
										skip_list.insert(__lowerCamelCase				,    __lowerCamelCase						)
					assert is_sorted(list(__lowerCamelCase						)						)
					skip_list.delete(5						)
					skip_list.delete(8						)
					skip_list.delete(2						)
					assert is_sorted(list(__lowerCamelCase						)						)
					skip_list.insert(-12				,    -12						)
					skip_list.insert(77				,    77						)
					assert is_sorted(list(__lowerCamelCase						)						)
def 							lowerCAmelCase(     ):
					for _ in range(100						):
										# Repeat test 100 times due to the probabilistic nature of skip list
										# random values == random bugs
										test_insert()
										test_insert_overrides_existing_value()

										test_searching_empty_list_returns_none()
										test_search()

										test_deleting_item_from_empty_list_do_nothing()
										test_deleted_items_are_not_founded_by_find_method()
										test_delete_removes_only_given_key()
										test_delete_doesnt_leave_dead_nodes()

										test_iter_always_yields_sorted_values()
def 							lowerCAmelCase(     ):
					__a		 =       SkipList()
					skip_list.insert(2				,    '2'						)
					skip_list.insert(4				,    '4'						)
					skip_list.insert(6				,    '4'						)
					skip_list.insert(4				,    '5'						)
					skip_list.insert(8				,    '4'						)
					skip_list.insert(9				,    '4'						)

					skip_list.delete(4						)

					print(__lowerCamelCase						)


if __name__ == "__main__":
	import doctest

	doctest.testmod()
	main()





import numpy as np
from sklearn.datasets import fetch_california_housing
from sklearn.metrics import mean_absolute_error, mean_squared_error
from sklearn.model_selection import train_test_split
from xgboost import XGBRegressor
def 							lowerCAmelCase(     __lowerCamelCase						):
					return (data["data"], data["target"])
def 							lowerCAmelCase(     __lowerCamelCase				,    __lowerCamelCase				,    __lowerCamelCase						):
					__a		 =       XGBRegressor(verbosity=0				,    random_state=42						)
					xgb.fit(__lowerCamelCase				,    __lowerCamelCase						)
					# Predict target for test data
					__a		 =       xgb.predict(__lowerCamelCase						)
					__a		 =       predictions.reshape(len(__lowerCamelCase						)				,    1						)
					return predictions
def 							lowerCAmelCase(     ):
					__a		 =       fetch_california_housing()
					__a ,				__a		 =       data_handling(__lowerCamelCase						)
					__a ,				__a ,				__a ,				__a		 =       train_test_split(
					    __lowerCamelCase				,    __lowerCamelCase				,    test_size=0.25				,    random_state=1						)
					__a		 =       xgboost(__lowerCamelCase				,    __lowerCamelCase				,    __lowerCamelCase						)
					# Error printing
					print(f'''Mean Absolute Error : {mean_absolute_error(__lowerCamelCase				,    __lowerCamelCase						)}'''						)
					print(f'''Mean Square Error  : {mean_squared_error(__lowerCamelCase				,    __lowerCamelCase						)}'''						)


if __name__ == "__main__":
	import doctest

	doctest.testmod(verbose=True)
	main()




