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 ShortestPath function to compute the weight of a

minimum 0-1 path for each graph. A weighted adjacency matrix A for an edge-weighted graph

G on n vertices is an n x 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

corresponds to the edge-weighted graph in the previous section. Note that the weighted adjacency matrix for an undirected graph is always symmetric.

The input format used by the testing code in main consists of the number of vertices n followed

by the n x n weighted adjacency matrix. The graph above would be specified as follows:

8

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 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.3

4 Sample Run

The output of a model solution on the graph above is given in the listing below. Console input

is shown inblue.

Reading input values from stdin.

Reading graph 1

8

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: Minimum weight of a 0-1 path is 18

Processed 1 graph.

Average Time (seconds): 0.00

5 Evaluation Criteria

The programming assignment will be marked out of 50, based on a combination of automated

testing and human inspection, based on the criteria in the table below. The running times in

the table assume an input graph with n vertices and m edges.

Score (/50) Description

0 – 5 Submission does not compile or does not conform to

the provided template.

6 – 25 The implemented algorithm is not that of Dijkstra or

is substantially inaccurate on the tested inputs.

26 – 35 The implemented algorithm is accurate on all tested

inputs and has an O(n2 + mlog(n)) running time.

36 -50 The implemented algorithm is accurate on all tested

inputs,usesaheap-basedpriorityqueuetoselectthe

nextvertex ateach step and hasan

O(n2 + mlog(n)) running time.

To be properly tested, every submission must compile correctly as submitted, and must running time. 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 50. The best way to make sure your submission is

correct is to download it from conneX after submitting and test it.

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