




from __future__ import annotations

from collections.abc import Callable
from typing import Any, Generic, TypeVar

a													=			TypeVar("T")




class       _A				(		Generic[T]     ):






		def __init__(    self						,		_SCREAMING_SNAKE_CASE						,		_SCREAMING_SNAKE_CASE			):
								_UpperCAmelCase      =			None

								_UpperCAmelCase      =			len(_SCREAMING_SNAKE_CASE			)
								_UpperCAmelCase      =			[any_type for _ in range(self.N			)] + arr
								_UpperCAmelCase      =			fnc
								self.build()






		def 				UpperCAmelCase (    self			):
								for p in range(self.N - 1						,		0						,		-1			):
														_UpperCAmelCase      =			self.fn(self.st[p * 2]						,		self.st[p * 2 + 1]			)






		def 				UpperCAmelCase (    self						,		_SCREAMING_SNAKE_CASE						,		_SCREAMING_SNAKE_CASE			):
								p += self.N
								_UpperCAmelCase      =			v
								while p > 1:
														_UpperCAmelCase      =			p // 2
														_UpperCAmelCase      =			self.fn(self.st[p * 2]						,		self.st[p * 2 + 1]			)






		def 				UpperCAmelCase (    self						,		_SCREAMING_SNAKE_CASE						,		_SCREAMING_SNAKE_CASE			):  # noqa: E741
								_UpperCAmelCase    ,					_UpperCAmelCase      =			l + self.N, r + self.N

								_UpperCAmelCase      =			None
								while l <= r:
														if l % 2 == 1:
																				_UpperCAmelCase      =			self.st[l] if res is None else self.fn(_SCREAMING_SNAKE_CASE						,		self.st[l]			)
														if r % 2 == 0:
																				_UpperCAmelCase      =			self.st[r] if res is None else self.fn(_SCREAMING_SNAKE_CASE						,		self.st[r]			)
														_UpperCAmelCase    ,					_UpperCAmelCase      =			(l + 1) // 2, (r - 1) // 2
								return res


if __name__ == "__main__":
						from functools import reduce

						a													=			[1, 10, -2, 9, -3, 8, 4, -7, 5, 6, 11, -12]

						a													=			{
						    0: 7,
						    1: 2,
						    2: 6,
						    3: -14,
						    4: 5,
						    5: 4,
						    6: 7,
						    7: -10,
						    8: 9,
						    9: 10,
						    10: 12,
						    11: 1,
						}

						a													=			SegmentTree(test_array, min)
						a													=			SegmentTree(test_array, max)
						a													=			SegmentTree(test_array, lambda a, b: a + b)




						def        _SCREAMING_SNAKE_CASE      (		)						->				Optional[Any]:






												for i in range(len(_snake_case       )       ):
																		for j in range(_snake_case			,     len(_snake_case       )       ):
																								_UpperCAmelCase      =			reduce(_snake_case			,     test_array[i : j + 1]       )
																								_UpperCAmelCase      =			reduce(_snake_case			,     test_array[i : j + 1]       )
																								_UpperCAmelCase      =			reduce(lambda snake_case			,     snake_case       : a + b			,     test_array[i : j + 1]       )
																								assert min_range == min_segment_tree.query(_snake_case			,     _snake_case       )
																								assert max_range == max_segment_tree.query(_snake_case			,     _snake_case       )
																								assert sum_range == sum_segment_tree.query(_snake_case			,     _snake_case       )

						test_all_segments()

						for index, value in test_updates.items():
												a													=			value
												min_segment_tree.update(index, value)
												max_segment_tree.update(index, value)
												sum_segment_tree.update(index, value)
												test_all_segments()





# Logistic Regression from scratch

# In[62]:

# In[63]:

# importing all the required libraries

import numpy as np
from matplotlib import pyplot as plt
from sklearn import datasets




def        _SCREAMING_SNAKE_CASE      (		snake_case       )						->				List[str]:
						return 1 / (1 + np.exp(-z       ))




def        _SCREAMING_SNAKE_CASE      (		snake_case			,     snake_case       )						->				Tuple:
						return (-y * np.log(snake_case       ) - (1 - y) * np.log(1 - h       )).mean()




def        _SCREAMING_SNAKE_CASE      (		snake_case			,     snake_case			,     snake_case       )						->				List[Any]:
						_UpperCAmelCase      =			np.dot(snake_case			,     snake_case       )
						return np.sum(y * scores - np.log(1 + np.exp(snake_case       )       )       )




def        _SCREAMING_SNAKE_CASE      (		snake_case			,     snake_case			,     snake_case			,     snake_case=7_0_0_0_0       )						->				Tuple:
						_UpperCAmelCase      =			np.zeros(x.shape[1]       )

						for iterations in range(snake_case       ):
												_UpperCAmelCase      =			np.dot(snake_case			,     snake_case       )
												_UpperCAmelCase      =			sigmoid_function(snake_case       )
												_UpperCAmelCase      =			np.dot(x.T			,     h - y       ) / y.size
												_UpperCAmelCase      =			theta - alpha * gradient  # updating the weights
												_UpperCAmelCase      =			np.dot(snake_case			,     snake_case       )
												_UpperCAmelCase      =			sigmoid_function(snake_case       )
												_UpperCAmelCase      =			cost_function(snake_case			,     snake_case       )
												if iterations % 1_0_0 == 0:
																		print(f"loss: {j} \t"       )  # printing the loss after every 100 iterations
						return theta


# In[68]:

if __name__ == "__main__":
				a													=			datasets.load_iris()
				a													=			iris.data[:, :2]
				a													=			(iris.target != 0) * 1

				a													=			0.1
				a													=			logistic_reg(alpha, x, y, max_iterations=70000)
				print("theta: ", theta)  # printing the theta i.e our weights vector




				def        _SCREAMING_SNAKE_CASE      (		snake_case       )						->				List[Any]:
										return sigmoid_function(
										    np.dot(snake_case			,     snake_case       )       )  # predicting the value of probability from the logistic regression algorithm

				plt.figure(figsize=(10, 6))
				plt.scatter(x[y == 0][:, 0], x[y == 0][:, 1], color="b", label="0")
				plt.scatter(x[y == 1][:, 0], x[y == 1][:, 1], color="r", label="1")
				((a)							,  (a))													=			(x[:, 0].min(), x[:, 0].max())
				((a)							,  (a))													=			(x[:, 1].min(), x[:, 1].max())
				((a)							,  (a))													=			np.meshgrid(np.linspace(xa_min, xa_max), np.linspace(xa_min, xa_max))
				a													=			np.c_[xxa.ravel(), xxa.ravel()]
				a													=			predict_prob(grid).reshape(xxa.shape)
				plt.contour(xxa, xxa, probs, [0.5], linewidths=1, colors="black")

				plt.legend()

				plt.show()