You have been provided a Python file, heap.py, which constructs a heap structure with a list. Using that code as a guide:

-- Develop a heap data structure using a binary tree structure

-- The heap must support add and remove from the heap

-- All operations most abide by the rules that govern a heap

Once you have your heap structure created, next you must use it as a backing structure to a priority queue.

-- Develop a priority queue data structure that is backed by the heap you just created

-- Implement the normal methods that accompany a priority queue structure:

-- Enqueue, dequeue, and peek by priority not position

-- Also length and whether or not the structure is empty (is_empty)

-- Perform the following operations to showcase your working structure:

-- Enqueue the following items: 4, 7, 5, 11, 8, 6, 9

-- Dequeue 3 items by priority, they should be 4, 5, & 6.

Provide a basic interface to allow users to interact with the Priority Queue. This can be a simple CLI that provides the user with the basic options of "Enqueue", "Dequeue", etc.

heap.py

class Heap:

def __init__(self):

self.heap = [0]

self.size = 0

def float(self, k):

while k // 2 > 0:

if self.heap[k] < self.heap[k//2]:

self.heap[k], self.heap[k//2] = self.heap[k//2], self.heap[k]

k //= 2

def insert(self, item):

self.heap.append(item)

self.size += 1

self.float(self.size)

def sink(self, k):

while k * 2 <= self.size:

mc = self.minchild(k)

if self.heap[k] > self.heap[mc]:

self.heap[k], self.heap[mc] = self.heap[mc], self.heap[k]

k = mc

def minchild(self, k):

if k * 2 + 1 > self.size:

return k * 2

elif self.heap[k*2] < self.heap[k*2+1]:

return k * 2

else:

return k * 2 + 1

def pop(self):

item = self.heap[1]

self.heap[1] = self.heap[self.size]

self.size -= 1

self.heap.pop()

self.sink(1)

return item

h = Heap()

for i in (4, 8, 7, 2, 9, 10, 5, 1, 3, 6):

h.insert(i)

print(h.heap)

for i in range(10):

n = h.pop()

print(n)

print(h.heap)