1. Let A[0..n-1] be an array containing a bitonic sequence of n distinct numbers. A sequence is called bitonic if it consists of a decreasing sequence followed by an increasing sequence. For example, 9, 5, 3, -1, -7, 1, 8, 10, 12, 15, 17, 20 is bitonic, while 8, 5, 3, 2, 1, 7, 6 is not. Describe a divide-and-conquer algorithm that finds the minimum element in a bitonic array in O(logn) time. Hint: you can use the bitonic sequence in the example to describe your algorithm. (10 points)
2. Using the substitution method in the Lecture Week 3 slides as an example, show that the solution of T(n) = T(n - 1) + n is O(n^2). (5 points)
3. Using MAX-HEAPIFY example in the Lecture Week 3 slides as a model, illustrate the operation of MAX-HEAPIFY(A, 3) on the array A = [36, 19, 2, 17, 14, 11, 1, 5, 7, 12, 3, 8, 9, 0]. (5 points)