Problem 1. Consider an array of size nine with the numbers in the following order 40, 20, 80, 60, 30, 90, 10, 70, 50. (a) Form the heap using the algorithm described in class. Show the heap as a tree. Show the heap as an array. Exactly how many comparisons did heap creation use? (b) Start with the heap created in Part (a). Show the array after each element sifts down during the Finish phase. How many comparisons does each sift use? What is the total number of comparisons after heap creation?