If Breadth first search is applied to the following graph starting from node A, what is the pi table at the end for nodes B, C, D, E, F, G, H, respectively. Fill in the blanks in the same order from left to right. A В D E F G H
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- A graph is given below with its path and heuristics values. Show the process of identifying the correct path from the start node (A) to end node (M) following the Best First Search searching algorithms: Heuristic Values State Value A 0 B 3 C 6 D 5 E 1 F 3 G 2 H 4 I 3 J 2 K 1 L 2 M 1Given the undirected graph below, show the sequence of nodes visited when carrying out (i) depth first search and (ii) breadth first search starting from the node “A”. Neighbors are visited in alphabetical order.Run BFS algorithm on the following graph starting with vertex s. Whenever there is a choice of vertices, choose the one that is alphabetically first. What is the order that the vertices are visited? What is the shortest path from vertex s to vertex b?
- In hill-climbing algorithms there are steps that make lots of progress and steps that make very little progress. For example, the first iteration on the input given might find a path through the augmentation graph through which a flow of 30 can be added. It might, however, find the path through which only a flow of 2 can be added. How bad might the running time be when the computation is unlucky enough to always take the worst legal step allowed by the algorithm? Start by taking the step that increases the flow by 2 for the input. Then continue to take the worst possible step. You could draw out each and every step, but it is better to use this opportunity to use loop invariants. What does the flow look like after i iterations? Repeat this process on the same graph except that the four edges forming the square now have capacities 1,000,000,000,000,000 and the crossover edge has capacity 1. (Also move t to c or give that last edge a large capacity.)1. What is the worst case number of….... Multiple choice: Consider a weighted graph where all the edges have weight=10. If we want to determine the shortest path between any two vertices, which algorithm can we use? Select all that applies: (select many) a. Bellman-Ford Algorithm b. Breadth First Search c. Dijkstra's Algorithm d. Floyd-Warshall AlgorithmHand run the breadth-first search algorithm on the graph below:
- For the undirected graph G shown in Exampleand reproduced here for convenience, undertake Breadth first search for the key 9, by refining the Breadth first traversal algorithm.Answer the following statements as true or false regarding Prim's algorithm: a. True or False: Prim's algorithm can only be used on weighted graphs. b. True or False: Prim's algorithm will produce a graph with equal number of vertices and edgesURGENT!!! Using the given graph, answer the following questions: a) Write the adjacency list of the graph. b)List all the nodes of the graph in depth-first traversal starting from node 0. Note: among the possible modes to visit, from the current one, choose the node with the smallest label when you have the possibility to select from several nodes. c) List all the nodes of the graph in breadth-first traversal starting from node 0. Note: among the possible modes to visit, from the current one, choose the node with the smallest label when you have the possibility to select from several nodes.
- A graph is called bipartite or 2-colorable if its vertices can be divided into two disjoint subsets can be divided in such a way that no edges run between the nodes within both subsets. Design an algorithm using breadth-first search (detailed description or pseudocode) that, given a graph G = (V;E), determines whether it is bipartite is. What is the running time of your algorithm?Given the following search tree, state the order in which the nodes will be searched for breadth first and depth first, until a solution B is reached.Input: A directed graph G with n vertices. Task: If one can add at most one directed edge to G such that every vertex can reach all other vertices, then print 'Yes'. Otherwise, print 'Unsatisfiable'. Give an efficient algorithm (to the best of your knowledge) and a formal proof of correctness for your algorithm. An answer without any formal proof will be considered incomplete. Analyze the running time of the algorithm. You must write down your algorithm as pseudocode