Given the graph G, using the Graph Breadth-First Search algorithm with a Queue, please do the following: a) Show the adjacency list for graph G. b) Assume that the start node is 7 (e.g. node = 7). Demonstrate a step-by-step, manual desk- check execution of the BFS algorithm, showing the values of all variables and arrays (e.g. visited, inqueue, Q) for each step in each cycle of each loop, as demonstrated in class...

4-Clique Problem The clique problem is to find cliques in a graph. A clique is a set of vertices that are all adjacent - connected - to each other. A 4-clique is a set of 4 vertices that are all connected to each other. So in this example of the 4-Clique Problem, we have a 7-vertex graph. A brute-force algorithm has searched every possible combination of 4 vertices and found a set that forms a clique: https://en.wikipedia.org/wiki/Clique_problem   You should read the Wikipedia page for the Clique Problem (and then read wider if need be) if you need to understand more about it. Note that the Clique Problem is NP-Complete and therefore when the graph size is large a deterministic search is impractical. That makes it an ideal candidate for an evolutionary search. For this assignment you must suppose that you have been tasked to implement the 4-clique problem as an evolutionary algorithm for any graph with any number of vertices (an n-vertex graph). The algorithm succeeds if it finds a…

What is the time complexity for inserting an item in the array implementation of priority queues? Explain “Why”. Please, note that inserting items should be in sorted order.

Please answer all questions in detail and with pseudo codes.

"Dijkstra's single-source shortest path algorithm returns a results grid that contains the lengths of the shortest paths from a given vertex [the source vertex] to the other vertices reachable from it. Develop a pseudocode algorithm that uses the results grid to build and return the actual [shortest] path, as a list of vertices, from the source vertex to a given [target] vertex. (Hint: This algorithm starts with a given vertex [the target vertex] in the grid's first column and gathers ancestor [parent] vertices, until the source vertex is reached.)" *For your algorithm, assume that grid is the name of the results grid produced by Dijkstra's single-source shortest path algorithm. *Each vertex is identified by its label/name, which is in column 1 of grid. *As the first step of your algorithm, find the name of the source vertex. *Next, get the name of the target vertex from the user. Pseudocode should avoid details through broad-stroke statements. However, it must give enough information…

1 6 0 2 4 7 3 5 Graph G

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

Let T be a binary search tree with n nodes, in which n > 0. When T is linear, the search algorithm makes key comparisons, in the unsuccassful case.

a.Given the steps of Kruskal’s algorithm, analyze each loop and find its running time cost in terms of V and E.   MST-KRUSKAL(G,w) A ←  for each vertex v  V MAKE-SET(v) sort E into non-decreasing order by w for each (u, v) taken from the sorted list if FIND-SET(u)  FIND-SET(v) then A ← A  {(u, v)} UNION(u, v) return A b. What is the total asymptotic running time of Kruskal’s algorithm

c. In graph traversal, Breadth-first Search (BFS) order is "Level order" in the sense that it explores the neighbour nodes first, before moving to the next level neighbours reachable from the source and its distance. A B E 3 5 F G Figure 2 ii) Perform Dijkstra's algorithm starting from node A. In which order does the algorithm visit the nodes, and what is the computed distance to each of them? There are several possible orders to visit the nodes; choose and show one possible path that can be taken.