"""simple docstring"""
import random





def    lowerCAmelCase__    (			_UpperCamelCase       :				int ,			_UpperCamelCase       :				float ,			_UpperCamelCase       :				bool = False					)					->				dict:





						"""simple docstring"""






						snake_case								=			{i: [] for i in range(_UpperCamelCase					)}

						# if probability is greater or equal than 1, then generate a complete graph
						if probability >= 1:
												return complete_graph(_UpperCamelCase					)
						# if probability is lower or equal than 0, then return a graph without edges
						if probability <= 0:
												return graph

						# for each couple of nodes, add an edge from u to v
						# if the number randomly generated is greater than probability probability
						for i in range(_UpperCamelCase					):
												for j in range(i + 1 ,			_UpperCamelCase					):
																		if random.random() < probability:
																								graph[i].append(_UpperCamelCase					)
																								if not directed:
																														# if the graph is undirected, add an edge in from j to i, either
																														graph[j].append(_UpperCamelCase					)
						return graph





def    lowerCAmelCase__    (			_UpperCamelCase       :				int					)					->				dict:





						"""simple docstring"""






						return {
						    i: [j for j in range(_UpperCamelCase					) if i != j] for i in range(_UpperCamelCase					)
						}


if __name__ == "__main__":
					import doctest

					doctest.testmod()



"""simple docstring"""
import numpy as np
from PIL import Image





def    lowerCAmelCase__    (			_UpperCamelCase       :				np.ndarray ,			_UpperCamelCase       :				int ,			_UpperCamelCase       :				int					)					->				np.ndarray:





						"""simple docstring"""






						snake_case								=			np.array(_UpperCamelCase					)
						if arr.shape[0] != arr.shape[1]:
												raise ValueError('The input array is not a square matrix'					)
						snake_case								=			0
						snake_case								=			0
						snake_case								=			0
						snake_case								=			0

						# compute the shape of the output matrix
						snake_case								=			(arr.shape[0] - size) // stride + 1
						# initialize the output matrix with zeros of shape maxpool_shape
						snake_case								=			np.zeros((maxpool_shape, maxpool_shape)					)

						while i < arr.shape[0]:
												if i + size > arr.shape[0]:
																		# if the end of the matrix is reached, break
																		break
												while j < arr.shape[1]:
																		# if the end of the matrix is reached, break
																		if j + size > arr.shape[1]:
																								break
																		# compute the maximum of the pooling matrix
																		snake_case								=			np.max(arr[i : i + size, j : j + size]					)
																		# shift the pooling matrix by stride of column pixels
																		j += stride
																		mat_j += 1

												# shift the pooling matrix by stride of row pixels
												i += stride
												mat_i += 1

												# reset the column index to 0
												snake_case								=			0
												snake_case								=			0

						return updated_arr





def    lowerCAmelCase__    (			_UpperCamelCase       :				np.ndarray ,			_UpperCamelCase       :				int ,			_UpperCamelCase       :				int					)					->				np.ndarray:





						"""simple docstring"""






						snake_case								=			np.array(_UpperCamelCase					)
						if arr.shape[0] != arr.shape[1]:
												raise ValueError('The input array is not a square matrix'					)
						snake_case								=			0
						snake_case								=			0
						snake_case								=			0
						snake_case								=			0

						# compute the shape of the output matrix
						snake_case								=			(arr.shape[0] - size) // stride + 1
						# initialize the output matrix with zeros of shape avgpool_shape
						snake_case								=			np.zeros((avgpool_shape, avgpool_shape)					)

						while i < arr.shape[0]:
												# if the end of the matrix is reached, break
												if i + size > arr.shape[0]:
																		break
												while j < arr.shape[1]:
																		# if the end of the matrix is reached, break
																		if j + size > arr.shape[1]:
																								break
																		# compute the average of the pooling matrix
																		snake_case								=			int(np.average(arr[i : i + size, j : j + size]					)					)
																		# shift the pooling matrix by stride of column pixels
																		j += stride
																		mat_j += 1

												# shift the pooling matrix by stride of row pixels
												i += stride
												mat_i += 1
												# reset the column index to 0
												snake_case								=			0
												snake_case								=			0

						return updated_arr


# Main Function
if __name__ == "__main__":
					from doctest import testmod

					testmod(name="avgpooling", verbose=True)

					# Loading the image
					SCREAMING_SNAKE_CASE__      						=  Image.open("path_to_image")

					# Converting the image to numpy array and maxpooling, displaying the result
					# Ensure that the image is a square matrix

					Image.fromarray(maxpooling(np.array(image), size=3, stride=2)).show()

					# Converting the image to numpy array and averagepooling, displaying the result
					# Ensure that the image is a square matrix

					Image.fromarray(avgpooling(np.array(image), size=3, stride=2)).show()


