Assignment 9 Digraphs and Dijkstra

CSCE 221 
Programming Assignment 9
Digraphs and Dijkstra
Approved Includes
Code Coverage
Starter Code
Files to Submit
Task 1: Directed Graph
Requirements
Files
Class
Functions
Constructors
Capacity
Element Access
Modifiers
Optional
Task 2: Dijkstra
Requirements
Files
Functions
Visualization
Example (for Tasks 1 and 2)
Example Output
Notes
Graph notation format
Testing Advice
CSCE 221 Spring 2021
Approved Includes
<cassert>
<cmath>
<cstddef>
<iostream>
<list>
<sstream>
<stack>
<queue>
<unordered_map>
<unordered_set>
<vector>
"graph.h"
Code Coverage
You must submit a test suite for each task that, when run, covers at least 90% of your code. You should,
at a minimum, invoke every function at least once. Best practice is to also check the actual behavior
against the expected behavior, e.g. verify that the result is correct. You should be able to do this
automatically, i.e. write a program that checks the actual behavior against the expected behavior.
Your test suite should include ALL tests that you wrote and used, including tests you used for debugging.
You should have MANY tests.
Starter Code
graph.h
graph_compile_test.cpp
graph_tests.cpp
Makefile
Files to Submit
graph.h
graph_tests.cpp
Task 1: Directed Graph
Implement a data structure to store a directed graph.
Requirements
Files
graph.h - contains the Graph class definition (define the methods inside the class)
CSCE 221 Spring 2021
graph_tests.cpp - contains the test cases and test driver (main)
Class
class Graph;
You can represent the Graph internally however you want. This could be adjacency lists, an adjacency
matrix, sets of Vertex and Edge objects, linked Vertex and/or Edge objects, or even some combination of
methods. In class, we learned the adjacency list and adjacency matrix representations, so I encourage
you to use those.
Performance Matters.
Advice: You want the speed of a matrix, but the space of a list. How can you get fast access with minimal
space?
Functions
Constructors
Graph() - makes an empty graph.
Graph(const Graph&) - constructs a deep copy of a graph
Graph& operator=(const Graph&) - assigns a deep copy of a graph
~Graph() - destructs a graph (frees all dynamically allocated memory)
Capacity
size_t vertex_count() const - the number of vertices in the graph
size_t edge_count() const - the number of edges in the graph
Element Access
bool contains_vertex(size_t id) const - return true if the graph contains a vertex with the
specified identifier, false otherwise.
bool contains_edge(size_t src, size_t dest) const - return true if the graph contains an
edge with the specified members (as identifiers), false otherwise.
double cost(size_t src, size_t dest) const - returns the weight of the edge between src
and dest, or INFINITY if none exists.
Modifiers
bool add_vertex(size_t id) - add a vertex with the specified identifier if it does not already exist,
return true on success or false otherwise.
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bool add_edge(size_t src, size_t dest, double weight=1) - add a directed edge from
src to dest with the specified weight if there is no edge from src to dest, return true on success, false
otherwise.
bool remove_vertex(size_t id) - remove the specified vertex from the graph, including all edges
of which it is a member, return true on success, false otherwise.
bool remove_edge(size_t src, size_t dest) - remove the specified edge from the graph, but
do not remove the vertices, return true on success, false otherwise.
Optional
Graph(Graph&&) - move constructs a deep copy of a graph
Graph& operator=(Graph&&) - move assigns a deep copy of a graph
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Task 2: Dijkstra’s Algorithm
Implement Dijkstra’s Algorithm as a method of the Graph class from Task 1.
Requirements
Files
graph.h - contains the Graph class definition (define the methods inside the class)
graph_tests.cpp - contains the test cases and test driver (main)
Functions
void dijkstra(size_t source_id) - compute the shortest path from the specified source vertex to
all other vertices in the graph using Dijkstra’s algorithm.
double distance(size_t id) const - assumes Dijkstra has been run, returns the cost of the
shortest path from the Dijkstra-source vertex to the specified destination vertex, or INFINITY if the
vertex or path does not exist.
Visualization
void print_shortest_path(size_t dest_id, std::ostream& os=std::cout) const -
assumes Dijkstra has been run, pretty prints the shortest path from the Dijkstra source vertex to the
specified destination vertex in a “ → “- separated list with “ distance: #####” at the end, where
<distance> is the minimum cost of a path from source to destination, or prints “<no path>\n” if the
vertex is unreachable.
CSCE 221 Spring 2021
Example (for Tasks 1 and 2)
std::cout << "make an empty digraph" << std::endl;
Graph G;
std::cout << "add vertices" << std::endl;
for (size_t n = 1; n <= 7; n++) {
G.add_vertex(n);
}
std::cout << "add directed edges" << std::endl;
G.add_edge(1,2,5); // 1 ->{5} 2; (edge from 1 to 2 with weight 5)
G.add_edge(1,3,3);
G.add_edge(2,3,2);
G.add_edge(2,5,3);
G.add_edge(2,7,1);
G.add_edge(3,4,7);
G.add_edge(3,5,7);
G.add_edge(4,1,2);
G.add_edge(4,6,6);
G.add_edge(5,4,2);
G.add_edge(5,6,1);
G.add_edge(7,5,1);
std::cout << "G has " << G.vertex_count() << " vertices" << std::endl;
std::cout << "G has " << G.edge_count() << " edges" << std::endl;
std::cout << "compute shortest path from 2" <<std::endl;
G.dijkstra(2);
std::cout << "print shortest paths" <<std::endl;
for (size_t n = 1; n <= 7; n++) {
std::cout << "shortest path from 2 to " << n << std::endl;
std::cout << " ";
G.print_shortest_path(n);
}
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Example Output
make an empty graph
add vertices
add edges
G has 7 vertices
G has 12 edges
compute shortest path from 2
print shortest paths
shortest path from 2 to 1
2 --> 7 --> 5 --> 4 --> 1 distance: 6
shortest path from 2 to 2
2 distance: 0
shortest path from 2 to 3
2 --> 3 distance: 2
shortest path from 2 to 4
2 --> 7 --> 5 --> 4 distance: 4
shortest path from 2 to 5
2 --> 7 --> 5 distance: 2
shortest path from 2 to 6
2 --> 7 --> 5 --> 6 distance: 3
shortest path from 2 to 7
2 --> 7 distance: 1
CSCE 221 Spring 2021
Notes
Graph notation format
<source_vertex_id> ->[{<cost>}] <destination_vertex_id>;
Examples:
● 1 ->{1} 2
○ “Vertex 1 has an edge to vertex 2 with cost 1”
● 3 -> 4
○ “Vertex 3 has an unweighted edge to vertex 4”
Testing Advice
1. Write tests before you write implementation.
2. Write more tests.
3. Don’t only add all the vertices all at once at the beginning.
a. Test adding vertices in random orders and interleaved with adding edges.