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Graphs

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Programming project 3
Task Title: Implementation of basic command-line interface to GraphApplication
Task Description:
Implement classes that will instantiate a graph editor. The system should accept various kinds of objects from user by given commands, and respond to these commands by creating node objects, creating arc objects, displaying them or deleting them. Implement the following classes: 1. GraphApplication class that will implement command line interface and interact with the user: This class needs to implement the following commands in its run() method: a. quit – exits the application b. nodes - lists the nodes in the graph c. arcs – lists the arcs in the graph these commands do not need index or parameters d. node - this command requires object for which the node will be created e. dir-arc – this command requires two objects that have nodes and relation name and makes a directed arc between them f. undir-arc – this command requires two objects that are added to nodes and relation name and makes non-directed (symmetric) arc between them these commands can take any object, but for now we will use strings g. printout, delete – these commands require an index or name for the object to be shown or deleted if delete takes two arguments it deletes the corresponding arc, of it gets only one, it deletes a node, if printout takes one argument it prints a node, if it takes two arguments it prints the fact that an arc exists between two nodes h. rectangle, circle – these commands take 3 (or 4) arguments and make corresponding instance of DrawObject subclasses
This class is the main class of the application. Implement main method in this class, which will create an instance of GraphApplication and execute its run method. 2. DrawObject class, an abstract class that will store common shape data and behavior, this class should include Point2D.Double data item which corresponds to a position of a geometric object in 2D space (x and y coordinates). This class needs to implement toString() methods and it needs to require printout() method from its subclasses. toString() method should report object position and type (use reflection to return class name!!). 3. Circle that will store the circle data (radius) that user enters in the window, this class extends DrawObject to represent a circle. This class needs to implement printout() method. 4. Rectangle that will store the rectangle data (width and height) that user enters in the window, this class extends DrawObject to represent a rectangle. This class needs to implement printout() method. 5. Node class that will store the data about an object that user enters in the command window, and also stores relations between this object and other objects. This class needs to implement printout() method. 6. Arc class that stores a relation between two objects and relation name 7. DirectedArc class that stores directed arc information. It extends Arc 8. UndirectedArc class that stores undirected arc information. It extends Arc 9. Graph class, which will keep a collection of Node-s and provides the methods for adding, listing and deleting objects.
Notes for creating programs: 1. Adhere strictly to object-oriented principles in making these classes. 2. Follow conventions in naming classes, methods and variables. (see distributed sheets) 3. Specifications for Node, Arc, DirectedArc and UndirectedArc, and Graph are given as attachment. For those classes implement only methods that you need to run your application correctly. Implement necessary constructors for those classes, for example You should have at least two constructors for arcs, one taking two nodes, and another taking two objects and finding nodes. 4. Comment your code, use javadoc convention for commenting each member variable and each method. 5. Make each class into separate file.
Testing
I will provide you scripts (sequence of commands) for testing your graph representation. However, you can introduce your own tests (think about family trees, streets - two-way and one-way, roads and cities, molecular structures, web links, facebook friends, …)
Deliverables:
You should submit a report that will describe your solution. The report should include: 1. Listing of all your programs (class code) – on USB disk 2. The screen printout of your program running on test data. 3. Copy your workspace onto USB disk into a folder project3 under your class folder (cs4500 or cs5500). Submit your USB disk to instructor by deadline.
Due date:
Program is due on Tuesday, February 19, 2013. at 1:30 pm.

Graph explanation

Graph definitions
The multigraph Gm = <N, R, A> is defined by a set of nodes N, set of relations R, and set of arcs A such that aE A implies that there exists an r E R, such that for two nodes n1 and n2 it is true that n1 ri n2. That is to say, a multigraph is defined by a set of nodes (objects), a set of relations between those objects and a set of arcs which correspond to facts that nodes are connected by specified relations.
Important property of the multigraph is transitivity of relations, which should be defined differently for a regular graph. In a multigraph transitivity is defined over two relations, which are defined in different dimensions. For relation ri to be transitive the following condition should be met: if N1 ri N2, and N1 rj N1’ and N2 rj N2’ than we define that N1’ ri N2’. An example of this transitivity can be explained on a precedence relation: if a process p1 should precede p2, and p1 is a member of p1’, and p2 is a member of p2’, than precedence relation should hold between p1’ and p2’.

public class Node { /** * Adds a node to this node connected by an undirected arc * @param aNode the node to connect to this node */ public void addNode(Node aNode); /** * Removes the relation between the parameter and this node * @param aNode the node whose relation is removed */ public void removeNode(Node aNode); /** * Adds a child node connected by a directed arc with this object as parent * @param child child node to this node */ public void addChild(Node child); /** * Removes the child node and the arc associated with it * @param child child node to this node * @throws IllegalArgumentException if input node is not a child node */ public void removeChild(Node child); /** * Adds a parent node connected by a directed arc with this object as parent * @param parent parent node to this node */ public void addParent(Node parent); /** * Removes the parent node and the arc associated with it * @param parent parent node to this node * @throws IllegalArgumentException if input node is not a parent node */ public void removeParent(Node parent); /** * Returns a list of graph nodes connected to this node by undirected arcs * @return List of connected Nodes */ public List<Node> getNodes(); /** * Returns a list of parent nodes connected to this node by directed arcs * @return List of parent Nodes */ public List<Node> getParents(); /** * Returns a list of child nodes connected to this node by directed arcs * @return List of child Nodes */ public List<Node> getChildren(); /** * Returns true if this node is root node having no parent nodes * @return true if root node */ public boolean isRoot(); /** * Returns true if this node is leaf node having no child nodes * @return true if child node */ public boolean isLeaf(); /** * Returns true if this node has at least one parent node * @return true if child */ public boolean isChild(); /** * Returns true if this node is child to the input node * @return true if child */ public boolean isChild(Node parent); /** * Returns true if this node has at least one child node * @return true if parent */ public boolean isParent(); /** * Returns true if this node is parent to the input node * @param child graph node * @return true if parent */ public boolean isParent(Node child); /** * Returns true if this node is connected to at least one node by an undirected arc * @return true if connected */ public boolean isConnected(); /** * Returns true if the input node is connected to this node * @param aNode * @return true if input node is connected */ public boolean isConnected(Node aNode); /** * Adds the directed arc to this node with this node as child * @param arc the DirectedArc to be added */ public void addInArc(DirectedArc arc); /** * Removes the directed arc to this node * @param arc the DirectedArc to be removed */ public void removeInArc(DirectedArc arc); /** * Adds the directed arc to this node with this node as parent * @param arc the DirectedArc to be added */ public void addOutArc(DirectedArc arc); /** * Removes the directed arc to this node * @param arc the DirectedArc to be removed */ public void removeOutArc(DirectedArc arc); /** * Adds the undirected arc to this node * @param arc the UndirectedArc to be added */ public void addArc(UndirectedArc arc); /** * Removes the undirected arc to this node * @param arc the UndirectedArc to be removed */ public void removeArc(Arc arc); /** * Returns the undirected arc between the input node and this node * @param aNode Node * @return the undirected arc between the nodes * @throws IllegalArgumentException if no arc exists */ public Arc getArc(Node aNode); /** * Returns the directed arc between the input node and this node * @param parent Node * @return the directed arc between the nodes * @throws IllegalArgumentException if no arc exists */ public DirectedArc getInArc(Node parent); /** * Returns the directed arc between the input node and this node * @param child Node * @return the undirected arc between the nodes * @throws IllegalArgumentException if no arc exists */ public DirectedArc getOutArc(Node child); /** * Returns a list of directed arcs to nodes having this node as child node * @return list of directed arcs */ public List<DirectedArc> getInArcs();

/** * Returns a list of directed arcs to nodes having this node as parent node * @return list of directed arcs */ public List<DirectedArc> getOutArcs(); /** * Returns a list of undirected arcs to nodes connected to this node * @return list of directed arcs */ public List<UndirectedArc> getArcs(); /** * Clears the relations (arcs) between this node and other connected nodes * and removes references to this node in other nodes */ public void clearArcs(); /** * Sets the user object associated with the node * @param o the user object * @throws IllegalArgumentException if o is null */ public void setUserObject(Object o); /** * Gets the user object associated with the arc * @return user object */ public Object getUserObject();

public class Arc {

/** * Determines whether a node belongs to the arc * @param aNode graph node */ public boolean nodeExists(Node aNode);

/** * Clears the arc and removes the relations in the nodes */ public void clear();

/** * Sets the user object associated with the arc * @param o the user object * @throws IllegalArgumentException if o is null */ public void setUserObject(Object o);

/** * Gets the user object associated with the arc * @return user object */ public Object getUserObject();

}

public class DirectedArc extends Arc {

/** * Returns the parent graph node in the arc * @return parent Graph node */ public Node getParent(); /** * Returns the child graph node in the arc * @return parent Graph node */ public Node getChild(); /** * Sets the parent graph node in the arc * @param parent Graph node */ public void setParent(Node parent); /** * Sets the parent graph node in the arc * @param child Graph node */ public void setChild(Node child);

}

public class UndirectedArc extends Arc { /** * Returns the other node associated with the arc given one node * @param aNode graph node in the arc * @throws IllegalArgumentException if node does not belong to arc */ public Node getOtherNode(Node aNode); public List<Node> getNodes();

}

public class Graph { /** * Adds a node to the graph * @param node Graph node */ public void addNode(Node node); /** * Removes a node from the graph * @param node Graph node */ public void removeNode(Node node); /** * Adds an undirected arc to the graph * @param node1 Node * @param node2 Node */ public void addBiArc(Node node1, Node node2); /** * Adds an directed arc to the graph * @param source graph node * @param sink graph node */ public void addDiArc(Node source, Node sink); /** * Removes an undirected arc from the graph * @param arc undirected arc */ public void removeArc(UndirectedArc arc); /** * Removes a directed arc from the graph * @param arc directed arc */ public void removeArc(DirectedArc arc); /** * Tests whether a graph node exists in the graph * @param node graph node * @return true if node exists */ public boolean nodeExists(Node node); /** * Tests whether an arc exists between two nodes in the graph * @param node1 graph node * @param node2 graph node * @return true if arc exists */ public boolean arcExists(Node node1, Node node2); /** * Tests whether a graph node is connected to other nodes by undirected or directed arcs * @param node graph node * @return true if node exists */ public boolean nodeHasArcs(Node node); public Node getNode(Object userObject); /** * Tests whether a graph node is connected to other nodes by directed arcs * @param node graph node * @return true if node exists */ public boolean nodeHasDirectedArcs(Node node); /** * Returns an iterator over the nodes connected to the input node * @param node graph nodes * @return an iterator */ public Iterator<Node> getConnectedNodes(Node node); /** * Returns an iterator over the children nodes to the input node * @param node graph nodes * @return an iterator */ public Iterator<Node> getChildNodes(Node node); /** * Returns an iterator over the parent nodes to the input node * @param node graph nodes * @return an iterator */ public Iterator<Node> getParentNodes(Node node); /** * Returns an iterator over all the nodes in the graph model * @param node graph nodes * @return an iterator */ public Iterator<Node> getNodes();

/** * Returns a subGraph based on the specified list of nodes * @param nodes graph nodes for the subgraph */ public Graph subGraph(List<Node> nodes); /** * Adds a listener to the graph * @param l an EventListener */

/** * Returns an iterator over the set of DirectedArcs present in the graph model * @return list of directed arcs */ public Iterator<DirectedArc> getDirectedArcs(); /** * Returns an iterator over the set of UndirectedArcs present in the graph model * @return list of undirected arcs */ public Iterator<UndirectedArc> getUndirectedArcs(); }

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Artificial Intelligence Questions

...3 I J Consider the graph above (not drawn to scale). Given the heuristic values for the distance to city F: h(A) = 5 h(B) = 3 h(C) = 6 h(D) = 3 h(E) = 2 h(F) = 0 h(G) = 7 h(H) = 8 h(I) = 29 h(J) = 9 h(K) = 8 Draw the search trees resulting from i) BFS can be performed on the graph ii) DFS iii) Uniform Cost iv) A* search on the graph with start node A. Q2) Consider the problem of finding a path in the grid shown below from the position s to the position g. A piece can move on the grid horizontally and vertically, one square at a time. No step may be made into a forbidden shaded area. 1. On the grid, number the nodes in the order in which they are removed from the frontier in a depth-first search from s to g, given that the order of the operators you will test is: up, left, right, then down. Assume there is a cycle check. 2. Number the nodes in order in which they are taken off the frontier for an A* search for the same graph. Manhattan distance should be used as the heuristic function. The Manhattan distance between two points is the distance in the x-direction plus the distance in the y-direction. It corresponds to the distance traveled along city streets arranged in a grid. For example, the Manhattan distance between g and s is 4. What is the path that is found? 3. Based on this experience, discuss which of the two algorithms is best suited for this problem. 4. Suppose that the graph extended infinitely in all directions...

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