Identify the k largest of the N items in the priority queue by creating a minimum-oriented priority queue of size k, then proving that N k substitute the minimum (insert followed by remove the minimum) procedures leave the priority queue with k largest items.

Build a Binary Search Tree with the given input order. You must show step by step process of inserting the inputs including both recursive calls and tree diagrams for each step. [ refer to the Insertitem function of Lecture 10 slides to get an idea of doing this.] N.B: Unique Input orders for each student to build the tree are given on a separate file. Write down the input order on your answer script before answering the question. You must use the assigned input order. Do not change the order. TREE INPUT: 4,1,9,3,2,5,6,8,7

A sequential search of a sorted list can halt when the target is less than a given element in the list. Define a modified version of this algorithm and state the computational complexity, using big-O notation, of its best-, worst-, and average- case performances.

Prove that building a minimum-oriented priority queue of size k then doing N k replace the minimum (insert followed by remove the minimum) operations leaves the k largest of the N items in the priority queue.

5. Given an efficient circular bent array-based queue q capable of holding 7 objects. Show the final contents of the array after the following code is executed: for (int k = 1; k <= 6; k++) q.enqueue(k); for (int k = 1; k <= 3; k++) { q.dequeue(); q.enqueue(q.dequeue()); } 0 1 2 3 4 5 6

Cliques The Clique problem is finding the subsets of vertices all adjacent to each other. The maximum clique is the largest complete subgraph with every vertex connected by an edge. Cliques are studied in social networks, bioinformatics, and computational chemistry. Describe the brute force algorithm to find the maximum clique. What algorithm complexity class is the brute force solution to the clique problem? What time complexity is the brute force algorithm to find the maximum clique? How does the graph of a clique differ from the graph of a social network influencer? List the number of algorithm steps for graphs with the following vertex count: 10,100,1000

Given two (singly) linked lists, determine if the two lists intersect. Return the intersecting node. Note that the intersection is defined based on reference, not value. That is, if the kthnode of the first linked list is the exact same node (by reference) as the jth node of the secondlinked list, then they are intersecting.