ALGORITHMS AND DATA STRUCTURES II ASSIGNMENT 3 - PROGRAM

ALGORITHMS AND DATA STRUCTURES II
ASSIGNMENT 3 - PROGRAM

1 Programming Assignment
The assignment is to implement an algorithm to determine if the minimum weight spanning tree of an
edge-weighted graph 𝐺 is the same as the single source spanning tree generated from a specific vertex
𝑠 in 𝐺. A Java template has been provided containing an empty method MSTvsSPT, which takes a single
argument consisting of a weighted adjacency matrix for an edge-weighted graph 𝐺 with distinct edge
weights all greater than 0. The expected behavior of the method is as follows:
Input: An 𝑛 × 𝑛 array 𝐺 representing an edge-weighted graph.
Output: A boolean value which is true if the MST equals the SPT and false otherwise.
A correct implementation of the MSTvsSPT function will find the minimum weight spanning tree and
the single-source shortest path tree from vertex 0 and compare. If they are the same it returns true,
otherwise false. For example, consider the edge-weighted graph below.
The darkened edges of the graph above form the minimum weight spanning tree, whereas the darkened
edges below form the single source shortest path tree from vertex 0.
3
6
5
10
7
9
8
11
1
12
13
2
4
3
6
5
10
7
9
8
11
1
12
13
2
4
0
0
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You must use the provided Java template as the basis of your submission, and put your implementation
inside the MSTvsSPT method in the template. You may not change the name, return type or parameters
of the MSTvsSPT method. You may add additional methods as needed. You may use the UF class,
IndexMinPQ class and Edge class from the text book. I have attached the code for these classes to the
assignment (I have changed Edge to have int weights). Also, you may use any code from the Prim,
Kruskal, Boruvka, Dijkstra and/or Bellman-Ford algorithms from the text in your code. The main
method in the template contains code to help you test your implementation by entering test data or
reading it from a file. You may modify the main method to help with testing, but only the contents of
the MSTvsSPT method (and any methods you have added) will be marked, since the main function will
be deleted before marking begins. Do not modify anything in the given files as these will be used in
marking as well. Please read through the comments in the template file before starting.
2 Input Format
The testing code in the main function of the template reads a sequence of graphs in a weighted adjacency
matrix format and uses the MSTvsSPT function to compare the minimum spanning tree to the singlesource shortest path tree. A weighted adjacency matrix 𝐴 for an edge-weighted graph 𝐺 on 𝑛 vertices is
an 𝑛 × 𝑛 matrix where entry (𝑖,𝑗) gives the weight of the edge between vertices 𝑖 and 𝑗 (or 0 if no edge
exists). For example, the matrix
𝐴 =
[







0 0 0 0 0 12 13 0
0 0 6 0 0 0 0 3
0 6 0 4 0 0 0 5
0 0 4 0 10 0 0 7
0 0 0 10 0 11 8 9
12 0 0 0 11 0 1 0
13 0 0 0 8 1 0 2
0 3 5 7 9 0 2 0]







corresponds to the edge-weighted graph below. Note that the weighted adjacency matrix for an
undirected graph is always symmetric.
1 2
3
7
6
0
5 4
3
6
5 4
10
7
9
8
11
1
12
13 2
3
The input format used by the testing code in main consists of the number of vertices 𝑛 followed by the
𝑛 × 𝑛 weighted adjacency matrix. The graph above would be specified as follows:
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0 0 0 0 0 12 13 0
0 0 6 0 0 0 0 3
0 6 0 4 0 0 0 5
0 0 4 0 10 0 0 7
0 0 0 10 0 11 8 9
12 0 0 0 11 0 1 0
13 0 0 0 8 1 0 2
0 3 5 7 9 0 2 0
3 Test Datasets
A collection of randomly generated edge-weighted graphs with positive, distinct edge weights has been
uploaded to conneX. Your assignment will be tested on graphs similar but not identical to the uploaded
graphs. You are encouraged to create your own test inputs to ensure that your implementation functions
correctly in all cases.
4 Sample Run
The output of a model solution on the graph above is given in the listing below. Console input is shown
in blue.
Reading input values from stdin.
Reading graph 1
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0 0 0 0 0 12 13 0
0 0 6 0 0 0 0 3
0 6 0 4 0 0 0 5
0 0 4 0 10 0 0 7
0 0 0 10 0 11 8 9
12 0 0 0 11 0 1 0
13 0 0 0 8 1 0 2
0 3 5 7 9 0 2 0
Graph 1: Does MST = SPT? false
Processed 1 graph.
Average Time (seconds): 0.00
5 Evaluation Criteria
The programming assignment will be marked out of 25, based on a combination of automated testing
and human inspection. To receive full marks, the algorithm will determine if the MST equals the SPT
from vertex 0, while building both trees simultaneously and including some kind of early false detection
technique. That is, to get full marks you cannot simply generate the MST then the SPT and then test if
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they are the same. You will need to build both simultaneously, while checking as they grow if the answer
is sure to be false, insuring a more efficient best-case run time. Of course this test should take constant
time.
Score (/50) Description
0 − 5 Submission does not compile or does not conform to the
provided template.
5 − 15 The implemented algorithm is inaccurate on the tested
inputs.
15 − 20 The implemented algorithm is accurate on all tested
inputs but doesn’t build the trees simultaneously.
20 − 25 The implemented algorithm is accurate and has a
constant time early false detection scheme.
To be properly tested, every submission must compile correctly as submitted, and must be based on the
provided template. You may only submit one source file. If your submission does not compile for any
reason (even trivial mistakes like typos), or was not based on the template, it will receive at most
5 out of 25. The best way to make sure your submission is correct is to download it from conneX after
submitting and test it. You are not permitted to revise your submission after the due date, and late
submissions will not be accepted, so you should ensure that you have submitted the correct version of
your code before the due date. conneX will allow you to change your submission before the due date if
you notice a mistake. After submitting your assignment, conneX will automatically send you a
confirmation email. If you do not receive such an email, your submission was not received. If you have
problems with the submission process, send an email to the instructor before the due date.