





'''simple docstring'''


from collections.abc import Callable
from math import log
from os import name, system
from random import gauss, seed
from typing import TypeVar
def 							UpperCAmelCase_						(		__lowerCamelCase      :      List[str]			,__lowerCamelCase      :      int			,__lowerCamelCase      :      Tuple				):
   seed(1				)
   return [gauss(__lowerCamelCase			,__lowerCamelCase				) for _ in range(__lowerCamelCase				)]
def 							UpperCAmelCase_						(		__lowerCamelCase      :      str			,__lowerCamelCase      :      Union[str, Any]				):
   return [k for k in range(__lowerCamelCase				) for _ in range(instance_count[k]				)]
def 							UpperCAmelCase_						(		__lowerCamelCase      :      Any			,__lowerCamelCase      :      List[Any]				):
   return sum(__lowerCamelCase				) / instance_count
def 							UpperCAmelCase_						(		__lowerCamelCase      :      Optional[Any]			,__lowerCamelCase      :      str				):
   return instance_count / total_count
def 							UpperCAmelCase_						(		__lowerCamelCase      :      str			,__lowerCamelCase      :      Union[str, Any]			,__lowerCamelCase      :      List[Any]				):
   lowercase_    :Any					    =				[]  # An empty list to store all squared differences
   # iterate over number of elements in items
   for i in range(len(__lowerCamelCase				)				):
      # for loop iterates over number of elements in inner layer of items
      for j in range(len(items[i]				)				):
         # appending squared differences to 'squared_diff' list
         squared_diff.append((items[i][j] - means[i]) ** 2				)

    # one divided by (the number of all instances - number of classes) multiplied by
    # sum of all squared differences
   lowercase_    :Optional[int]					    =				len(__lowerCamelCase				)  # Number of classes in dataset
   return 1 / (total_count - n_classes) * sum(__lowerCamelCase				)
def 							UpperCAmelCase_						(		__lowerCamelCase      :      List[str]			,__lowerCamelCase      :      Optional[Any]			,__lowerCamelCase      :      Optional[Any]			,__lowerCamelCase      :      Dict				):
   lowercase_    :Optional[Any]					    =				[]
   # for loop iterates over number of elements in list
   for i in range(len(__lowerCamelCase				)				):
      # for loop iterates over number of inner items of each element
      for j in range(len(x_items[i]				)				):
         lowercase_    :int					    =				[]  # to store all discriminant values of each item as a list
         # for loop iterates over number of classes we have in our dataset
         for k in range(len(__lowerCamelCase				)				):
            # appending values of discriminants for each class to 'temp' list
            temp.append(
                x_items[i][j] * (means[k] / variance)
                - (means[k] ** 2 / (2 * variance))
                + log(probabilities[k]				)				)
         # appending discriminant values of each item to 'results' list
         results.append(__lowerCamelCase				)

   return [result.index(max(__lowerCamelCase				)				) for result in results]
def 							UpperCAmelCase_						(		__lowerCamelCase      :      List[Any]			,__lowerCamelCase      :      Union[str, Any]				):
   lowercase_    :Tuple					    =				sum(1 for i, j in zip(__lowerCamelCase			,__lowerCamelCase				) if i == j				)
   # percentage of accuracy equals to number of correct predictions divided by number
   # of all data and multiplied by 100
   return (correct / len(__lowerCamelCase				)) * 1_00


lowerCAmelCase      :  Dict      							=TypeVar('''num''')
def 							UpperCAmelCase_						(		__lowerCamelCase      :      List[str]			,__lowerCamelCase      :      str			,__lowerCamelCase      :      Tuple			,__lowerCamelCase      :      Tuple = lambda __lowerCamelCase				: True			,__lowerCamelCase      :      Union[str, Any] = None			,):

   while True:
      try:
         lowercase_    :Optional[int]					    =				input_type(input(__lowerCamelCase				).strip() or default				)
         if condition(__lowerCamelCase				):
            return user_input
         else:
            print(F'{user_input}: {err_msg}'				)
            continue
      except ValueError:
         print(
             F'{user_input}: Incorrect input type, expected {input_type.__name__!r}'				)
def 							UpperCAmelCase_						(		):

   while True:
      print(" Linear Discriminant Analysis ".center(50			,"*"				)				)
      print("*" * 50			,"\n"				)
      print("First of all we should specify the number of classes that"				)
      print("we want to generate as training dataset"				)
      # Trying to get number of classes
      lowercase_    :Optional[int]					    =				valid_input(
          input_type=__lowerCamelCase			,condition=lambda __lowerCamelCase				: x > 0			,input_msg="Enter the number of classes (Data Groupings): "			,err_msg="Number of classes should be positive!"			,)

      print("-" * 1_00				)

      # Trying to get the value of standard deviation
      lowercase_    :Union[str, Any]					    =				valid_input(
          input_type=__lowerCamelCase			,condition=lambda __lowerCamelCase				: x >= 0			,input_msg=(
              "Enter the value of standard deviation"
              "(Default value is 1.0 for all classes): "
          )			,err_msg="Standard deviation should not be negative!"			,default="1.0"			,)

      print("-" * 1_00				)

      # Trying to get number of instances in classes and theirs means to generate
      # dataset
      lowercase_    :Optional[int]					    =				[]  # An empty list to store instance counts of classes in dataset
      for i in range(__lowerCamelCase				):
         lowercase_    :Optional[int]					    =				valid_input(
             input_type=__lowerCamelCase			,condition=lambda __lowerCamelCase				: x > 0			,input_msg=(F'Enter The number of instances for class_{i+1}: ')			,err_msg="Number of instances should be positive!"			,)
         counts.append(__lowerCamelCase				)
      print("-" * 1_00				)

      # An empty list to store values of user-entered means of classes
      lowercase_    :List[str]					    =				[]
      for a in range(__lowerCamelCase				):
         lowercase_    :Union[str, Any]					    =				valid_input(
             input_type=__lowerCamelCase			,input_msg=(F'Enter the value of mean for class_{a+1}: ')			,err_msg="This is an invalid value."			,)
         user_means.append(__lowerCamelCase				)
      print("-" * 1_00				)

      print("Standard deviation: "			,__lowerCamelCase				)
      # print out the number of instances in classes in separated line
      for i, count in enumerate(__lowerCamelCase			,1				):
         print(F'Number of instances in class_{i} is: {count}'				)
      print("-" * 1_00				)

      # print out mean values of classes separated line
      for i, user_mean in enumerate(__lowerCamelCase			,1				):
         print(F'Mean of class_{i} is: {user_mean}'				)
      print("-" * 1_00				)

      # Generating training dataset drawn from gaussian distribution
      lowercase_    :Tuple					    =				[
          gaussian_distribution(user_means[j]			,__lowerCamelCase			,counts[j]				)
          for j in range(__lowerCamelCase				)
      ]
      print("Generated Normal Distribution: \n"			,__lowerCamelCase				)
      print("-" * 1_00				)

      # Generating Ys to detecting corresponding classes
      lowercase_    :Any					    =				y_generator(__lowerCamelCase			,__lowerCamelCase				)
      print("Generated Corresponding Ys: \n"			,__lowerCamelCase				)
      print("-" * 1_00				)

      # Calculating the value of actual mean for each class
      lowercase_    :Tuple					    =				[calculate_mean(counts[k]			,x[k]				) for k in range(__lowerCamelCase				)]
      # for loop iterates over number of elements in 'actual_means' list and print
      # out them in separated line
      for i, actual_mean in enumerate(__lowerCamelCase			,1				):
         print(F'Actual(Real) mean of class_{i} is: {actual_mean}'				)
      print("-" * 1_00				)

      # Calculating the value of probabilities for each class
      lowercase_    :List[str]					    =				[
          calculate_probabilities(counts[i]			,sum(__lowerCamelCase				)				) for i in range(__lowerCamelCase				)
      ]

      # for loop iterates over number of elements in 'probabilities' list and print
      # out them in separated line
      for i, probability in enumerate(__lowerCamelCase			,1				):
         print(F'Probability of class_{i} is: {probability}'				)
      print("-" * 1_00				)

      # Calculating the values of variance for each class
      lowercase_    :List[str]					    =				calculate_variance(__lowerCamelCase			,__lowerCamelCase			,sum(__lowerCamelCase				)				)
      print("Variance: "			,__lowerCamelCase				)
      print("-" * 1_00				)

      # Predicting Y values
      # storing predicted Y values in 'pre_indexes' variable
      lowercase_    :Optional[Any]					    =				predict_y_values(__lowerCamelCase			,__lowerCamelCase			,__lowerCamelCase			,__lowerCamelCase				)
      print("-" * 1_00				)

      # Calculating Accuracy of the model
      print(F'Accuracy: {accuracy(__lowerCamelCase			,__lowerCamelCase				)}'				)
      print("-" * 1_00				)
      print(" DONE ".center(1_00			,"+"				)				)

      if input("Press any key to restart or 'q' for quit: "				).strip().lower() == "q":
         print("\n" + "GoodBye!".center(1_00			,"-"				) + "\n"				)
         break
      system("cls" if name == "nt" else "clear"				)  # noqa: S605


if __name__ == "__main__":
      main()









'''simple docstring'''


class    a_     :





     def __init__(				self	:      str			,   lowercase	:      List[Any]		):





        """simple docstring"""




        lowercase_    :List[str]					    =				val
        # Number of nodes in left subtree
        lowercase_    :Optional[int]					    =				0
        lowercase_    :List[str]					    =				None
        lowercase_    :List[Any]					    =				None
        lowercase_    :Optional[Any]					    =				None







     def 							lowercase__   (				self	:      Union[str, Any]			,   lowercase	:      Dict		):





        """simple docstring"""




        assert self.left_tree_size == other.left_tree_size, "Unequal Sizes of Blocks"

        if self.val < other.val:
           lowercase_    :List[Any]					    =				self.right
           lowercase_    :str					    =				None
           if self.right:
              lowercase_    :Optional[int]					    =				other
           lowercase_    :Optional[Any]					    =				other
           lowercase_    :str					    =				self.left_tree_size * 2 + 1
           return self
        else:
           lowercase_    :Any					    =				other.right
           lowercase_    :Any					    =				None
           if other.right:
              lowercase_    :List[Any]					    =				self
           lowercase_    :Union[str, Any]					    =				self
           lowercase_    :Optional[int]					    =				other.left_tree_size * 2 + 1
           return other







class    a_     :





     def __init__(				self	:      Optional[Any]			,   lowercase	:      Any=None			,   lowercase	:      Optional[Any]=None			,   lowercase	:      int=0		):





        """simple docstring"""




        lowercase_    :Optional[int]					    =				heap_size
        lowercase_    :List[str]					    =				bottom_root
        lowercase_    :Dict					    =				min_node





     def 							lowercase__   (				self	:      List[str]			,   lowercase	:      List[Any]		):





        """simple docstring"""




        if other.size == 0:
           return None
        if self.size == 0:
           lowercase_    :Dict					    =				other.size
           lowercase_    :int					    =				other.bottom_root
           lowercase_    :Tuple					    =				other.min_node
           return None
        # Update size
        lowercase_    :Optional[int]					    =				self.size + other.size

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

        # Order roots by left_subtree_size
        lowercase_    :Any					    =				[]
        lowercase_    ,							lowercase_    :List[str]					    =				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)		)
              lowercase_    :str					    =				i.parent
           else:
              combined_roots_list.append((j, False)		)
              lowercase_    :Dict					    =				j.parent
        # Insert links between them
        for i in range(len(lowercase		) - 1		):
           if combined_roots_list[i][1] != combined_roots_list[i + 1][1]:
              lowercase_    :Dict					    =				combined_roots_list[i + 1][0]
              lowercase_    :str					    =				combined_roots_list[i][0]
        # Consecutively merge roots with same left_tree_size
        lowercase_    :int					    =				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
              lowercase_    :List[Any]					    =				i.left
              lowercase_    :Any					    =				i.parent.parent

              # Merging trees
              lowercase_    :Any					    =				i.merge_trees(i.parent		)

              # Updating links
              lowercase_    :List[Any]					    =				previous_node
              lowercase_    :int					    =				next_node
              if previous_node:
                 lowercase_    :int					    =				i
              if next_node:
                 lowercase_    :str					    =				i
           else:
              lowercase_    :str					    =				i.parent
        # Updating self.bottom_root
        while i.left:
           lowercase_    :List[str]					    =				i.left
        lowercase_    :List[str]					    =				i

        # Update other
        lowercase_    :Any					    =				self.size
        lowercase_    :Optional[Any]					    =				self.bottom_root
        lowercase_    :int					    =				self.min_node

        # Return the merged heap
        return self





     def 							lowercase__   (				self	:      int			,   lowercase	:      List[Any]		):





        """simple docstring"""




        if self.size == 0:
           lowercase_    :Dict					    =				Node(lowercase		)
           lowercase_    :Optional[Any]					    =				1
           lowercase_    :Optional[Any]					    =				self.bottom_root
        else:
           # Create new node
           lowercase_    :Union[str, Any]					    =				Node(lowercase		)

           # Update size
           self.size += 1

           # update min_node
           if val < self.min_node.val:
              lowercase_    :Union[str, Any]					    =				new_node
           # Put new_node as a bottom_root in heap
           lowercase_    :int					    =				new_node
           lowercase_    :List[str]					    =				self.bottom_root
           lowercase_    :Any					    =				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
              lowercase_    :int					    =				self.bottom_root.parent.parent

              # Merge
              lowercase_    :Union[str, Any]					    =				self.bottom_root.merge_trees(self.bottom_root.parent		)

              # Update Links
              lowercase_    :Optional[Any]					    =				next_node
              lowercase_    :Any					    =				None
              if next_node:
                 lowercase_    :Union[str, Any]					    =				self.bottom_root





     def 							lowercase__   (				self	:      str		):





        """simple docstring"""




        return self.min_node.val





     def 							lowercase__   (				self	:      Optional[int]		):





        """simple docstring"""




        return self.size == 0





     def 							lowercase__   (				self	:      str		):





        """simple docstring"""




        lowercase_    :str					    =				self.min_node.val

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

           # Update bottom root
           lowercase_    :int					    =				None

           # Update min_node
           lowercase_    :Tuple					    =				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
           lowercase_    :Optional[Any]					    =				self.bottom_root.parent
           lowercase_    :Tuple					    =				None

           # Update min_node
           lowercase_    :Dict					    =				self.bottom_root
           lowercase_    :List[str]					    =				self.bottom_root.parent
           while i:
              if i.val < self.min_node.val:
                 lowercase_    :Union[str, Any]					    =				i
              lowercase_    :Dict					    =				i.parent
           return min_value
        # General case
        # Find the BinomialHeap of the right subtree of min_node
        lowercase_    :List[str]					    =				self.min_node.right
        lowercase_    :Dict					    =				None
        lowercase_    :str					    =				bottom_of_new
        lowercase_    :Optional[int]					    =				1

        # Size, min_node and bottom_root
        while bottom_of_new.left:
           lowercase_    :List[Any]					    =				size_of_new * 2 + 1
           lowercase_    :Union[str, Any]					    =				bottom_of_new.left
           if bottom_of_new.val < min_of_new.val:
              lowercase_    :Optional[int]					    =				bottom_of_new
        # Corner case of single root on top left path
        if (not self.min_node.left) and (not self.min_node.parent):
           lowercase_    :Optional[int]					    =				size_of_new
           lowercase_    :Union[str, Any]					    =				bottom_of_new
           lowercase_    :Dict					    =				min_of_new
           # print("Single root, multiple nodes case")
           return min_value
        # Remaining cases
        # Construct heap of right subtree
        lowercase_    :Tuple					    =				BinomialHeap(
            bottom_root=lowercase			,   min_node=lowercase			,   heap_size=lowercase		)

        # Update size
        lowercase_    :Dict					    =				self.size - 1 - size_of_new

        # Neighbour nodes
        lowercase_    :Optional[Any]					    =				self.min_node.left
        lowercase_    :str					    =				self.min_node.parent

        # Initialize new bottom_root and min_node
        lowercase_    :int					    =				previous_node or next_node
        lowercase_    :Any					    =				next_node

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

           # Update bottom_root and search for min_node below
           lowercase_    :str					    =				previous_node
           lowercase_    :List[Any]					    =				previous_node
           while self.bottom_root.left:
              lowercase_    :List[str]					    =				self.bottom_root.left
              if self.bottom_root.val < self.min_node.val:
                 lowercase_    :List[Any]					    =				self.bottom_root
        if next_node:
           lowercase_    :List[Any]					    =				previous_node

           # Search for new min_node above min_node
           lowercase_    :Dict					    =				next_node
           while i:
              if i.val < self.min_node.val:
                 lowercase_    :Optional[Any]					    =				i
              lowercase_    :str					    =				i.parent
        # Merge heaps
        self.merge_heaps(lowercase		)

        return min_value





     def 							lowercase__   (				self	:      Dict		):





        """simple docstring"""




        lowercase_    :Optional[Any]					    =				self.bottom_root
        while top_root.parent:
           lowercase_    :int					    =				top_root.parent
        # preorder
        lowercase_    :List[str]					    =				[]
        self.__traversal(lowercase			,   lowercase		)
        return heap_pre_order





     def 							lowercase__   (				self	:      Union[str, Any]			,   lowercase	:      List[Any]			,   lowercase	:      List[str]			,   lowercase	:      Dict=0		):





        """simple docstring"""




        if curr_node:
           preorder.append((curr_node.val, level)		)
           self.__traversal(curr_node.left			,   lowercase			,   level + 1		)
           self.__traversal(curr_node.right			,   lowercase			,   level + 1		)
        else:
           preorder.append(("#", level)		)







     def __str__(				self	:      Optional[int]		):





        """simple docstring"""




        if self.is_empty():
           return ""
        lowercase_    :int					    =				self.pre_order()

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


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

 doctest.testmod()


