The heap data structure, specifically the binary heap, was introduced by J. W. J. Williams in 1964, as a data structure for the heapsort sorting algorithm. A common implementation of a heap is the binary heap, in which the tree is a binary tree (see figure).

COMING SOON!

```
class BinaryHeap:
"""
A max-heap implementation in Python
>>> binary_heap = BinaryHeap()
>>> binary_heap.insert(6)
>>> binary_heap.insert(10)
>>> binary_heap.insert(15)
>>> binary_heap.insert(12)
>>> binary_heap.pop()
15
>>> binary_heap.pop()
12
>>> binary_heap.get_list
[10, 6]
>>> len(binary_heap)
2
"""
def __init__(self):
self.__heap = [0]
self.__size = 0
def __swap_up(self, i: int) -> None:
""" Swap the element up """
temporary = self.__heap[i]
while i // 2 > 0:
if self.__heap[i] > self.__heap[i // 2]:
self.__heap[i] = self.__heap[i // 2]
self.__heap[i // 2] = temporary
i //= 2
def insert(self, value: int) -> None:
""" Insert new element """
self.__heap.append(value)
self.__size += 1
self.__swap_up(self.__size)
def __swap_down(self, i: int) -> None:
""" Swap the element down """
while self.__size >= 2 * i:
if 2 * i + 1 > self.__size:
bigger_child = 2 * i
else:
if self.__heap[2 * i] > self.__heap[2 * i + 1]:
bigger_child = 2 * i
else:
bigger_child = 2 * i + 1
temporary = self.__heap[i]
if self.__heap[i] < self.__heap[bigger_child]:
self.__heap[i] = self.__heap[bigger_child]
self.__heap[bigger_child] = temporary
i = bigger_child
def pop(self) -> int:
""" Pop the root element """
max_value = self.__heap[1]
self.__heap[1] = self.__heap[self.__size]
self.__size -= 1
self.__heap.pop()
self.__swap_down(1)
return max_value
@property
def get_list(self):
return self.__heap[1:]
def __len__(self):
""" Length of the array """
return self.__size
if __name__ == "__main__":
import doctest
doctest.testmod()
# create an instance of BinaryHeap
binary_heap = BinaryHeap()
binary_heap.insert(6)
binary_heap.insert(10)
binary_heap.insert(15)
binary_heap.insert(12)
# pop root(max-values because it is max heap)
print(binary_heap.pop()) # 15
print(binary_heap.pop()) # 12
# get the list and size after operations
print(binary_heap.get_list)
print(len(binary_heap))
```