1. Can both insert and find Min be implemented in constant time?
2. a. Show the result of inserting 10, 12, 1, 14, 6, 5, 8, 15, 3, 9, 7, 4, 11, 13, and 2, one at a time, into an initially empty binary heap.
b. Show the result of using the linear-time algorithm to build a binary heap using the same input.
3. Show the result of performing three deleteMin operations in the heap of the previous exercise.
4. A complete binary tree of N elements uses array positions 1 to N. Suppose we try to use an array representation of a binary tree that is not complete. Determine how large the array must be for the following:
a. a binary tree that has two extra levels (that is, it is very slightly unbalanced)
b. a binary tree that has a deepest node at depth 2 log N
c. a binary tree that has a deepest node at depth 4.1 log N
d. the worst-case binary tree