Homework 13: Single Points of Failure

The goal of this homework is to practice using undirected graphs.

Instructions

We encourage you to work with a partner.

In this assignment, you will identify vertices and edges which serve as “single points of failure” (SPOF). Specifically, you will identify vertices and edges which, if removed, would partition the graph into multiple components.

For example, consider the map of Marblehead shown below:

6 vertices superimposed over a map of Marblehead, MA

Imagine that each vertex, labeled 0 to 5, represents a location of interest, and the edges represent roads between them. If vertices 3 or 4 were removed, the graph would be partitioned into two components. The graph could also be partitioned if either the 3 4 or 4 5 edges were removed.

In this assignment, you will complete a program, SPOF.java, which will find these single points of failure. SPOF.java should accept one argument, the name of a text file describing a graph. First, the text file contains the number of vertices, then the number of edges. Next, the file contains a list of edges, represented as pairs of vertices. Consider marblehead.txt, shown below:

6
7
0 1
0 3
1 2
1 3
2 3
3 4
4 5

When your program is finished, it should give the following output:

> java-algs4 SPOF marblehead.txt
SPOF vertices:
3
4

SPOF edges:
3 4
4 5

Task 1: Download Starter Files

spof.zip contains the starter files for this assignment.

Task 2: Implement SPOF.java

Load the Graph

Add code to the main method to create a Graph object from a text file. Refer to the Graph(In in) constructor of the Graph class. GraphDOT’s main method from the Graphs lab may also be helpful.

Hint: Since Graph has a nice toString() method, you can easily print the graph to verify that you loaded it correctly.

Hint: You may need to include: import edu.princeton.cs.algs4.Graph;

Note: One of the Gradescope tests will hide the details of any bugs in your code. To diagnose such bugs, create your own test data and unit tests.

Detect SPOF Vertices

Next, write code to detect and print single point of failure vertices. Here is some pseudocode:

Detect SPOF Edges

Next, write code to detect and print single point of failure edges. Here is some pseudocode:

Hint: Consider creating an Edge class to represent each edge from the original graph.

Hint: To avoid duplicate edges, consider storing each Edge in a set. Your Edge implementation can consider edges 0 1 and 1 0 to be equal, for example. Essentially, sets are symbol tables with just keys, not values (see the “Sets” slides). Multiple set implementations are available, so select the most appropriate:

To be stored in a HashSet, your Edge class should implement equals() and hashCode() methods. To be stored in a TreeSet, your Edge class should implement equals() and Comparable. Refer to the “Hash Tables” slides for the hashCode() method recipe, and to the “Symbol Tables” slides for recipes for the Comparable interface and the equals() method. Implementing Comparable for Edge is challenging, because it isn’t obvious how to establish a total ordering between Edges, and without a total ordering, Edges may not be stored correctly in a TreeSet.

Hint: A solution that doesn’t use sets is also possible.

Handle Corner Cases

If the graph isn’t connected to begin with, your code should print an error:

> java-algs4 SPOF island.txt
ERROR: Graph is not connected

Submit

Upload the following files to Gradescope:

For full credit, your code should be reasonably efficient (the autograder will check this).

Also, be sure to indicate your group member on Gradescope.