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Homework 10: Graph Algorithms Solution
For this assignment, you will be coding 4 di erent graph algorithms. This homework has quite a few les in it, so you should make sure to read ALL of the documentation given to you before asking a question. As has been stated in lecture, you cannot use grade replacement on this homework.
Search Algorithms
Breadth-First Search is a search algorithm that visits vertices in order of "levels", visiting all vertices one away from the start, then two away, etc. Similar to levelorder traversal in BSTs, it depends on a Queue data structure to work.
Depth-First Search is a search algorithm that visits vertices in a depth based order. It depends on a Stack based data structure to work, which for your implementation will be recursion. It searches along one path of vertices from the start vertex and backtracks once it hits a dead end or a visited vertex until it nds another path to continue along. Your implementation of DFS must be recursive to receive credit.
Single-Source Shortest Path (Dijkstra's Algorithm)
The next algorithm is Dijkstra's Algorithm. This algorithm nds the shortest path from one vertex to all of the other vertices in the graph. This algorithm only works for non-negative edge weights, so you may assume all edge weights for this algorithm will be non-negative.
There are two main variants of Dijkstra's Algorithm related to the termination condition of the algo-rithm. The classic variant is the version where you maintain a visited set to terminate early once you've visited all the vertices. The other variant is where you depend purely on the PriorityQueue to determine when to terminate the algorithm. You should implement the classic variant for this assignment.
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Homework 10: Graph Algorithms Due: See T-Square
Minimal Spanning Trees (Prim's Algorithm)
An MST has two components. By de nition, it is a tree, which means that it is a graph that is acyclic and connected. A spanning tree is a tree that connects the entire graph. It must also be minimal, meaning the sum of edge weights of the graph must be the smallest possible while still being a spanning tree.
By the properties of a spanning tree, any valid MST must have jV j 1 edges in it. However, since all undirected edges are speci ed as two directional edges, a valid MST for your implementation will have 2(jV j 1) edges in it.
Prim's algorithm is a greedy algorithm for nding an MST of the graph. It takes in a start vertex and works outwards, adding the cheapest edge that has not yet been reached until either all reachable edges have been explored or until an MST has been formed.
Self-Loops and Parallel Edges
In this framework, self-loops and parallel edges work as you would expect. These cases are valid test cases, and you should expect them to be tested. However, most implementations of these algorithms handle these cases automatically, so you shouldn't have to worry too much about them when implementing the algorithms.
Grading
Here is the grading breakdown for the assignment. There are various deductions not listed that are incurred when breaking the rules listed in this PDF, and in other various circumstances.
Methods:
BFS
15pts
DFS
15pts
Dijkstra's
25pts
Prim's
20pts
Other:
Checkstyle
10pts
E ciency
15pts
Total:
100pts
A note on JUnits
We have provided a very basic set of tests for your code, in GraphAlgorithmsStudentTests.java. These tests do not guarantee the correctness of your code (by any measure), nor does it guarantee you any grade. You may additionally post your own set of tests for others to use on the Georgia Tech GitHub as a gist. Do NOT post your tests on the public GitHub. There will be a link to the Georgia Tech GitHub as well as a list of JUnits other students have posted on the class Piazza.
If you need help on running JUnits, there is a guide, available on T-Square under Resources, to help you run JUnits on the command line or in IntelliJ.
Visualizations of Graphs
The directed graph used in the student tests is:
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Homework 10: Graph Algorithms Due: See T-Square
1 4 6
2 3 5 7
The undirected graph used in the student tests is:
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A B
5
8
3
C
F
2
D
E
6
1
Style and Formatting
It is important that your code is not only functional but is also written clearly and with good style. We will be checking your code against a style checker that we are providing. It is located in T-Square, under Resources, along with instructions on how to use it. We will take o a point for every style error that occurs. If you feel like what you wrote is in accordance with good style but still sets o the style checker please email Raymond Ortiz (rortiz9@gatech.edu) with the subject header of \CheckStyle XML".
Javadocs
Javadoc any helper methods you create in a style similar to the existing Javadocs. If a method is overridden or implemented from a superclass or an interface, you may use @Override instead of writing Javadocs. Any Javadocs you write must be useful and describe the contract, parameters, and return value of the method; random or useless javadocs added only to appease Checkstyle will lose points.
Exceptions
When throwing exceptions, you must include a message by passing in a String as a parameter. The mes-sage must be useful and tell the user what went wrong. \Error", \BAD THING HAPPENED", and \fail" are not good messages. The name of the exception itself is not a good message.
For example:
Bad: throw new IndexOutOfBoundsException("Index is out of bounds.");
Good: throw new IllegalArgumentException("Cannot insert null data into data structure.");
Generics
If available, use the generic type of the class; do not use the raw type of the class. For example, use new LinkedList<Integer() instead of new LinkedList(). Using the raw type of the class will result in a
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Homework 10: Graph Algorithms Due: See T-Square
penalty.
Forbidden Statements
You may not use these in your code at any time in CS 1332.
break may only be used in switch-case statements
continue package
System.arraycopy() clone()
assert()
Arrays class Array class
Collections class
Collection.toArray()
Re ection APIs
Inner or nested classes Lambda Expressions Method References
If you're not sure on whether you can use something, and it's not mentioned here or anywhere else in the homework les, just ask.
Debug print statements are ne, but nothing should be printed when we run your code. We expect clean runs - printing to the console when we're grading will result in a penalty. If you submit these, we will take o points.
Provided
The following le(s) have been provided to you. There are several, but you will only edit one of them.
GraphAlgorithms.java
This is the class in which you will implement the di erent graph algorithms. Feel free to add private static helper methods but do not add any new public methods, new classes, instance variables, or static variables.
GraphAlgorithmsStudentTests.java
This is the test class that contains a set of tests covering the basic operations on the GraphAlgorithms class. It is not intended to be exhaustive and does not guarantee any type of grade. Write your own tests to ensure you cover all edge cases. The graphs used for these tests are shown above in the pdf.
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Homework 10: Graph Algorithms Due: See T-Square
Graph.java
This class represents a graph. Do not modify this le.
Vertex.java
This class represents a vertex in the graph. Do not modify this le.
Edge.java
This class represents an edge in the graph. It contains the vertices connected to this edge and its weight. Do not modify this le.
Deliverables
You must submit all of the following le(s). Please make sure the lename matches the lename(s) below, and that only the following le(s) are present. T-Square does not delete les from old uploads; you must do this manually. Failure to do so may result in a penalty.
After submitting, be sure you receive the con rmation email from T-Square, and then download your uploaded les to a new folder, copy over the interfaces, recompile, and run. It is your responsibility to re-test your submission and discover editing oddities, upload issues, etc.
GraphAlgorithms.java
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