Your project leader has been quite impressed by your performance on binary search trees, and started entertaining the idea of keeping you full time after you graduate. However, she needs to make a case to her manager about how magnificent a problem solver you are. Thus, she decided to put a few more challenges for you. This time she wants to test how well versed you are with heaps. You are given an unsorted array of size n. Below are the set of questions that you need to solve to prove your worth by using this unsorted array. (a)  The naive way of generating a heap with that array is by using a separate list of the same size and generating the heap by inserting elements one by one. Give a O(n log n) time algorithm to generate the heap. (b) That was easy. How about generating the heap in place? Give pseudocode or explain in plain English of a function, that generates a heap without using a second list. You can only use upheap/downheap functions that we used in class, while other…

There is an algorithm for making the heap complete:1. Remove the node at the root.2. Move the node in the last position to the root.3. Trickle the last node down until it is below.When this algorithm is applied continually, the data is removed from the heap in sorted order. Write the code for the Remove and TrickleDown methods in c#.

an application has a huge number of find the maximum operations, but a relatively small number of insert and remove the maximum operations. Which priority- queue implementation do you think would be most effective: heap, unordered array, or ordered array? Explain your Answer.