A max-heap is a data structure wherein each nodes value is larger than both of its children. A max-heap is stored in an array and can also be logically represented by a complete binary tree. We showed two ways to build a max-heap. One is to assume the array is empty and to insert the values one by one. The other is to assume the values are already stored in an array and build the max-heap accordingly. Consider the followings values: 5, 7, 8, 1, 2, 3, 12.

1. If the array initially stores the values in the order as above, draw the complete binary tree and the array of the max-heap once it is constructed.

2. If the array is initially empty, draw the complete binary tree as well as the array of the max-heap once it is constructed.

3. After deleting the maximum value, draw the complete binary tree as well as the array of the max-heap.

d. After inserting a new value 15, draw the complete binary tree as well as the array of the max-heap.