Problem #2: (45 pts) (a) Consider a binary min-heap. Assume that 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 traversal. (b) Propose a O(n) running time complexity algorithm (only pseudo-code) to find all nodes less than some value X in a binary min-heap. Analyze its complexity, Justify (c) 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 and in the giver order , into an initially empty binary min heap. (d) Show the result of performing three deleteMin operations in the heap of the previous binary min heap. (e) Write a method replaceKey in the MinHeap class with the following signature: public void replaceKey(Integer oldKey, Integer newKey) The method will replace the first occurrence of oldKey with the newKey, and restore the Min-Heap property after the change, If the oldKey does not exist in the heap, the method prints an appropriate message and returns without changing the heap. Example: Suppose our binary heap object (bh) has the following keys