






from itertools import product

from cva import COLOR_BGR2GRAY, cvtColor, imread, imshow, waitKey
from numpy import dot, exp, mgrid, pi, ravel, square, uinta, zeros


def        _a  (     UpperCamelCase_					:				Optional[Any]    ,   UpperCamelCase_					:				List[Any]   ) ->   Optional[Any]:
						"""simple docstring"""







						lowerCAmelCase__       =						k_size // 2
						lowerCAmelCase__       =						mgrid[0 - center : k_size - center, 0 - center : k_size - center]
						lowerCAmelCase__       =						1 / (2 * pi * sigma) * exp(-(square(__lowerCAmelCase   ) + square(__lowerCAmelCase   )) / (2 * square(__lowerCAmelCase   ))   )
						return g


def        _a  (     UpperCamelCase_					:				Dict    ,   UpperCamelCase_					:				List[str]    ,   UpperCamelCase_					:				str   ) ->   str:
						"""simple docstring"""







						lowerCAmelCase__       =						image.shape[0], image.shape[1]
						# dst image height and width
						lowerCAmelCase__       =						height - k_size + 1
						lowerCAmelCase__       =						width - k_size + 1

						# im2col, turn the k_size*k_size pixels into a row and np.vstack all rows
						lowerCAmelCase__       =						zeros((dst_height * dst_width, k_size * k_size)   )
						lowerCAmelCase__       =						0
						for i, j in product(range(__lowerCAmelCase   )    ,   range(__lowerCAmelCase   )   ):
												lowerCAmelCase__       =						ravel(image[i : i + k_size, j : j + k_size]   )
												lowerCAmelCase__       =						window
												row += 1

						#  turn the kernel into shape(k*k, 1)
						lowerCAmelCase__       =						gen_gaussian_kernel(__lowerCAmelCase    ,   __lowerCAmelCase   )
						lowerCAmelCase__       =						ravel(__lowerCAmelCase   )

						# reshape and get the dst image
						lowerCAmelCase__       =						dot(__lowerCAmelCase    ,   __lowerCAmelCase   ).reshape(__lowerCAmelCase    ,   __lowerCAmelCase   ).astype(__lowerCAmelCase   )

						return dst


if __name__ == "__main__":
	# read original image
	a_     :   Tuple							=    imread(r'''../image_data/lena.jpg''')
	# turn image in gray scale value
	a_     :   str							=    cvtColor(img, COLOR_BGR2GRAY)

	# get values with two different mask size
	a_     :   Tuple							=    gaussian_filter(gray, 3, sigma=1)
	a_     :   Dict							=    gaussian_filter(gray, 5, sigma=0.8)

	# show result images
	imshow('''gaussian filter with 3x3 mask''', gaussianaxa)
	imshow('''gaussian filter with 5x5 mask''', gaussianaxa)
	waitKey()














def        _a  (     UpperCamelCase_					:				Any    ,   UpperCamelCase_					:				List[str]   ) ->   List[Any]:
						"""simple docstring"""







						lowerCAmelCase__       =						0
						lowerCAmelCase__       =						len(UpperCamelCase_   ) - 1

						while left <= right:
												# avoid divided by 0 during interpolation
												if sorted_collection[left] == sorted_collection[right]:
																		if sorted_collection[left] == item:
																								return left
																		else:
																								return None

												lowerCAmelCase__       =						left + ((item - sorted_collection[left]) * (right - left)) // (
												    sorted_collection[right] - sorted_collection[left]
												)

												# out of range check
												if point < 0 or point >= len(UpperCamelCase_   ):
																		return None

												lowerCAmelCase__       =						sorted_collection[point]
												if current_item == item:
																		return point
												else:
																		if point < left:
																								lowerCAmelCase__       =						left
																								lowerCAmelCase__       =						point
																		elif point > right:
																								lowerCAmelCase__       =						right
																								lowerCAmelCase__       =						point
																		else:
																								if item < current_item:
																														lowerCAmelCase__       =						point - 1
																								else:
																														lowerCAmelCase__       =						point + 1
						return None


def        _a  (     UpperCamelCase_					:				List[str]    ,   UpperCamelCase_					:				Optional[Any]    ,   UpperCamelCase_					:				int    ,   UpperCamelCase_					:				int   ) ->   List[Any]:
						"""simple docstring"""







						if sorted_collection[left] == sorted_collection[right]:
												if sorted_collection[left] == item:
																		return left
												else:
																		return None

						lowerCAmelCase__       =						left + ((item - sorted_collection[left]) * (right - left)) // (
						    sorted_collection[right] - sorted_collection[left]
						)

						# out of range check
						if point < 0 or point >= len(UpperCamelCase_   ):
												return None

						if sorted_collection[point] == item:
												return point
						elif point < left:
												return interpolation_search_by_recursion(UpperCamelCase_    ,   UpperCamelCase_    ,   UpperCamelCase_    ,   UpperCamelCase_   )
						elif point > right:
												return interpolation_search_by_recursion(UpperCamelCase_    ,   UpperCamelCase_    ,   UpperCamelCase_    ,   UpperCamelCase_   )
						else:
												if sorted_collection[point] > item:
																		return interpolation_search_by_recursion(
																		    UpperCamelCase_    ,   UpperCamelCase_    ,   UpperCamelCase_    ,   point - 1   )
												else:
																		return interpolation_search_by_recursion(
																		    UpperCamelCase_    ,   UpperCamelCase_    ,   point + 1    ,   UpperCamelCase_   )


def        _a  (     UpperCamelCase_					:				Optional[Any]   ) ->   Tuple:
						"""simple docstring"""







						if collection != sorted(UpperCamelCase_   ):
												raise ValueError("Collection must be ascending sorted"   )
						return True


if __name__ == "__main__":
	import sys
	a_							=    0
	if debug == 1:
		a_							=    [10, 30, 40, 45, 50, 66, 77, 93]
		try:
			__assert_sorted(collection)
		except ValueError:
			sys.exit('''Sequence must be ascending sorted to apply interpolation search''')
		a_							=    67

	a_							=    interpolation_search(collection, target)
	if result is not None:
		print(F"{target} found at positions: {result}")
	else:
		print('''Not found''')






