
class 						__lowercase:


       """simple docstring"""







       def __init__(     self					:			List[str]  ,      _lowerCAmelCase					:			List[Any]       )					->   Optional[Any]:
         _lowerCAmelCase						=		val
         # Number of nodes in left subtree
         _lowerCAmelCase						=		0
         _lowerCAmelCase						=		None
         _lowerCAmelCase						=		None
         _lowerCAmelCase						=		None






       def SCREAMING_SNAKE_CASE_				(     self					:			List[Any]  ,      _lowerCAmelCase					:			List[Any]       )					->   List[Any]:
         assert self.left_tree_size == other.left_tree_size, "Unequal Sizes of Blocks"

         if self.val < other.val:
           _lowerCAmelCase						=		self.right
           _lowerCAmelCase						=		None
           if self.right:
             _lowerCAmelCase						=		other
           _lowerCAmelCase						=		other
           _lowerCAmelCase						=		self.left_tree_size * 2 + 1
           return self
         else:
           _lowerCAmelCase						=		other.right
           _lowerCAmelCase						=		None
           if other.right:
             _lowerCAmelCase						=		self
           _lowerCAmelCase						=		self
           _lowerCAmelCase						=		other.left_tree_size * 2 + 1
           return other





class 						__lowercase:


       """simple docstring"""







       def __init__(     self					:			Dict  ,      _lowerCAmelCase					:			List[Any]=None  ,      _lowerCAmelCase					:			Optional[int]=None  ,      _lowerCAmelCase					:			Optional[Any]=0       )					->   str:
         _lowerCAmelCase						=		heap_size
         _lowerCAmelCase						=		bottom_root
         _lowerCAmelCase						=		min_node



       def SCREAMING_SNAKE_CASE_				(     self					:			int  ,      _lowerCAmelCase					:			List[Any]       )					->   str:

         # Empty heaps corner cases
         if other.size == 0:
           return None
         if self.size == 0:
           _lowerCAmelCase						=		other.size
           _lowerCAmelCase						=		other.bottom_root
           _lowerCAmelCase						=		other.min_node
           return None
         # Update size
         _lowerCAmelCase						=		self.size + other.size

         # Update min.node
         if self.min_node.val > other.min_node.val:
           _lowerCAmelCase						=		other.min_node
         # Merge

         # Order roots by left_subtree_size
         _lowerCAmelCase						=		[]
         _lowerCAmelCase	,       _lowerCAmelCase						=		self.bottom_root, other.bottom_root
         while i or j:
           if i and ((not j) or i.left_tree_size < j.left_tree_size):
             combined_roots_list.append((i, True)       )
             _lowerCAmelCase						=		i.parent
           else:
             combined_roots_list.append((j, False)       )
             _lowerCAmelCase						=		j.parent
        # Insert links between them
         for i in range(len(_lowerCAmelCase       ) - 1       ):
           if combined_roots_list[i][1] != combined_roots_list[i + 1][1]:
             _lowerCAmelCase						=		combined_roots_list[i + 1][0]
             _lowerCAmelCase						=		combined_roots_list[i][0]
        # Consecutively merge roots with same left_tree_size
         _lowerCAmelCase						=		combined_roots_list[0][0]
         while i.parent:
           if (
               (i.left_tree_size == i.parent.left_tree_size) and (not i.parent.parent)
           ) or (
               i.left_tree_size == i.parent.left_tree_size
               and i.left_tree_size != i.parent.parent.left_tree_size
           ):
             # Neighbouring Nodes
             _lowerCAmelCase						=		i.left
             _lowerCAmelCase						=		i.parent.parent

             # Merging trees
             _lowerCAmelCase						=		i.merge_trees(i.parent       )

             # Updating links
             _lowerCAmelCase						=		previous_node
             _lowerCAmelCase						=		next_node
             if previous_node:
               _lowerCAmelCase						=		i
             if next_node:
               _lowerCAmelCase						=		i
           else:
             _lowerCAmelCase						=		i.parent
        # Updating self.bottom_root
         while i.left:
           _lowerCAmelCase						=		i.left
         _lowerCAmelCase						=		i

         # Update other
         _lowerCAmelCase						=		self.size
         _lowerCAmelCase						=		self.bottom_root
         _lowerCAmelCase						=		self.min_node

         # Return the merged heap
         return self



       def SCREAMING_SNAKE_CASE_				(     self					:			Dict  ,      _lowerCAmelCase					:			str       )					->   Union[str, Any]:
         if self.size == 0:
           _lowerCAmelCase						=		Node(_lowerCAmelCase       )
           _lowerCAmelCase						=		1
           _lowerCAmelCase						=		self.bottom_root
         else:
           # Create new node
           _lowerCAmelCase						=		Node(_lowerCAmelCase       )

           # Update size
           self.size += 1

           # update min_node
           if val < self.min_node.val:
             _lowerCAmelCase						=		new_node
           # Put new_node as a bottom_root in heap
           _lowerCAmelCase						=		new_node
           _lowerCAmelCase						=		self.bottom_root
           _lowerCAmelCase						=		new_node

           # Consecutively merge roots with same left_tree_size
           while (
               self.bottom_root.parent
               and self.bottom_root.left_tree_size
               == self.bottom_root.parent.left_tree_size
           ):
             # Next node
             _lowerCAmelCase						=		self.bottom_root.parent.parent

             # Merge
             _lowerCAmelCase						=		self.bottom_root.merge_trees(self.bottom_root.parent       )

             # Update Links
             _lowerCAmelCase						=		next_node
             _lowerCAmelCase						=		None
             if next_node:
               _lowerCAmelCase						=		self.bottom_root



       def SCREAMING_SNAKE_CASE_				(     self					:			Any       )					->   Dict:
         return self.min_node.val



       def SCREAMING_SNAKE_CASE_				(     self					:			Optional[int]       )					->   Optional[Any]:
         return self.size == 0



       def SCREAMING_SNAKE_CASE_				(     self					:			Any       )					->   List[str]:
         _lowerCAmelCase						=		self.min_node.val

         # Last element in heap corner case
         if self.size == 1:
           # Update size
           _lowerCAmelCase						=		0

           # Update bottom root
           _lowerCAmelCase						=		None

           # Update min_node
           _lowerCAmelCase						=		None

           return min_value
         # No right subtree corner case
         # The structure of the tree implies that this should be the bottom root
         # and there is at least one other root
         if self.min_node.right is None:
           # Update size
           self.size -= 1

           # Update bottom root
           _lowerCAmelCase						=		self.bottom_root.parent
           _lowerCAmelCase						=		None

           # Update min_node
           _lowerCAmelCase						=		self.bottom_root
           _lowerCAmelCase						=		self.bottom_root.parent
           while i:
             if i.val < self.min_node.val:
               _lowerCAmelCase						=		i
             _lowerCAmelCase						=		i.parent
           return min_value
         # General case
         # Find the BinomialHeap of the right subtree of min_node
         _lowerCAmelCase						=		self.min_node.right
         _lowerCAmelCase						=		None
         _lowerCAmelCase						=		bottom_of_new
         _lowerCAmelCase						=		1

         # Size, min_node and bottom_root
         while bottom_of_new.left:
           _lowerCAmelCase						=		size_of_new * 2 + 1
           _lowerCAmelCase						=		bottom_of_new.left
           if bottom_of_new.val < min_of_new.val:
             _lowerCAmelCase						=		bottom_of_new
        # Corner case of single root on top left path
         if (not self.min_node.left) and (not self.min_node.parent):
           _lowerCAmelCase						=		size_of_new
           _lowerCAmelCase						=		bottom_of_new
           _lowerCAmelCase						=		min_of_new
           # print("Single root, multiple nodes case")
           return min_value
         # Remaining cases
         # Construct heap of right subtree
         _lowerCAmelCase						=		BinomialHeap(
             bottom_root=_lowerCAmelCase  ,      min_node=_lowerCAmelCase  ,      heap_size=_lowerCAmelCase       )

         # Update size
         _lowerCAmelCase						=		self.size - 1 - size_of_new

         # Neighbour nodes
         _lowerCAmelCase						=		self.min_node.left
         _lowerCAmelCase						=		self.min_node.parent

         # Initialize new bottom_root and min_node
         _lowerCAmelCase						=		previous_node or next_node
         _lowerCAmelCase						=		next_node

         # Update links of previous_node and search below for new min_node and
         # bottom_root
         if previous_node:
           _lowerCAmelCase						=		next_node

           # Update bottom_root and search for min_node below
           _lowerCAmelCase						=		previous_node
           _lowerCAmelCase						=		previous_node
           while self.bottom_root.left:
             _lowerCAmelCase						=		self.bottom_root.left
             if self.bottom_root.val < self.min_node.val:
               _lowerCAmelCase						=		self.bottom_root
         if next_node:
           _lowerCAmelCase						=		previous_node

           # Search for new min_node above min_node
           _lowerCAmelCase						=		next_node
           while i:
             if i.val < self.min_node.val:
               _lowerCAmelCase						=		i
             _lowerCAmelCase						=		i.parent
        # Merge heaps
         self.merge_heaps(_lowerCAmelCase       )

         return min_value



       def SCREAMING_SNAKE_CASE_				(     self					:			Union[str, Any]       )					->   Union[str, Any]:
         _lowerCAmelCase						=		self.bottom_root
         while top_root.parent:
           _lowerCAmelCase						=		top_root.parent
         # preorder
         _lowerCAmelCase						=		[]
         self.__traversal(_lowerCAmelCase  ,      _lowerCAmelCase       )
         return heap_pre_order



       def SCREAMING_SNAKE_CASE_				(     self					:			Optional[Any]  ,      _lowerCAmelCase					:			Dict  ,      _lowerCAmelCase					:			Dict  ,      _lowerCAmelCase					:			Union[str, Any]=0       )					->   str:
         if curr_node:
           preorder.append((curr_node.val, level)       )
           self.__traversal(curr_node.left  ,      _lowerCAmelCase  ,      level + 1       )
           self.__traversal(curr_node.right  ,      _lowerCAmelCase  ,      level + 1       )
         else:
           preorder.append(('#', level)       )






       def __str__(     self					:			str       )					->   Tuple:
         if self.is_empty():
           return ""
         _lowerCAmelCase						=		self.pre_order()

         return "\n".join(('-' * level + str(_lowerCAmelCase       )) for value, level in preorder_heap       )


# Unit Tests
if __name__ == "__main__":
       import doctest

       doctest.testmod()


import cva
import numpy as np

from digital_image_processing.filters.convolve import img_convolve
from digital_image_processing.filters.sobel_filter import sobel_filter

_UpperCamelCase:					Tuple     =180



def 	_a  (					__SCREAMING_SNAKE_CASE					:  List[Any]		,				__SCREAMING_SNAKE_CASE					:  int    ):






  """simple docstring"""




  _lowerCAmelCase						=		k_size // 2
  _lowerCAmelCase	,       _lowerCAmelCase						=		np.mgrid[0 - center : k_size - center, 0 - center : k_size - center]
  _lowerCAmelCase						=		(
      1
      / (2 * np.pi * sigma)
      * np.exp(-(np.square(__SCREAMING_SNAKE_CASE    ) + np.square(__SCREAMING_SNAKE_CASE    )) / (2 * np.square(__SCREAMING_SNAKE_CASE    ))    )
  )
  return g



def 	_a  (					__SCREAMING_SNAKE_CASE					:  List[str]		,				__SCREAMING_SNAKE_CASE					:  Tuple		,				__SCREAMING_SNAKE_CASE					:  Optional[Any]    ):






  """simple docstring"""




  _lowerCAmelCase						=		np.zeros(__SCREAMING_SNAKE_CASE    )

  for row in range(1		,				image_shape[0] - 1    ):
    for col in range(1		,				image_shape[1] - 1    ):
      _lowerCAmelCase						=		gradient_direction[row, col]

      if (
          0 <= direction < PI / 8
          or 15 * PI / 8 <= direction <= 2 * PI
          or 7 * PI / 8 <= direction <= 9 * PI / 8
      ):
        _lowerCAmelCase						=		sobel_grad[row, col - 1]
        _lowerCAmelCase						=		sobel_grad[row, col + 1]
        if sobel_grad[row, col] >= w and sobel_grad[row, col] >= e:
          _lowerCAmelCase						=		sobel_grad[row, col]

      elif (
          PI / 8 <= direction < 3 * PI / 8
          or 9 * PI / 8 <= direction < 11 * PI / 8
      ):
        _lowerCAmelCase						=		sobel_grad[row + 1, col - 1]
        _lowerCAmelCase						=		sobel_grad[row - 1, col + 1]
        if sobel_grad[row, col] >= sw and sobel_grad[row, col] >= ne:
          _lowerCAmelCase						=		sobel_grad[row, col]

      elif (
          3 * PI / 8 <= direction < 5 * PI / 8
          or 11 * PI / 8 <= direction < 13 * PI / 8
      ):
        _lowerCAmelCase						=		sobel_grad[row - 1, col]
        _lowerCAmelCase						=		sobel_grad[row + 1, col]
        if sobel_grad[row, col] >= n and sobel_grad[row, col] >= s:
          _lowerCAmelCase						=		sobel_grad[row, col]

      elif (
          5 * PI / 8 <= direction < 7 * PI / 8
          or 13 * PI / 8 <= direction < 15 * PI / 8
      ):
        _lowerCAmelCase						=		sobel_grad[row - 1, col - 1]
        _lowerCAmelCase						=		sobel_grad[row + 1, col + 1]
        if sobel_grad[row, col] >= nw and sobel_grad[row, col] >= se:
          _lowerCAmelCase						=		sobel_grad[row, col]

  return destination



def 	_a  (					__SCREAMING_SNAKE_CASE					:  Tuple		,				__SCREAMING_SNAKE_CASE					:  List[str]		,				__SCREAMING_SNAKE_CASE					:  Tuple		,				__SCREAMING_SNAKE_CASE					:  Union[str, Any]		,				__SCREAMING_SNAKE_CASE					:  Dict		,				__SCREAMING_SNAKE_CASE					:  List[Any]    ):






  """simple docstring"""




  for row in range(1		,				image_shape[0] - 1    ):
    for col in range(1		,				image_shape[1] - 1    ):
      if destination[row, col] >= threshold_high:
        _lowerCAmelCase						=		strong
      elif destination[row, col] <= threshold_low:
        _lowerCAmelCase						=		0
      else:
        _lowerCAmelCase						=		weak



def 	_a  (					__SCREAMING_SNAKE_CASE					:  List[Any]		,				__SCREAMING_SNAKE_CASE					:  Optional[int]		,				__SCREAMING_SNAKE_CASE					:  Optional[int]		,				__SCREAMING_SNAKE_CASE					:  Union[str, Any]    ):






  """simple docstring"""




  for row in range(1		,				image_shape[0]    ):
    for col in range(1		,				image_shape[1]    ):
      if destination[row, col] == weak:
        if 255 in (
            destination[row, col + 1],
            destination[row, col - 1],
            destination[row - 1, col],
            destination[row + 1, col],
            destination[row - 1, col - 1],
            destination[row + 1, col - 1],
            destination[row - 1, col + 1],
            destination[row + 1, col + 1],
        ):
          _lowerCAmelCase						=		strong
        else:
          _lowerCAmelCase						=		0



def 	_a  (					__SCREAMING_SNAKE_CASE					:  List[str]		,				__SCREAMING_SNAKE_CASE					:  int=15		,				__SCREAMING_SNAKE_CASE					:  int=30		,				__SCREAMING_SNAKE_CASE					:  Tuple=128		,				__SCREAMING_SNAKE_CASE					:  List[Any]=255    ):






  """simple docstring"""




  _lowerCAmelCase						=		img_convolve(__SCREAMING_SNAKE_CASE		,				gen_gaussian_kernel(9		,				sigma=1.4    )    )
  # get the gradient and degree by sobel_filter
  _lowerCAmelCase	,       _lowerCAmelCase						=		sobel_filter(__SCREAMING_SNAKE_CASE    )
  _lowerCAmelCase						=		PI + np.radadeg(__SCREAMING_SNAKE_CASE    )

  _lowerCAmelCase						=		suppress_non_maximum(image.shape		,				__SCREAMING_SNAKE_CASE		,				__SCREAMING_SNAKE_CASE    )

  detect_high_low_threshold(
      image.shape		,				__SCREAMING_SNAKE_CASE		,				__SCREAMING_SNAKE_CASE		,				__SCREAMING_SNAKE_CASE		,				__SCREAMING_SNAKE_CASE		,				__SCREAMING_SNAKE_CASE    )

  track_edge(image.shape		,				__SCREAMING_SNAKE_CASE		,				__SCREAMING_SNAKE_CASE		,				__SCREAMING_SNAKE_CASE    )

  return destination


if __name__ == "__main__":
       # read original image in gray mode
       _UpperCamelCase:					Optional[Any]     =cva.imread(R'../image_data/lena.jpg', 0)
       # canny edge detection
       _UpperCamelCase:					Tuple     =canny(lena)
       cva.imshow('canny', canny_destination)
       cva.waitKey(0)
