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- (3) Using the following graph, draw the Minimum Spanning Tree, and by using Dijkstra’s Algorithm give the shortest path from A to F (do not confuse F with E). You may either draw the shortest path, or write out the steps needed to follow the route you find.Suppose Dr. WhyLie comes up to you and claims that he has invented a super-fastcomparison based priority queue. The speed of the priority queue operations are as follows(n is the number of items currently in the priority queue):a. insert a new item in O(sqrt(log n)) timeb. extract (remove and return) the smallest item from the priority queue in O(sqrt(logn)) time.Explain why Dr. WhyLie must be lying.Consider the following graph: Start with node s and apply the Dijkstra’s algorithm step by step. Show the priority queue at each step of traversing a node. Also, show final paths (along with the path length) from node ‘s’ to every other reachable node.
- Explain The Maximum Capacity Path Problem and the Minimum Spanning Tree ProblemProblem Suppose, there are three producers P1, P2, and P3 who want to produce and put items in the buffer. And, there are four consumers C1, C2, C3, and C4 who want to consume items from the buffer. No process takes more than 5 units of time to complete unless the process goes to the waiting queue(S->list) of semaphore. At a certain point of the execution, following are the values of the semaphores: mutex=1 , countEmpty=8, countFull=2 Find the output of the following sequence of commands. At time 0 : C1 started At time 0: C2 started At time 10: C3 started Value of countEmpty: ANSWER: Value of countFull: ANSWER: Processes in the waiting queue of the semaphore: [Write process names with Capital letter, For example: P7. If there are multiple process writes their names using comma, For example: P6,P7. If there is no process in the semaphore's list, write EMPTY in the box] ANSWER: At time 15 : P1 started At time 20 : P2 started Value of countEmpty: ANSWER: Value of countFull: ANSWER:…Find the minimum spanning tree using Prims algorithm and show the process step by step. (I gave here the picture of this question)
- 5.04-2. Bellman Ford Algorithm (1, part 2). Consider the scenario shown below, where at t=1, node e receives distance vectors from neighboring nodes d, b, h and f. The (old) distance vector at e (the node at the center of the network) is also shown, before receiving the new distance vector from its neighbors. Indicate which of the components of new distance vector at e below have a value of 2 after e has received the distance vectors from its neighbors and updated its own distance vector.Dynamic ProgrammingConsider the following network below: (a) Label all of the nodes such that for every arc, (i,j), where i is the start and j the end node for the arc, the labels satisfy i < j.(b) Why can we use the node labeling algorithm to label the nodes in this network? (c) Use forward DP to find the shortest path from your first labeled node to every node in the network.(d) What fundamental characteristic of dynamic programs allow us to breakdown large-sized problems into a series of smaller-sized problems? What does this characteristic establishes?i)- Write an algorithm to find the longest path in a DAG, where the length of the path is measured by the number of edges that it contains. What is the asymptotic complexity of your algorithm? ii) - Write an algorithm to find a maximum cost spanning tree, that is, the spanning tree with highest possible cost.
- Solve those Two questions: i)- Write an algorithm to find the longest path in a DAG, where the length of the path is measured by the number of edges that it contains. What is the asymptotic complexity of your algorithm? ii) - Write an algorithm to find a maximum cost spanning tree, that is, the spanning tree with highest possible cost.P5. Consider the network shown below, and assume that each node initially knows the costs to each of its neighbors. Consider the distance-vector algorithm and show the distance table entries at node z. The resulting answer should replicate the technique used in Fig 5.6, though it will vary slightly as there are more than three variables in this specific problem.8. without using any standard template library Write code for DAG shortest path algorithm to find shortest path from a given source node to all other nodes using adjacency list representations Write code for DAG shortest path algorithm to find shortest path from a given source node to all other nodes using adjacency matrix representations.