Programming Assignment 10 Minimum Spanning Tree (Prim’s Algorithm)

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
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Task 1: Undirected Graph

Implement a data structure to store an undirected graph. You should modify your digraph code.

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)

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 would encourage you to use one of those.

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 u, size_t v) const - return true if the graph contains an edge with the specified members (as identifiers), false otherwise.
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double cost(size_t u, size_t v) const - returns the weight of the edge between u and v, 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.

bool add_edge(size_t u, size_t v, double weight=1) - add an undirected edge between u and v with the specified weight if there is not one already, return true on success, false otherwise. If you use adjacency lists, make sure to update both u’s and v’s lists.

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 u, size_t v) - 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: Prim’s Algorithm

Implement Prim’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

std::list<std::pair<size_t,size_t>> prim() - compute a minimum spanning tree using Prim’s algorithm. Return a list of edges. There may be more than one possible spanning tree depending on the starting vertex. Any correct (minimum weight) tree will be recognized as such. If a MST does not exist, then the return value should be an empty list.

double distance(size_t id) const - assumes Prim has been run, returns the cost of the edge that connects this vertex to the minimum spanning tree, or 0 is the vertex is the root of the tree, or INFINITY if the vertex is not part of the tree (i.e. the graph is not connected).

Visualization (optional)

void print_minimum_spanning_tree(std::ostream& os=std::cout) const - assumes Prim has been run, pretty prints the minimum spanning tree as a sequences of lines with the format <vertex> --{<edge weight>} <vertex>
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Example (for Tasks 1 and 2)

std::cout << "make an empty graph" << 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 undirected edges" << std::endl;

G.add_edge(1,2,5);    // 1 --{5} 2; (edge between 1 and 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 and "; std::cout << G.edge_count() << " edges" << std::endl;

std::cout << "compute a minimum spanning tree" <<std::endl; std::list<std::pair<size_t,size_t>> = G.prim();

std::cout << "print minimum spanning tree" <<std::endl; double tree_cost = 0;

for (const std::pair<size_t,size_t>& edge : mst) {

std::cout << edge.first << " --{"<<G.cost(edge.first,edge.second)<<"} " << edge.second << ";" << std::endl;

tree_cost += G.cost(edge.first,edge.second);

}

std::cout << "tree cost = " << tree_cost <<std::endl;
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Example Output

make an empty graph

add vertices

add undirected edges

G has 7 vertices and 12 edges

compute a minimum spanning tree

print minimum spanning tree

2 --{1} 7;

5 --{1} 7;

6 --{1} 5;

3 --{2} 2;

4 --{2} 5;

1 --{2} 4;

tree cost = 9