HW 5: Graph Algorithms

CSCI 335 
HW 5: Graph Algorithms
100 points (85 points deliverables, 15 points for design)

Instructions:
1. Read and follow the contents of 335 Spring2202 335 Programming Rules
document on the blackboard (Course Information Section).
2. Read the assignment description below.
3. Submit only the files requested in the deliverables at the bottom of this
description to Gradescope by the deadline.
Learning Outcome: The goal of this assignment is to become familiar with heaps,
disjoint sets and graph algorithms. Acknowledge the sources you use in the README
file.
Q1: Adjacency 25 points
You will read a directed graph from a text file. Below is an example, found in Graph1.txt:
5
1 2 0.2 4 10.1 5 0.5
2 1 1.5
3 2 100.0 4 50.2
4
5 2 10.5 3 13.9
The first line is the number of vertices. Each vertex is represented by an integer from 1 to N. Each line
is of the form:
<vertex> <connected vertex 1> <weight 1> <connected vertex 2> <weight 2> …
For each vertex, you have a list of the adjacent vertices with positive edge weights. For instance, in
the above example, vertex 1 is connected to vertex 2 (edge weight 0.2), to vertex 4 (edge weight
10.1) and to vertex 5 (edge weight 0.5). Vertex 2 is connected to vertex 1 (edge weight 1.5), vertex 4
has no outgoing edges, etc.
Represent the graph using an adjacency list.
Create your graph class inside graph.h
In order to test your implementation, you will read a second text file (let us call it
AdjacencyQueries1.txt) that will contain a set of pair of vertices. Your program (name it
CreateGraphAndTest.cc) will have to first create the graph by reading it from text file Graph1.txt. It
will then open the file AdjacencyQueries1.txt and for each pair of vertices in it, your program will
print whether the vertices are adjacent or not, and if they are, your program will print the weight of
the edge that connects them.
For example, if the file AdjacencyQueries1.txt contains:
4 1
3 4
1 5
5 1
1 3
Then the output should be:
4 1: not_connected
3 4: connected 50.2
1 5: connected 0.5
5 1: not_connected
1 3: not_connected
where the numbers to the right of “connected” are the weight of this edge.
Note: This example is consistent with Graph1.txt. It is very important that you follow this format
exactly. Make sure you have the “_” underscore in “not_connected”. Make sure there is nothing
extra printed.
So, your program can be called for example as:
./CreateGraphAndTest <GRAPH_FILE> <ADJECENCY_QUERYFILE>
Exact deliverables are described at the bottom of the file.
Q2: Dijkstra’s Algorithm Implementation (60 points)
Using your graph implementation in Q1, implement Dijkstra’s Algorithm, using a priority queue (i.e.
heap). Write a program that runs as follows:
./FindPaths <GRAPH_FILE> <STARTING_VERTEX>
This program should use Dijkstra’s Algorithm to find the shortest paths from a given starting vertex
to all vertices in the graph file.
The priority queue data structure is provided for you under the file, binary_heap.h, and included
inside graph.h. Do not modify binary_heap.h, we will use the original automatically.
You should then print out the paths to every destination. For example, if you run the program having
as input Graph2.txt (provided) starting from vertex 1, i.e.
./FindPaths Graph2.txt 1
Then the output should be:
1: 1 cost: 0.0
2: 1 2 cost: 2.0
3: 1 4 3 cost: 3.0
4: 1 4 cost: 1.0
5: 1 4 5 cost: 3.0
6: 1 4 7 6 cost: 6.0
7: 1 4 7 cost: 5.0
The first number is the target vertex. (Aka: the last line beginning with 7: is the shortest path from
the input starting vertex 1, to the target vertex 7.) Your output should always be ordered this way,
starting from target vertex 1, to the maximum target vertex for that graph.
Following the target vertex, display the path taken, inclusive of the starting and ending vertices.
Finally, display “cost:” followed by the cost of that path.
Note: This is an example using the inputs provided in Graph2.txt. It is very important that you follow
the output format exactly. Do not print any extra lines or characters.
If there does NOT exist a path to a particular vertex in the graph, the output for the path to that
vertex should display: not_possible
Example: Vertex 3 has no vertices pointing to it. Under the command ./FindPaths <graph_file> 2
the result for the path to 3 should be:
3: not_possible
If a vertex does not point to any other vertex, and that vertex is used as the starting vertex argument,
your program should output not_possible for every path, besides the path to itself.
Example: Vertex 3 is a vertex that does not point to any other vertex. Under the command,
./FindPaths <graph_file> 3 the output should display:
1: not_possible
2: not_possible
3: 3 cost: 0
4: not_possible
These examples do not represent every possible graph, but this is enough to determine the output for
every possible situation.
Deliverables: You should submit these files:
**MAKE SURE TO SUBMIT ALL RELEVANT FILES. CHECK YOUR INCLUDE STATEMENTS. DO NOT
PRINT ANYTHING OTHER THAN WHAT IS ASKED**
• README file (for all questions as described in class)
Q1
• CreateGraphAndTest.cc
o graphTestDriver() – All functionality should be in here, NOT the main.
• graph.h
o Use this for the relevant graph class and its routines.
Q2
• FindPaths.cc
o pathfindDriver() – All functionality should be in here, NOT the main.
• graph.h
o Use this for the relevant graph class and its routines. Modify with the relevant functions
needed by pathfindDriver()
Do not submit or modify binary_heap.h and dsexceptions.h. The originals will be
included automatically when you submit.