
'''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   snake_case_       (							_a     :							float ,					_a     :							float ,					_a     :							int			):
      seed(1			)
      return [gauss(_a ,					_a			) for _ in range(_a			)]
def   snake_case_       (							_a     :							int ,					_a     :							list			):
      return [k for k in range(_a			) for _ in range(instance_count[k]			)]
def   snake_case_       (							_a     :							int ,					_a     :							list			):
      return sum(_a			) / instance_count
def   snake_case_       (							_a     :							int ,					_a     :							int			):
      return instance_count / total_count
def   snake_case_       (							_a     :							list ,					_a     :							list ,					_a     :							int			):
      snake_case_						       =							[]  # An empty list to store all squared differences
      # iterate over number of elements in items
      for i in range(len(_a			)			):
            # 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
      snake_case_						       =							len(_a			)  # Number of classes in dataset
      return 1 / (total_count - n_classes) * sum(_a			)
def   snake_case_       (							_a     :							list ,					_a     :							list ,					_a     :							float ,					_a     :							list			):
      snake_case_						       =							[]
      # for loop iterates over number of elements in list
      for i in range(len(_a			)			):
            # for loop iterates over number of inner items of each element
            for j in range(len(x_items[i]			)			):
                  snake_case_						       =							[]  # 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(_a			)			):
                        # 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(_a			)

      return [result.index(max(_a			)			) for result in results]
def   snake_case_       (							_a     :							list ,					_a     :							list			):
      snake_case_						       =							sum(1 for i, j in zip(_a ,					_a			) 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(_a			)) * 100


A           =   TypeVar("num")
def   snake_case_       (							_a     :							Callable[[object], num] ,					_a     :							str ,					_a     :							str ,					_a     :							Callable[[num], bool] = lambda _a			: True ,					_a     :							str | None = None ,					):
      while True:
            try:
                  snake_case_						       =							input_type(input(_a			).strip() or default			)
                  if condition(_a			):
                        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   snake_case_       (							):
      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
            snake_case_						       =							valid_input(
                input_type=_a ,					condition=lambda _a			: x > 0 ,					input_msg="Enter the number of classes (Data Groupings): " ,					err_msg="Number of classes should be positive!" ,					)

            print("-" * 100			)

            # Trying to get the value of standard deviation
            snake_case_						       =							valid_input(
                input_type=_a ,					condition=lambda _a			: 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("-" * 100			)

            # Trying to get number of instances in classes and theirs means to generate
            # dataset
            snake_case_						       =							[]  # An empty list to store instance counts of classes in dataset
            for i in range(_a			):
                  snake_case_						       =							valid_input(
                      input_type=_a ,					condition=lambda _a			: x > 0 ,					input_msg=(F'''Enter The number of instances for class_{i+1}: ''') ,					err_msg="Number of instances should be positive!" ,					)
                  counts.append(_a			)
            print("-" * 100			)

            # An empty list to store values of user-entered means of classes
            snake_case_						       =							[]
            for a in range(_a			):
                  snake_case_						       =							valid_input(
                      input_type=_a ,					input_msg=(F'''Enter the value of mean for class_{a+1}: ''') ,					err_msg="This is an invalid value." ,					)
                  user_means.append(_a			)
            print("-" * 100			)

            print("Standard deviation: " ,					_a			)
            # print out the number of instances in classes in separated line
            for i, count in enumerate(_a ,					1			):
                  print(F'''Number of instances in class_{i} is: {count}'''			)
            print("-" * 100			)

            # print out mean values of classes separated line
            for i, user_mean in enumerate(_a ,					1			):
                  print(F'''Mean of class_{i} is: {user_mean}'''			)
            print("-" * 100			)

            # Generating training dataset drawn from gaussian distribution
            snake_case_						       =							[
                gaussian_distribution(user_means[j] ,					_a ,					counts[j]			)
                for j in range(_a			)
            ]
            print("Generated Normal Distribution: \n" ,					_a			)
            print("-" * 100			)

            # Generating Ys to detecting corresponding classes
            snake_case_						       =							y_generator(_a ,					_a			)
            print("Generated Corresponding Ys: \n" ,					_a			)
            print("-" * 100			)

            # Calculating the value of actual mean for each class
            snake_case_						       =							[calculate_mean(counts[k] ,					x[k]			) for k in range(_a			)]
            # for loop iterates over number of elements in 'actual_means' list and print
            # out them in separated line
            for i, actual_mean in enumerate(_a ,					1			):
                  print(F'''Actual(Real) mean of class_{i} is: {actual_mean}'''			)
            print("-" * 100			)

            # Calculating the value of probabilities for each class
            snake_case_						       =							[
                calculate_probabilities(counts[i] ,					sum(_a			)			) for i in range(_a			)
            ]

            # for loop iterates over number of elements in 'probabilities' list and print
            # out them in separated line
            for i, probability in enumerate(_a ,					1			):
                  print(F'''Probability of class_{i} is: {probability}'''			)
            print("-" * 100			)

            # Calculating the values of variance for each class
            snake_case_						       =							calculate_variance(_a ,					_a ,					sum(_a			)			)
            print("Variance: " ,					_a			)
            print("-" * 100			)

            # Predicting Y values
            # storing predicted Y values in 'pre_indexes' variable
            snake_case_						       =							predict_y_values(_a ,					_a ,					_a ,					_a			)
            print("-" * 100			)

            # Calculating Accuracy of the model
            print(F'''Accuracy: {accuracy(_a ,					_a			)}'''			)
            print("-" * 100			)
            print(" DONE ".center(100 ,					"+"			)			)

            if input("Press any key to restart or 'q' for quit: "			).strip().lower() == "q":
                  print("\n" + "GoodBye!".center(100 ,					"-"			) + "\n"			)
                  break
            system("cls" if name == "nt" else "clear"			)  # noqa: S605


if __name__ == "__main__":
     main()



'''simple docstring'''





from __future__ import annotations

A           =   [2, 1, 4, 5, 6, 0, 8, 9, 1, 2, 0, 6, 4, 2, 0, 6, 5, 3, 2, 7]



class  lowerCAmelCase__   :



  '''simple docstring'''






  def __init__(self  : Optional[int]	, lowerCAmelCase_  : int    )   ->       None:
        snake_case_						       =							-1
        snake_case_						       =							-1
        snake_case_						       =							[-1] * length
        snake_case_						       =							None
        snake_case_						       =							None


  def __repr__(self  : List[Any]    )   ->       str:
        return f'''Node(min_value={self.minn} max_value={self.maxx})'''

def   snake_case_       (							_a     :							list[int]			):
      snake_case_						       =							Node(len(_a			)			)
      snake_case_       ,	snake_case_						       =							min(_a			), max(_a			)
      # Leaf node case where the node contains only one unique value
      if root.minn == root.maxx:
            return root
      snake_case_						       =							(root.minn + root.maxx) // 2

      snake_case_						       =							[]
      snake_case_						       =							[]

      for index, num in enumerate(_a			):
            if num <= pivot:
                  left_arr.append(_a			)
            else:
                  right_arr.append(_a			)
            snake_case_						       =							len(_a			)
      snake_case_						       =							build_tree(_a			)
      snake_case_						       =							build_tree(_a			)
      return root
def   snake_case_       (							_a     :							Node | None ,					_a     :							int ,					_a     :							int			):
      if index < 0 or node is None:
            return 0
      # Leaf node cases
      if node.minn == node.maxx:
            return index + 1 if node.minn == num else 0
      snake_case_						       =							(node.minn + node.maxx) // 2
      if num <= pivot:
            # go the left subtree and map index to the left subtree
            return rank_till_index(node.left ,					_a ,					node.map_left[index] - 1			)
      else:
            # go to the right subtree and map index to the right subtree
            return rank_till_index(node.right ,					_a ,					index - node.map_left[index]			)
def   snake_case_       (							_a     :							Node | None ,					_a     :							int ,					_a     :							int ,					_a     :							int			):
      if start > end:
            return 0
      snake_case_						       =							rank_till_index(_a ,					_a ,					_a			)
      snake_case_						       =							rank_till_index(_a ,					_a ,					start - 1			)
      return rank_till_end - rank_before_start
def   snake_case_       (							_a     :							Node | None ,					_a     :							int ,					_a     :							int ,					_a     :							int			):
      if index > (end - start) or start > end or node is None:
            return -1
      # Leaf node case
      if node.minn == node.maxx:
            return node.minn
      # Number of elements in the left subtree in interval [start, end]
      snake_case_						       =							node.map_left[end] - (
          node.map_left[start - 1] if start else 0
      )
      if num_elements_in_left_tree > index:
            return quantile(
                node.left ,					_a ,					(node.map_left[start - 1] if start else 0) ,					node.map_left[end] - 1 ,					)
      else:
            return quantile(
                node.right ,					index - num_elements_in_left_tree ,					start - (node.map_left[start - 1] if start else 0) ,					end - node.map_left[end] ,					)
def   snake_case_       (							_a     :							Node | None ,					_a     :							int ,					_a     :							int ,					_a     :							int ,					_a     :							int			):
      if (
          start > end
          or node is None
          or start_num > end_num
          or node.minn > end_num
          or node.maxx < start_num
      ):
            return 0
      if start_num <= node.minn and node.maxx <= end_num:
            return end - start + 1
      snake_case_						       =							range_counting(
          node.left ,					(node.map_left[start - 1] if start else 0) ,					node.map_left[end] - 1 ,					_a ,					_a ,					)
      snake_case_						       =							range_counting(
          node.right ,					start - (node.map_left[start - 1] if start else 0) ,					end - node.map_left[end] ,					_a ,					_a ,					)
      return left + right


if __name__ == "__main__":
     import doctest

     doctest.testmod()

