



'''simple docstring'''





from __future__ import annotations

from abc import abstractmethod
from collections.abc import Iterable
from typing import Generic, Protocol, TypeVar






class __A      (  _a						):



 '''simple docstring'''







 @abstractmethod
 def __lt__(self			,       A	)   ->					Tuple:


      """simple docstring"""



      pass



 @abstractmethod
 def __gt__(self			,       A	)   ->					Optional[Any]:


      """simple docstring"""



      pass



 @abstractmethod
 def __eq__(self			,       A	)   ->					Dict:


      """simple docstring"""



      pass





lowercase_			=  TypeVar("T", bound=Comparable)






class __A      (  Generic[T]						):



 '''simple docstring'''







 def __init__(self	)   ->					List[Any]:


      """simple docstring"""



      _a     =  []
      _a     =  0



 def __repr__(self	)   ->					Optional[Any]:


      """simple docstring"""



      return str(self.h	)



 def  a__  (self			,       A	)   ->					Optional[int]:


      """simple docstring"""



      if child_idx > 0:
           return (child_idx - 1) // 2
      return None



 def  a__  (self			,       A	)   ->					Optional[int]:


      """simple docstring"""



      _a     =  2 * parent_idx + 1
      if left_child_index < self.heap_size:
           return left_child_index
      return None



 def  a__  (self			,       A	)   ->					Dict:


      """simple docstring"""



      _a     =  2 * parent_idx + 2
      if right_child_index < self.heap_size:
           return right_child_index
      return None



 def  a__  (self			,       A	)   ->					Optional[Any]:


      """simple docstring"""



      if index < self.heap_size:
           _a     =  index
           _a     =  self.left_child_idx(snake_case_	)
           _a     =  self.right_child_idx(snake_case_	)
           # check which child is larger than its parent
           if left_child is not None and self.h[left_child] > self.h[violation]:
                _a     =  left_child
           if right_child is not None and self.h[right_child] > self.h[violation]:
                _a     =  right_child
           # if violation indeed exists
           if violation != index:
                # swap to fix the violation
                _a     =  self.h[index], self.h[violation]
                # fix the subsequent violation recursively if any
                self.max_heapify(snake_case_	)



 def  a__  (self			,       A	)   ->					Optional[Any]:


      """simple docstring"""



      _a     =  list(snake_case_	)
      _a     =  len(self.h	)
      if self.heap_size > 1:
           # max_heapify from right to left but exclude leaves (last level)
           for i in range(self.heap_size // 2 - 1			,       -1			,       -1	):
                self.max_heapify(snake_case_	)



 def  a__  (self	)   ->					Union[str, Any]:


      """simple docstring"""



      if self.heap_size >= 2:
           _a     =  self.h[0]
           _a     =  self.h.pop(-1	)
           self.heap_size -= 1
           self.max_heapify(0	)
           return me
      elif self.heap_size == 1:
           self.heap_size -= 1
           return self.h.pop(-1	)
      else:
           raise Exception('''Empty heap'''	)



 def  a__  (self			,       A	)   ->					str:


      """simple docstring"""



      self.h.append(snake_case_	)
      _a     =  (self.heap_size - 1) // 2
      self.heap_size += 1
      while idx >= 0:
           self.max_heapify(snake_case_	)
           _a     =  (idx - 1) // 2



 def  a__  (self	)   ->					List[str]:


      """simple docstring"""



      _a     =  self.heap_size
      for j in range(size - 1			,       0			,       -1	):
           _a     =  self.h[j], self.h[0]
           self.heap_size -= 1
           self.max_heapify(0	)
      _a     =  size


if __name__ == "__main__":
  import doctest

  # run doc test
  doctest.testmod()

  # demo
  for unsorted in [
      [0],
      [2],
      [3, 5],
      [5, 3],
      [5, 5],
      [0, 0, 0, 0],
      [1, 1, 1, 1],
      [2, 2, 3, 5],
      [0, 2, 2, 3, 5],
      [2, 5, 3, 0, 2, 3, 0, 3],
      [6, 1, 2, 7, 9, 3, 4, 5, 10, 8],
      [103, 9, 1, 7, 11, 15, 25, 201, 209, 107, 5],
      [-45, -2, -5],
  ]:
    print(F"""unsorted array: {unsorted}""")

    lowercase_			=  Heap()
    heap.build_max_heap(unsorted)
    print(F"""after build heap: {heap}""")

    print(F"""max value: {heap.extract_max()}""")
    print(F"""after max value removed: {heap}""")

    heap.insert(100)
    print(F"""after new value 100 inserted: {heap}""")

    heap.heap_sort()
    print(F"""heap-sorted array: {heap}\n""")








'''simple docstring'''





import warnings
from collections.abc import Callable
from typing import Any

import numpy
from matplotlib import pyplot

lowercase_			=  0.25 + 0.0J
lowercase_			=  -0.4 + 0.6J
lowercase_			=  -0.1 + 0.651J
lowercase_			=  -2.0
lowercase_			=  56
lowercase_			=  2.0
lowercase_			=  666




def lowerCAmelCase  (__A  ,     __A):



     """simple docstring"""



     return numpy.exp(__A) + c_parameter




def lowerCAmelCase  (__A  ,     __A):



     """simple docstring"""



     return z_values * z_values + c_parameter




def lowerCAmelCase  (__A  ,     __A):



     """simple docstring"""



     _a     =  numpy.linspace(-window_size  ,     __A  ,     __A)
     _a     =  x.reshape((nb_pixels, 1))
     _a     =  numpy.linspace(-window_size  ,     __A  ,     __A)
     _a     =  y.reshape((1, nb_pixels))
     return x + 1.0J * y




def lowerCAmelCase  (__A  ,     __A  ,     __A  ,     __A  ,     __A = None  ,     ):



     """simple docstring"""



     _a     =  z_a.astype('''complex64''')
     for _ in range(__A):
          _a     =  eval_function(__A  ,     __A)
          if infinity is not None:
               numpy.nan_to_num(__A  ,     copy=__A  ,     nan=__A)
               _a     =  infinity
     return z_n




def lowerCAmelCase  (__A  ,     __A  ,     __A  ,     __A  ,     ):



     """simple docstring"""



     _a     =  (abs(__A)).transpose()
     _a     =  abs_z_final[::-1, :]
     pyplot.matshow(abs_z_final < escape_radius)
     pyplot.title(F'''Julia set of ${function_label}$, $c={function_params}$''')
     pyplot.show()




def lowerCAmelCase  ():



     """simple docstring"""



     warnings.filterwarnings(
         '''ignore'''  ,     category=__A  ,     message='''overflow encountered in multiply''')
     warnings.filterwarnings(
         '''ignore'''  ,     category=__A  ,     message='''invalid value encountered in multiply'''  ,     )
     warnings.filterwarnings(
         '''ignore'''  ,     category=__A  ,     message='''overflow encountered in absolute''')
     warnings.filterwarnings(
         '''ignore'''  ,     category=__A  ,     message='''overflow encountered in exp''')


if __name__ == "__main__":
  lowercase_			=  prepare_grid(window_size, nb_pixels)

  ignore_overflow_warnings()  # See file header for explanations

  lowercase_			=  24
  lowercase_			=  2 * abs(c_cauliflower) + 1
  lowercase_			=  iterate_function(
      eval_quadratic_polynomial,
      c_cauliflower,
      nb_iterations,
      z_a,
      infinity=1.1 * escape_radius,
  )
  show_results("z^2+c", c_cauliflower, escape_radius, z_final)

  lowercase_			=  64
  lowercase_			=  2 * abs(c_polynomial_a) + 1
  lowercase_			=  iterate_function(
      eval_quadratic_polynomial,
      c_polynomial_a,
      nb_iterations,
      z_a,
      infinity=1.1 * escape_radius,
  )
  show_results("z^2+c", c_polynomial_a, escape_radius, z_final)

  lowercase_			=  161
  lowercase_			=  2 * abs(c_polynomial_a) + 1
  lowercase_			=  iterate_function(
      eval_quadratic_polynomial,
      c_polynomial_a,
      nb_iterations,
      z_a,
      infinity=1.1 * escape_radius,
  )
  show_results("z^2+c", c_polynomial_a, escape_radius, z_final)

  lowercase_			=  12
  lowercase_			=  1_0000.0
  lowercase_			=  iterate_function(
      eval_exponential,
      c_exponential,
      nb_iterations,
      z_a + 2,
      infinity=1.0e10,
  )
  show_results("e^z+c", c_exponential, escape_radius, z_final)



