Use the given Fibonacci heap in the figure and solve the following question. It’s a heap with a single tree. Only the node with value 31 is marked. Give a sequence of legal Fibonacci heap operations that could have created this tree starting from the empty heap.

Let's assume that a binary heap is represented using a binary tree such that each node may have a left child node and a right child node. For this type of representation, we can still label the nodes of the tree in the same way as we label the nodes for an array representation. That is, the root node has a label 1. In general, for a node with label i, its left child node will have a label 2i and the right child  has a label 2i+1.  For any i with 1 <= I <= n , Terry says that the following easy algorithm will walk you from the root node to the node with label i: First find the binary representation P of i.   Start with the rightmost bit (least significant bit) of P, walk down from the root as follow: For a 0 bit, walk to the left child, for a 1 bit walk to the right child. At the end, you’ll reach the node with label i.  Which of the following is the most appropriate? A. Terry’s algorithm is wrong and not fixable. B. Terry’s algorithm is right. C. Terry's algorithm can be…

Suppose we have an ArrayHeap that uses the array representation from class (also called "tree representation 3B" in lecture). Recall that in this representation that the leftmost item is unused. Consider a heap with the following underlying array: | •| | 2|•| • | •| | -8 5 1 10 | 10 | 12 --- Suppose we are using our heap to represent a priority queue. If we call removeSmallest on the heap above, where will the 12 end up after removeSmallest has completed execution? Assume removeSmallest works as described in the lecture. By "completed execution", we mean the entire operation is done and the array again obeys our heap properties. O 12 will not move. O 12 will not be present in the heap. O In the root position previously occupied by a -8. O In a position previously occupied by a 5. O In a position previously occupied by a -2. O In a position previously occupied by a 9. O In a position previously occupied by a 8. O In a position previously occupied by a 0. O In a position previously…

You are given a list of numbers for which you need to construct a min-heap. (A min-heap is a complete binary tree in which every key is less than or equal to the keys in its children.) How would you use an algorithm for constructing a max-heap (a heap as defined in Section 6.4) to construct a min-heap? You need to describe your algorithm in pseudo code.