Explain the Bellman-Ford Algorithm using the Single Source Shortest Path Algorithm (given a graph with a negative cycle)

Consider a graph with five nodes labeled A, B, C, D, and E. Let's say we have the following edges with their weights: A to B with weight 3 A to C with weight 1 B to C with weight 2 B to D with weight 1 C to E with weight 4 D to E with weight 2 a. Find the shortest path from A to E using Dijkstra's algorithm b. Use Prim to find the MST c. Use Kruskal to find the MST d. What's the difference between Prim and Kruskal algorithms? Do they always have the same result? Why or why not.

I need an example of a graph where using Floyd's algorithm to find the shortest path doesn't give the right answer because of negative edge weights

1. Consider the weighted, directed graph containing the following vertices and edges.(Weights are in the parentheses.)Vertices: {A, B, C, D} Edges: {AB(5), BC(3), CA(4), AD(2), DA(4), CB(3)}a. Starting at vertex C, determine the shortest path tree using Dijkstrab. If you were to apply Floyd-Warshall’s algorithm to this tree, would it include the shortest path tree you found using Dijkstra? Why or why not?c. Starting at vertex C, determine the minimum spanning tree using Prim.d. Would Kruskal’s algorithm always result in the same MST as Prim’s? Why or why not?   Please provide graphs if possible.

Design an algorithm to find the maximum spanning tree  of any graph with a run time of O(m log m).

Question 4: Find the Shortest Path Tree for the given graph using Dijkstra’s algorithm and writeall the steps. The source is from “Home”

There are many applications of Shortest Path Algorithm. Consider the problem of solving a jumbled Rubik's Cube in the fewest number of moves. I claim that this problem can be solved using a Shortest Path Algorithm. Determine whether this statement is TRUE or FALSE. NOTE: if you want to check if this statement is TRUE, think about how the Rubik's Cube Problem can be represented as a graph. What are the vertices? Which pairs of vertices are connected with edges? What is your source vertex and what is your destination vertex? How would Dijkstra's Algorithm enable you to find the optimal sequence of moves to solve a jumbled cube in the fewest number of moves?

Question 2 What is the shortest path between A and Z in the graph below? (The length of a path is the sum of the numbers along the edges on the path.) Explain briefly how you have found this solution: what algorithm or solution strategy did you use? Does it work on any graph? Path (e.g., A-B-E-Z) : A- - Z Explanation : E 1 G 2 2 1 3 A 3 3 2 3 B 4 1 F 2.

3. Given the directed Graph as below. B A 10 C 8 2 D E Using A as the source, illustrate the Dijkstra algorithm to find the shortest path from vertex A to any other vertex. Make sure to show all the steps.

3. Given the graph below. Illustrate Dijkstra algorithm to find the shortest path from vertex s as the source. G 10 15 2 2 5 d