Write a C++ program called heap.cpp to conduct heap operations. When the program starts, it should read a set of numbers from a user. After that, your program should display if its a heap or not. If its not a heap, your program should construct a heap with the numbers. Then, your program should conduct heap operation(s). For the program, your heap should be implemented using a dynamic array.

IT NEEDS TO RUN EXACTLY LIKE BELOW, USING A DYNAMIC ARRAY:

Input size: 5

Enter numbers: 20 7 8 1 3

This is a heap.

Select an operation

1: Insert a number

2. Delete the max

3. Heapsort & Quit

1

Enter a number: 5

Updated heap: 20 7 8 1 3 5

Select an operation

1: Insert a number

2. Delete the max

3. Heapsort & Quit

2

Updated heap: 8 7 5 1 3

Select an operation

1: Insert a number

2. Delete the max

3. Heapsort & Quit

2

Updated heap: 7 3 5 1

Select an operation

1: Insert a number

2. Delete the max

3. Heapsort & Quit

3

Heapsort: 7 5 3 1

Bye!

This is another sample run:

Input size: 3

Enter numbers: 1 3 7

This is NOT a heap.

Heap constructed: 7 3 1

Select an operation

1: Insert a number

2. Delete the max

3. Heapsort & Quit

1

Enter a number: 100

Updated heap: 100 7 1 3

Select an operation

1: Insert a number

2. Delete the max

3. Heapsort & Quit

3

Heapsort: 100 7 3 1

Bye!