CSC212 Lab 13 2014

--D. Thiebaut (talk) 11:19, 17 November 2014 (EST)

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Problem #1: DFS

• Create a new program called Graph1.java and copy the code from this page.
• Implement the DFS function, with the main function calling a recursive helper function.

Question 1

Make your new DFS start with a vertex of your choice, and display all the vertices it visits. Below is an example of the output for G.DFS( 0 ).

DFS starting on 0: 0, 1, 2, 4, 3, 7, 8, 5, 6,

Question 2

Same question, but this time make DFS print the edges of the graph it visits. Below is an example of the output for G.DFS(0).

DFS starting on 0:
visiting Edge (0)---(1)
visiting Edge (1)---(2)
visiting Edge (1)---(4)
visiting Edge (4)---(3)
visiting Edge (3)---(7)
visiting Edge (7)---(8)
visiting Edge (1)---(5)
visiting Edge (5)---(6)

Problem #2: Connected Components

• A graph is connected if there is a path from any vertex to any other vertex in the graph.
• Create a new method called isConnected( ) that is based on DFS, and that returns true if the graph is connected, and false otherwise.
• The graph created by the init1() method is connected. You will need to add a new method called, say, init2() that initializes the graph with several disconnected components. (Hints: You can probably remove some edges from the graph generated by init1() to get a graph with several components!)

Problem #3: GraphViz & Dot

• Add a method to your graph that will print the graph in dot language, as we did with trees a while back.
• Here's the dot version of the graph generated by init1():

graph G { 1 -- 0; 2 -- 1; 3 -- 0; 4 -- 1; 4 -- 3; 5 -- 1; 6 -- 5; 7 -- 3; 8 -- 4; 8 -- 7; }

• You can test your dot definition at this URL: http://sandbox.kidstrythisathome.com/erdos/

Problem #4: 6 degrees of Separation

• Have you ever heard of Kevin Bacon's degrees of separation? The idea is explained here.

• Assume that we take 100 Hollywood stars and record the connections that they have had during the past year. This generates a graph shown here:

Problem #3

All-Pairs Shortest Paths