CSC 6520 Kahoot Session 2

Which of the statements are correct? (Select all that applies.) Group of answer choices A digraph is a graph whose edges are all directed. Digraphs can be applicable for detecting wash trade in financial market. Dijkstra's algorithm is based on the greedy method. Kruskal algorithm can be used to create a Minimum Spanning Tree. BFS runs in O(V+E) , where V is the number of vertices and E is the number of edges in the graph. DFS runs in O(V+E) as well.

a) Given a depth-first search tree T, the set of edges in T are referred to as "tree edges" while those not in T are referred to as "back edges". Modify the implementation of the Depth-First Search algorithm to print out the set of tree edges and the set of back edges for the following graph. 1(0 1 1 0 0 1 0) 210 100 0 0 31 10 10 1 4 0 0 1 0 0 0 0 50 0 0 00 1 1 1 0 1 70 0 1 0 1 1 0 6 1 0 0 0

java binary tree: For the following graph: (A) Find the adjacency matrix representation of the graph. (B) Find the sequence of vertices in the graph, if the graph is traversed using Breadth-FirstTraversal algorithm. Assume vertex 0 as the starting vertex.

Specifications: You will create an implementation of this algorithm. Your driver program should provide a graph and a source vertex in the graph.  Your implementation should use Dijkstra's Algorithm to determine the shortest path using adjacency matrix representation. Specifically, given a graph and a source vertex in the graph, find the shortest paths from source to all vertices in the given graph, using Dijkstra's Algorithm.

Which of the following statements are true. Do not show your explanations. (g) A minimal vertex-cut has minimum number of vertices among all vertex-cuts. (h) Prim’s algorithm and Kruscal’s algorithm will produce different minimum spanning trees. (i) Prim’s algorithm and Kruscal’s algorithm will produce the same minimum spanning tree.

Kruskal’s algorithm is best suited for the sparse graphs than the prim’s algorithm. a) True b) False

2. Use a deep-first search to find a spanning tree of the following graph starting from vertex а. (a) Write the list of the edges of the spanning tree in the order you add them. (b) Draw the minimal spanning tree.

Python and a graph Implement the heap-sort algorithm. Experimentally compare its running time with that of insertion sort and the built-in Python sorted function. You could use dummy functions with O(n^2) and O(nlogn) and use them as benchmarks in your graph. Results: 1. A graph showing the curves for heap-sort, insertion sort, and built-in the sorted function. 2. code that generates the data used in the graph.

Minimum Spanning Tree of a graph includes all its nodes Both the lazy and eager versions of Prims Algorithm use priority queue of edges. Both the lazy version of Prims Algorithm and Kruskal’s algorithm uses priority queue of edges. A crossing edge connects vertices that are in the same partition.5.Minimum Spanning Tree of a graph includes all its edges.6.A crossing edge connects vertices that are in different partitions. 7.Breadth First Search Algorithm can be used for weighted graph traversal.8.Depth First Search Algorithm can be used for weighted graph traversal.9.A spanning tree of a graph is a tree but not a graph.10.Kruskal algorithm starts with an initial vertex v and always adds next smallest edge to the same tree that is connected to the initial vertex v. Which are the following true or false ?

2. Perform topological sort on the following graph starting at node B: A D C E

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please solve in algorithm

H F D 3 2 B G E Recall that Dijkstra's Algorithm asks you to label vertices as "current" as you visit them. List all 8 vertices in the order in which they become the "current" vertex. Write your answer as a sequence of vertices like ACDEFGHB. (Note that you can either start with A as the current vertex or start with B as the current vertex and execute the algorithm---this problem accepts either solution.) What is the shortest path from A to B? Write your answer as a sequence of vertices like ACDGEB.

13 D 20 Show the execution of Dijkstra's shortest path algorithm, starting from vertex A. Draw the graph. After each relaxation, you will cross the previous best length and assign a new best length. Which list below shows the list of "best lengths" of the node C? O a. 6,5 O b. 0,6,5 O c. 00,6 O d. 0,5

Python Graph Algorithms: Minimum Spanning Trees Note: There are helper functions (see 'required' below), and some of them (like Kruskal's Algorithm, WeightedQuickUnion, and such) can help answering this problem. Problem: Suppose you are an engineer working on designing a road network for a new town. The town has many residential areas and commercial centers that need to be connected efficiently. You decided to represent the town as a connected, undirected graph where each vertex represents a location, and each edge represents a road connecting two locations. The weight of each edge represents the distance between the two locations. To ensure the road network is efficient, you need to find the minimum spanning tree of the graph. However, due to budget constraints, you can only construct roads with a maximum distance limit. You need to determine for how many pairs of locations, the minimum spanning tree of the graph remains the same when the maximum distance limit of a road is increased…

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…

DATA STRUCTURES AND ALGORITHMS C++ Write an algorithm which provides a path from a specific source to destination node in a graph withminimum stops. Draw a directed graph from the following adjacency list. Simulate/dry run your algorithm on it and provide step-by-step updates of values in used data structure(s) considering “A” as source and “J” asdestination.

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3. What is the shortest path from vertex 'd' to 'h'? You may use Dijkstra's algorithm or any other method. Answer in this format: a-b-c-d-e-f (h 3 b 2 2. 4 2 5 1 3

Dijkstra's single-source shortest-path algorithm returns a results grid that contains the lengths of the shortest paths from a given vertex to the other vertices reachable from it. Develop a pseudocode algorithm that uses the results grid to build and return the actual path, as a list of vertices, from the source vertex to a given vertex. (Hint: This algorithm starts with a given vertex in the grid's first column and gathers ancestor vertices, until the source vertex is reached.)

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Write a program for depth-first traversal on the following graph using the algo-rithm defined in this week

Question 2: Find the Breadth-first search for the following graph starting from vertex ‘A’ andinclude the steps.

A. Use Prim’s algorithm starting at node A to compute the Minimum Spanning Tree (MST) of the following graph. In particular, write down the edges of the MST in the order in which Prim’s algorithm adds them to the MST. Use the format (node1; node2) to denote an edge   B.  For the same graph as above, write down the edges of the MST in the order in which Kruskal’s algorithm adds them to the MST. NB: Graph in image

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Dijkstra's shortest path algorithm is run on the graph, starting at vertex C. When a vertex is dequeued, 0 or more adjacent vertices' distances are updated. For each iteration of the while loop in Dijkstra's algorithm, find the vertex dequeued and the adjacent vertices updated. Enter updated vertices as A, B, C or "none" if no adjacent vertices are updated. 3 A E 2 10 4 D 8 B 6 C Iteration Vertex dequeued Adjacent vertices updated 1 Ex: C Ex: A, B, C or none 2 3 A 5