Problem 3. Perform Depth-First Search on the directed graph shown in figure 3 (or show the order in which all the vertices will be discovered or visited). The starting vertex is 'A'. Classify all the edges (Tree edges, Back edges, Forward edges and Cross edges) in your graph after performing DFS. А B D E F G H Figure 3

We have the following directed graph G, where the number on each edge is the cost of the edge. 1. Step through Dijkstra’s Algorithm on the graph starting from vertex s, and complete the table below to show what the arrays d and p are at each step of the algorithm. For any vertex x, d[x] stores the current shortest distance from s to x, and p[x] stores the current parent vertex of x. 2. After you complete the table, provide the returned shortest path from s to t and the cost of the path.

Consider the following graph: a Specify a simple cycle. Use only lower case letters. If the graph has any cycles which are not simple and which have no repeated edges, specify one. If there are none enter none Use only lower case letters.

1. Run DFS-with-timing on this graph G: give the pre and post number of each vertex. Whenever there is a choice of vertices to explore, always pick the one that is alphabetically first. 2. Draw the meta-graph of G. 3. What is the minimum number of edges you must add to G to make it strongly connected (i.e., it consists of a single connected component after adding these edges)? Give such a set of edges. b.

One can model a maze by having a vertex for a starting point, a finishing point, dead ends, and all the points in the maze where more than one path can be taken, and then connecting the vertices according to the paths in the maze. a. Construct such a graph for the following maze. 鷗 b. Which traversal DFS or BFS- would you use if you found yourself in a maze and why?

Alert dont submit AI generated answer.   Write a program that reads a weighted graph and an initial vertex.The program must print on the screen the minimum paths obtained by Dijkstra's algorithm. Input: Receives n, m and s; n is the total number of vertices, m the total number of arcs and s is the initial vertex.Next, m lines, each line with a trio of integers, corresponding to the beginning and end of the arc, followed by the weight of the arc.(Vertices are identified from 0 to n-1.) Output: Prints the shortest paths obtained by Dijkstra's algorithm. Exemple: Input: 5 10 00 1 100 4 51 2 11 4 22 3 43 2 63 0 74 1 34 2 94 3 2 Output: [0, 8, 9, 7, 5][-1, 4, 1, 4, 0]

2. Consider the graph G2(V2, E2) below. 2a. Find the MST of this graph with Kruskal’s algorithm. Draw the MST, and show the table [edge] [w(u, v)] [mark]. 2b. Find the MST of this graph with Prim’s algorithm starting at vertex 'a'. Draw the MST and list the vertices in order you added them to the MST. 2c. Would you get a different MST if you repeat 2b starting at vertex 'e'? Why or why not?

A. Let G be a graph on 17 vertices. We know that G contains at most one cycle. How many edges can G contain at the most? B. The expression r is written in post-order notation (also referred to as RPN). What value does r evaluate to? r = 1 6 7 + - 5 3 + 2 * +

Please make a graph by hand for each step. no code

Write a function that returns true (1) if there is an edge between two vertices u and v in an adjacency-listed directed graph.