Problem 1: Consider a binary heap. We have a method that print the keys as encountered in a preorder traversal. Is the output sorted? Justify your answer Attempt the same question for inorder and postorder traversals.

Problem 2: Propose an algorithm to find all nodes less than some value X in a binary min heap. Analyze its complexity.

Problem 3:

(a) Given a sorted array of N distinct integers that has been rotated an unknown number of times. Implement (in Java) an efficient algorithm that finds an element in the array.

(b) What is the running time complexity of your algorithm? Note: You may assume that the array was originally sorted in increasing order.

Example:

Input: find 5 in array (15 16 19 20 25 1 3 4 5 7 10 14)

Output: 8 (the index of 5 in the array)