



'''simple docstring'''

# 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 		_snake_case		( _SCREAMING_SNAKE_CASE					:						List[str]							)      ->						Optional[Any]:







	"""simple docstring"""
	return 1 / (1 + np.exp(-z							))






def 		_snake_case		( _SCREAMING_SNAKE_CASE					:						Optional[Any]							,		_SCREAMING_SNAKE_CASE					:						Tuple							)      ->						int:







	"""simple docstring"""
	return (-y * np.log(_snake_case							) - (1 - y) * np.log(1 - h							)).mean()






def 		_snake_case		( _SCREAMING_SNAKE_CASE					:						Tuple							,		_SCREAMING_SNAKE_CASE					:						List[Any]							,		_SCREAMING_SNAKE_CASE					:						int							)      ->						Optional[Any]:







	"""simple docstring"""
	lowerCAmelCase   =     np.dot(_snake_case							,		_snake_case							)
	return np.sum(y * scores - np.log(1 + np.exp(_snake_case							)							)							)






def 		_snake_case		( _SCREAMING_SNAKE_CASE					:						Tuple							,		_SCREAMING_SNAKE_CASE					:						Optional[Any]							,		_SCREAMING_SNAKE_CASE					:						Optional[int]							,		_SCREAMING_SNAKE_CASE					:						List[Any]=70_000							)      ->						List[Any]:







	"""simple docstring"""
	lowerCAmelCase   =     np.zeros(x.shape[1]							)

	for iterations in range(_snake_case							):
		lowerCAmelCase   =     np.dot(_snake_case							,		_snake_case							)
		lowerCAmelCase   =     sigmoid_function(_snake_case							)
		lowerCAmelCase   =     np.dot(x.T							,		h - y							) / y.size
		lowerCAmelCase   =     theta - alpha * gradient  # updating the weights
		lowerCAmelCase   =     np.dot(_snake_case							,		_snake_case							)
		lowerCAmelCase   =     sigmoid_function(_snake_case							)
		lowerCAmelCase   =     cost_function(_snake_case							,		_snake_case							)
		if iterations % 100 == 0:
			print(f'loss: {j} \t'							)  # printing the loss after every 100 iterations
	return theta


# In[68]:

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

				UpperCAmelCase     		=   0.1
				UpperCAmelCase     		=   logistic_reg(alpha, x, y, max_iterations=7_0000)
				print('theta: ', theta)  # printing the theta i.e our weights vector






				def 		_snake_case		( _SCREAMING_SNAKE_CASE					:						Dict							)      ->						Dict:







					"""simple docstring"""
					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')
				(UpperCAmelCase)     		=   (x[:, 0].min(), x[:, 0].max())
				(UpperCAmelCase)     		=   (x[:, 1].min(), x[:, 1].max())
				(UpperCAmelCase)     		=   np.meshgrid(np.linspace(xa_min, xa_max), np.linspace(xa_min, xa_max))
				UpperCAmelCase     		=   np.c_[xxa.ravel(), xxa.ravel()]
				UpperCAmelCase     		=   predict_prob(grid).reshape(xxa.shape)
				plt.contour(xxa, xxa, probs, [0.5], linewidths=1, colors='black')

				plt.legend()





				plt.show()




'''simple docstring'''

from __future__ import annotations

UpperCAmelCase     		=   []






def 		_snake_case		( _SCREAMING_SNAKE_CASE					:						list[list[int]]							,		_SCREAMING_SNAKE_CASE					:						int							,		_SCREAMING_SNAKE_CASE					:						int							)      ->						bool:







	"""simple docstring"""
	for i in range(len(_SCREAMING_SNAKE_CASE							)							):
		if board[row][i] == 1:
			return False
	for i in range(len(_SCREAMING_SNAKE_CASE							)							):
		if board[i][column] == 1:
			return False
	for i, j in zip(range(_SCREAMING_SNAKE_CASE							,		-1							,		-1							)							,		range(_SCREAMING_SNAKE_CASE							,		-1							,		-1							)							):
		if board[i][j] == 1:
			return False
	for i, j in zip(range(_SCREAMING_SNAKE_CASE							,		-1							,		-1							)							,		range(_SCREAMING_SNAKE_CASE							,		len(_SCREAMING_SNAKE_CASE							)							)							):
		if board[i][j] == 1:
			return False
	return True






def 		_snake_case		( _SCREAMING_SNAKE_CASE					:						list[list[int]]							,		_SCREAMING_SNAKE_CASE					:						int							)      ->						bool:







	"""simple docstring"""
	if row >= len(_SCREAMING_SNAKE_CASE							):
		solution.append(_SCREAMING_SNAKE_CASE							)
		printboard(_SCREAMING_SNAKE_CASE							)
		print()
		return True
	for i in range(len(_SCREAMING_SNAKE_CASE							)							):
		if is_safe(_SCREAMING_SNAKE_CASE							,		_SCREAMING_SNAKE_CASE							,		_SCREAMING_SNAKE_CASE							):
			lowerCAmelCase   =     1
			solve(_SCREAMING_SNAKE_CASE							,		row + 1							)
			lowerCAmelCase   =     0
	return False






def 		_snake_case		( _SCREAMING_SNAKE_CASE					:						list[list[int]]							)      ->						None:







	"""simple docstring"""
	for i in range(len(_SCREAMING_SNAKE_CASE							)							):
		for j in range(len(_SCREAMING_SNAKE_CASE							)							):
			if board[i][j] == 1:
				print("""Q"""							,		end=""" """							)
			else:
				print("""."""							,		end=""" """							)
		print()


# n=int(input("The no. of queens"))
UpperCAmelCase     		=   8
UpperCAmelCase     		=   [[0 for i in range(n)] for j in range(n)]
solve(board, 0)





print('The total no. of solutions are :', len(solution))