Advanced Java Concepts Unit 9: Graph Exercises

Transcription

1 dvanced Java oncepts Unit : Graph Exercises. Which one of the following data structures would be best suited for representing a street map for pedestrians? graph with... a) undirected, unweighted edges. b) undirected, weighted edges. c) directed, unweighted edges. d) directed, weighted edges. 2. Which one of the following data structures would be best suited for representing an online street map, with updated traffic reports for use in your car? graph with... a) undirected, unweighted edges. b) undirected, weighted edges. c) directed, unweighted edges. d) directed, weighted edges. 3. What is the cost of the path B? 4. List two unique simple paths from to D and their costs 4 B D Problems to 8 refer to the graph below.. What is the cost of the path EB?. List three unique simple paths from to D and their costs.. What is the minimum cost to go from B to E? 8. What is the minimum cost to go from to? 4 8 B D 8 F 2 E Page

2 . This graph is a) not weighted, not directed b) not weighted, directed c) weighted, not directed d) weighted, directed From/To B D B D Based on the graph shown in problem, list the unique paths from to and their costs.. This graph is a) not weighted, not directed b) not weighted, directed c) weighted, not directed d) weighted, directed From/To B D - - B D Based on the graph shown in problem, list the unique paths from B to D and their costs. From/To G R P H S G R P H S What is the cost of the path H to G to P to H? If this path through the graph is not possible, write N/. 4. What is the cost of the path G to R to to P to H? If this path through the graph is not possible, write N/.. What is the cheapest path from G to S? List the order of the vertices and the total cost? If it not possible to go from G to S, write umulig.. What is the cheapest path from R to P? List the order of the vertices and the total cost? If it not possible to go from R to P, write umulig.. Program. You are going to write a class that implements a weighted, directed graph. Each node will be represented as a String and the weights are all positive integer values stored in a two-dimensional array (i.e. an adjacency matrix). In this simple implementation, once you create a graph you will not be able to add or delete any vertices though you could add and remove edges. Page 2

3 Step. Write the constructor and the tostring method. Test your solution with the provided RunTest class. import java.util.*; public class Graph{ private int [][] edges; private List<String> nodes = new rraylist<string>(); public Graph( List<String> vertices ){ Set<String> set = new HashSet<String>( vertices); if ( set.size() < vertices.size() ) throw new IllegalrgumentException( "list contains duplicates" ); reate an appropriated sized adjacency matrix and initialize all values to - dd the items in vertices to nodes public String tostring(){ Return a string representation of the graph consistent with the results below. Use a period to represent weights of -; show the actual weight for all positive values. You will need to use \t and \n when constructing the string. Test your code using the RunTest.java file found online. Step 2. dd the following method to the Graph class and then execute RunTest2 to check your solution. The starting vertex of the edge is from and the ending vertex is to. public boolean addedge( String from, String to, int weight ){ This returns true if the adjacency matrix was updated; otherwise it returns false. Return false if from and/or to is not a vertex in the graph. Return false if from and to are the same vertices. Return false if the weight is not positive. You will want to use the indexof method of the List interface in order to figure out which element of the matrix should be changed. Be sure to return true after changing the adjacency matrix. Test your code using the RunTest2.java file found online. Page 3

4 Step 3. omplete the following method for the Graph class and then execute RunTest3 to check your solution. The parameter path contains a list of vertices in the graph. The method should return the total distance/weight when moving from one element to the next in the path. public int finddistance( List<String> path ) { throw an illegal argument exception if the path contains vertices not in the graph if it is possible to traverse the vertices, return total/distance otherwise return - to indicate that the path does not exist return zero if there is size of the path is less than 2 Test your code using the RunTest3.java file found online. Page 4

5 3 D E 4 B F. bove is a weighted, undirected graph. Find the minimum distance from F to all the other nodes using Dijkstra s algorithm. Unsettled List Settled B D E F List 8. bove is a weighted, undirected graph. Find the minimum distance from B to all the other nodes using Dijkstra s algorithm. Unsettled List Settled B D E F List Page

6 4 G 2 H 2 P 3 4 E 3 0 R S. bove is a weighted, directed graph. Find the minimum distance from E to all the other nodes using Dijkstra s algorithm. Settled List Unsettled List E G R P H S 20. bove is a weighted, directed graph. Find the minimum distance from G to all the other nodes using Dijkstra s algorithm. Settled List Unsettled List E G R P H S Page

7 Program 2 is really problem continued. dd the following methods to the Graph class. There is one public method and two private helper methods. fterwards run RunTest2 to check you solution. /* The parameter is one of the vertices in the graph. The method returns the shortest distance from that vertex to each of the other nodes using Dijkstra's algorithm. It should return 0 for the distance to itself. If there is no path from the vertex to a particular vertex in the graph then the distance equals Integer.MX_Value. If the vertex is not in the graph the method returns null. */ public Map<String, Integer> getshortestdistance( String startvertex ){ if (! nodes.contains( startvertex ) ) return null; Map<String, Integer> unsettled = new HashMap<String, Integer>(); dd all the nodes to the unsettled map. The integer values should be set to Integer.MX_VLUE except for the node that matches startvertex - initialize that distance to zero. Map<String, Integer> settled = new HashMap<String, Integer>(); // starts empty while ( unsettled.size() > 0 ){ String vertex = getnodewithlowestdistance( unsettled ); int dist = unsettled.remove( vertex ); settled.put( vertex, dist ); updateunsettled( vertex, dist, unsettled ); return settled; private String getnodewithlowestdistance( Map<String, Integer> unset ){ Returns the string/vertex in the unsettled map with the lowest integer value. If there s a tie, return either one. Do not remove anything from the unsettled map here. private void updateunsettled(string settledv, int disttovertex, Map<String, Integer> unset){ settledv is the vertex that was just added to the Settled map disttovertex is the shortest distance to settled check each node in the unsetmap; if there is an edge from the settledv to that node then: newdistance = disttovertex + edge from vertex to the node if ( newdistance < integer value associated with this node ) update the distance value for this node in the unsettled map Test your code using the RunTest4.java file found online. The graph is identical to the map used in problems and 20. Page

8 Expert Level Problem. dd the following method to the Graph class. It should use Dijkstra s algorithm to determine the shortest path from vertex start to vertex end and return a list with the vertices in order. public List<String> getbestpath( String start, String end ){ Preconditions: start and end are vertices in the graph. Post condition: the graph is unchanged. If there is no path from start to end then return null. The key to writing this method is to recognize that whenever you update the distance to a particular vertex, you must also save the vertex that preceded it. For example, consider the following graph and supposed we want to find the shortest path from to D. We will do the same thing we ve did earlier but this time we will add the name of the vertex that preceded the updated vertex. Unsettled B D 0 () 2 () B 8 (B) 2 (B) () B So the shortest path from to D is. nd the vertex previous to D is. Looking back we can see that the shortest path to passes through B and the shortest path to B starts at. onsequently, when writing the getbestpath method, you obviously track the vertices that are in the settled and unsettled groups. You must also track the distances and the predecessor vertices for each vertex. Here s a start: public List<String> getbestpath( String start, String end ){ Set<String> settled = new HashSet<String>(); Set<String> unsettled = new HashSet<String>(); Map<String, String> predecessors = new HashMap<String, String>(); Map<String, Integer> distances = new HashMap<String, Integer>(); For predecessors and distances, the keys are the names of the vertices. I used 3 helper methods ( more than the original approach). Note. If there is no path from start to end then return null. 2 3 D Test your code using the RunTest.java file found online. Page 8