$27.$ Write the code to $[$enqueue $|$ dequeue$]$ from a priority queue stored as $[$a sorted dynamic array $|$ an unsorted linked list $|$ a heap$].$ Make sure to maintain the optimal Big$-$O for the given queue storage. $28.$ How can you determine the $[$min $|$ max$]$ value in a heap? Show the steps to remove the $[$min $|$ max$]$ value from the heap. Show the steps to insert a value into a heap and keep the heap order. $29.$ Given an array representation of binary heap, show the corresponding tree structure. Given a binary heap tree representation, show the corresponding array assuming root is at index $[0|1].30.$ What is the difference between "delete" in a heap and "delete" in other types of trees we discussed in class? $31.$ Explain how heapsort is O$($n lg n$)$ and can be done $"$in place". $32.$ Given an array of numbers, show the steps of the optimal heapify algorithm.