






from __future__ import annotations

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







class 							UpperCAmelCase_     (		a_		):




     @abstractmethod
     def __lt__(							self  ,	_lowerCAmelCase		):
          pass




     @abstractmethod
     def __gt__(							self  ,	_lowerCAmelCase		):
          pass




     @abstractmethod
     def __eq__(							self  ,	_lowerCAmelCase		):
          pass



SCREAMING_SNAKE_CASE__		:       int   							=							TypeVar("""T""", bound=Comparable)







class 							UpperCAmelCase_     (		Generic[T]		):




     def __init__(							self		):
          UpperCAmelCase__			:     list[T]										= []
          UpperCAmelCase__			:     int										= 0




     def __repr__(							self		):
          return str(self.h		)




     def      __UpperCAmelCase     (							self  ,	_lowerCAmelCase		):
          if child_idx > 0:
               return (child_idx - 1) // 2
          return None




     def      __UpperCAmelCase     (							self  ,	_lowerCAmelCase		):
          UpperCAmelCase__			:     Any										= 2 * parent_idx + 1
          if left_child_index < self.heap_size:
               return left_child_index
          return None




     def      __UpperCAmelCase     (							self  ,	_lowerCAmelCase		):
          UpperCAmelCase__			:     List[Any]										= 2 * parent_idx + 2
          if right_child_index < self.heap_size:
               return right_child_index
          return None




     def      __UpperCAmelCase     (							self  ,	_lowerCAmelCase		):
          if index < self.heap_size:
               UpperCAmelCase__			:     int										= index
               UpperCAmelCase__			:     int										= self.left_child_idx(_snake_case		)
               UpperCAmelCase__			:     int										= 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]:
                    UpperCAmelCase__			:     Optional[Any]										= left_child
               if right_child is not None and self.h[right_child] > self.h[violation]:
                    UpperCAmelCase__			:     int										= right_child
               # if violation indeed exists
               if violation != index:
                    # swap to fix the violation
                    UpperCAmelCase__			:     Any										= self.h[index], self.h[violation]
                    # fix the subsequent violation recursively if any
                    self.max_heapify(_snake_case		)




     def      __UpperCAmelCase     (							self  ,	_lowerCAmelCase		):
          UpperCAmelCase__			:     Optional[int]										= list(_snake_case		)
          UpperCAmelCase__			:     Union[str, Any]										= 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      __UpperCAmelCase     (							self		):
          if self.heap_size >= 2:
               UpperCAmelCase__			:     Optional[Any]										= self.h[0]
               UpperCAmelCase__			:     Optional[int]										= 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      __UpperCAmelCase     (							self  ,	_lowerCAmelCase		):
          self.h.append(_snake_case		)
          UpperCAmelCase__			:     Tuple										= (self.heap_size - 1) // 2
          self.heap_size += 1
          while idx >= 0:
               self.max_heapify(_snake_case		)
               UpperCAmelCase__			:     List[Any]										= (idx - 1) // 2




     def      __UpperCAmelCase     (							self		):
          UpperCAmelCase__			:     List[str]										= self.heap_size
          for j in range(size - 1  ,	0  ,	-1		):
               UpperCAmelCase__			:     str										= self.h[j], self.h[0]
               self.heap_size -= 1
               self.max_heapify(0		)
          UpperCAmelCase__			:     List[str]										= 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],
        [1_03, 9, 1, 7, 11, 15, 25, 2_01, 2_09, 1_07, 5],
        [-45, -2, -5],
    ]:
        print(f'''unsorted array: {unsorted}''')

        SCREAMING_SNAKE_CASE__		:       Heap[int]   							=							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(1_00)
        print(f'''after new value 100 inserted: {heap}''')

        heap.heap_sort()
        print(f'''heap-sorted array: {heap}\n''')














from ..utils import requires_backends


SCREAMING_SNAKE_CASE__		:       int   							=							None







class 							UpperCAmelCase_     :




     def __init__(							self  ,	*_lowerCAmelCase  ,	**_lowerCAmelCase		):
          requires_backends(self  ,	["""detectron2"""]		)




     @classmethod
     def      __UpperCAmelCase     (							cls  ,	*_lowerCAmelCase  ,	**_lowerCAmelCase		):
          requires_backends(cls  ,	["""detectron2"""]		)






