This is a Python program to implement a binary heap.

The program creates a binary max-heap and presents a menu to the user to perform various operations on it.

1. Create a class BinaryHeap with an instance variable items set to an empty list. This empty list is used to store the binary heap.

2. Define methods size, parent, left, right, get, get_max, extract_max, max_heapify, swap and insert.

3. The method size returns the number of elements in the heap.

4. The method parent takes an index as argument and returns the index of the parent.

5. The method left takes an index as argument and returns the index of its left child.

6. The method right takes an index as argument and returns the index of its right child.

7. The method get takes an index as argument and returns the key at the index.

8. The method get_max returns the maximum element in the heap by returning the first element in the list items.

9. The method extract_max returns the the maximum element in the heap and removes it.

10. The method max_heapify takes an index as argument and modifies the heap structure at and below the node at this index to make it satisfy the heap property.

11. The method swap takes two indexes as arguments and swaps the corresponding elements in the heap.

12. The method insert takes a key as argument and adds that key to the heap.

Here is the source code of a Python program to implement a binary heap. The program output is shown below.

class BinaryHeap: def __init__(self): self.items = [] def size(self): return len(self.items) def parent(self, i): return (i - 1)//2 def left(self, i): return 2*i + 1 def right(self, i): return 2*i + 2 def get(self, i): return self.items[i] def get_max(self): if self.size() == 0: return None return self.items[0] def extract_max(self): if self.size() == 0: return None largest = self.get_max() self.items[0] = self.items[-1] del self.items[-1] self.max_heapify(0) return largest def max_heapify(self, i): l = self.left(i) r = self.right(i) if (l <= self.size() - 1 and self.get(l) > self.get(i)): largest = l else: largest = i if (r <= self.size() - 1 and self.get(r) > self.get(largest)): largest = r if (largest != i): self.swap(largest, i) self.max_heapify(largest) def swap(self, i, j): self.items[i], self.items[j] = self.items[j], self.items[i] def insert(self, key): index = self.size() self.items.append(key) while (index != 0): p = self.parent(index) if self.get(p) < self.get(index): self.swap(p, index) index = p bheap = BinaryHeap() print('Menu') print('insert <data>') print('max get') print('max extract') print('quit') while True: do = input('What would you like to do? ').split() operation = do[0].strip().lower() if operation == 'insert': data = int(do[1]) bheap.insert(data) elif operation == 'max': suboperation = do[1].strip().lower() if suboperation == 'get': print('Maximum value: {}'.format(bheap.get_max())) elif suboperation == 'extract': print('Maximum value removed: {}'.format(bheap.extract_max())) elif operation == 'quit': break

1. Create an instance of BinaryHeap.

2. The user is presented with a menu to perform various operations on the heap.

3. The corresponding methods are called to perform each operation.

Case 1: Menu insert <data> max get max extract quit What would you like to do? insert 5 What would you like to do? insert 3 What would you like to do? insert -3 What would you like to do? insert 10 What would you like to do? insert 8 What would you like to do? max get Maximum value: 10 What would you like to do? max extract Maximum value removed: 10 What would you like to do? max extract Maximum value removed: 8 What would you like to do? max extract Maximum value removed: 5 What would you like to do? max extract Maximum value removed: 3 What would you like to do? max get Maximum value: -3 What would you like to do? quit Case 2: Menu insert <data> max get max extract quit What would you like to do? insert 3 What would you like to do? insert 11 What would you like to do? insert 5 What would you like to do? max extract Maximum value removed: 11 What would you like to do? max get Maximum value: 5 What would you like to do? max extract Maximum value removed: 5 What would you like to do? insert 15 What would you like to do? max get Maximum value: 15 What would you like to do? quit

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