Programming Assignment 9 Digraphs and Dijkstra

Approved Includes

<cassert>    <stack>

<cmath>    <queue>

<cstddef>    <unordered_map>

<iostream>    <unordered_set>

<list>    <vector>

<sstream>    "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)
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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.
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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
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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.