LAB 10: GRAPHS
Exercise 1 Implement a Template Class
Problem statement:
Implement a new template class that is derived from the graph. The new class
should permit both edges and vertices to have labels.
Learning Objectives:
The learner will be able to:
Write a new template class derived from the graph template class that permits
both edges and vertices to have labels.
Exercise 2 Implement a Graph Function
Problem statement:
Implement a function with three arguments: a graph, a starting vertex number, and
an ending vertex number. The function determines whether there is a directed
path from the starting vertex to the ending vertex.
Learning Objectives:
The learner will be able to:
Write a three-argument function to determine if a directed path exists from a
starting vertex to an ending vertex.
Equipment:
Typical Computer Lab setup
Components/Materials:
Microsoft Visual C++
Classroom Configuration:
N/A
Lab Procedures:
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Complete the following tasks: Exercise 1
1. Implement a new template class that is derived from the graph.
2. The new class should permit both edges and vertices to have labels.
Complete the following tasks: Exercise 2
1. Implement a function with three arguments: a graph, a starting vertex number, and
an ending vertex number.
2. The function determines whether there is a directed path from the starting vertex to
the ending vertex.
Validation/Evaluation
Answers to Lab Exercises
Solutions to Lab Exercises can be found at the Curriculum Knowledge Network
(CKN) section of the ITT Technical Institute Employee Portal, http://myportal.itttech.edu. The solutions are also listed below.
Exercise 1
// FILE: graph.h (part of the namespace main_savitch_15)
// From Chapter 15 of Data Structures and Other Objects (Second Edition)
//
________________________________________________________________________
//
// This file has been modified to work with Microsoft Visual C++ 6.0,
// as described in www.cs.colorado.edu/~main/vc6.html
//
________________________________________________________________________
//
// TEMPLATE CLASS PROVIDED: graph<Item> (a class for labeled graphs)
// The vertices of an n-vertex graph are numbered from zero to n-1. Each vertex
// has a label of type Item. It may be any of the C++ built-in types (int,
// char, etc.), or any class with a default constructor and an assignment
// operator. The graph may not have multiple edges.
//
// MEMBER CONSTANTS for the graph<Item> template class:
// static const size_t MAXIMUM = ______
// graph::MAXIMUM is the maximum number of vertices that a graph can have.
//
// CONSTRUCTOR for the graph<Item> template class:
// graph( )
// Postcondition: The graph has been initialized with no vertices and no edges.
//
// MODIFICATION MEMBER FUNCTIONS for the graph<Item> template class:
// void add_vertex(const Item& label)
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// Precondition: size( ) < MAXIMUM.
// Postcondition: The size of the graph has been increased by adding one new
// vertex. This new vertex has the specified label and no edges.
//
// void add_edge(size_t source, size_t target)
// Precondition: (source < size( )) and (target < size( )).
// Postcondition: The graph has all the edges that it originally had, and it
// also has another edge from the specified source to the specified target.
// (If this edge was already present, then the graph is unchanged.)
//
// void remove_edge(size_t soure, size_t target)
// Precondition: (source < size( )) and (target < size( )).
// Postcondition: The graph has all the edges that it originally had except
// for the edge from the specified source to the specified target. (If this
// edge was not originally present, then the graph is unchanged.)
//
// Item& operator [ ] (size_t vertex)
// Precondition: vertex < size( ).
// Postcondition: The return value is a reference to the label of the
// specified vertex.
//
// CONSTANT MEMBER FUNCTIONS for the graph<Item> template class:
// size_t size( ) const
// Postcondition: The return value is the number of vertices in the graph.
//
// bool is_edge(size_t source, size_t target) const
// Precondition: (source < size( )) and (target < size( )).
// Postcondition: The return value is true if the graph has an edge from
// source to target. Otherwise the return value is false.
//
// set<size_t> neighbors(size_t vertex) const
// Precondition: (vertex < size( )).
// Postcondition: The return value is a set that contains all the vertex
// numbers of vertices that are the target of an edge whose source is at
// the specified vertex.
//
// Item operator [ ] (size_t vertex) const
// Precondition: vertex < size( ).
// Postcondition: The return value is a reference to the label of the
// specified vertex.
// NOTE: This function differs from the other operator [ ] because its
// return value is simply a copy of the Item (rather than a reference of
// type Item&). Since this function returns only a copy of the Item, it is
// a const member function.
//
// VALUE SEMANTICS for the graph<Item> template class:
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//
Assignments and the copy constructor may be used with graph<Item> objects.
#ifndef MAIN_SAVITCH_GRAPH_H
#define MAIN_SAVITCH_GRAPH_H
#include <cstdlib> // Provides size_t
#include <set>
// Provides set
namespace main_savitch_15
{
template <class Item>
class graph
{
public:
// MEMBER CONSTANTS
// * For VC++ 6.0 we are using size_t instead of std::size_t. And we
// * have defined CAPACITY using an enum instead of a static member
// * constant. See www.cs.colorado.edu/~main/vc6.html for details.
enum { MAXIMUM = 20 };
// CONSTRUCTOR
graph( ) { many_vertices = 0; }
// MODIFICATION MEMBER FUNCTIONS
void add_vertex(const Item& label);
void add_edge(size_t source, size_t target);
void remove_edge(size_t source, size_t target);
Item& operator [ ] (size_t vertex);
// CONSTANT MEMBER FUNCTIONS
size_t size( ) const { return many_vertices; }
bool is_edge(size_t source, size_t target) const;
std::set<size_t> neighbors(size_t vertex) const;
Item operator[ ] (size_t vertex) const;
private:
bool edges[MAXIMUM][MAXIMUM];
Item labels[MAXIMUM];
size_t many_vertices;
};
}
#include "graph.template" // Include the implementation.
#endif
// FILE: graph.template (part of the namespace main_savitch_15)
// From Chapter 15 of Data Structures and Other Objects (Second Edition)
//
________________________________________________________________________
//
// This file has been modified to work with Microsoft Visual C++ 6.0,
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// as described in www.cs.colorado.edu/~main/vc6.html
//
________________________________________________________________________
//
// TEMPLATE CLASS IMPLEMENTED: graph<Item> (See graph.h for
documentation.)
// This file is included in the header file and not compiled separately.
// INVARIANT for the graph class:
// 1. The number of vertices in the graph is stored in the member variable
//
many_vertices.
// 1. These vertices are numbered from 0 to many_vertices-1.
// 2. edges is the adjacency matrix for the graph (with true in edges[i][j]
//
to indicate an edge from vertex i to vertex j).
// 3. For each i < many_vertices, labels[i] is the label of vertex i.
#include <cassert> // Provides assert
#include <cstdlib> // Provides size_t
#include <set>
// Provides set
namespace main_savitch_15
{
/* Not needed for VC++
template <class Item>
const std::size_t graph<Item>::MAXIMUM;
*/
template <class Item>
void graph<Item>::add_edge(size_t source, size_t target)
// Library facilities used: cassert, cstdlib
{
assert(source < size( ));
assert(target < size( ));
edges[source][target] = true;
}
template <class Item>
void graph<Item>::add_vertex(const Item& label)
// Library facilities used: cassert, cstdlib
{
size_t new_vertex_number;
size_t other_number;
assert(size( ) < MAXIMUM);
new_vertex_number = many_vertices;
many_vertices++;
for (other_number = 0; other_number < many_vertices; ++other_number)
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{
edges[other_number][new_vertex_number] = false;
edges[new_vertex_number][other_number] = false;
}
labels[new_vertex_number] = label;
}
template <class Item>
bool graph<Item>::is_edge(size_t source, size_t target) const
// Library facilities used: cassert, cstdlib
{
assert(source < size( ));
assert(target < size( ));
return edges[source][target];
}
template <class Item>
Item& graph<Item>::operator[ ] (size_t vertex)
// Library facilities used: cassert, cstdlib
{
assert(vertex < size( ));
return labels[vertex]; // Returns a reference to the label
}
template <class Item>
Item graph<Item>::operator[ ] (size_t vertex) const
// Library facilities used: cassert, cstdlib
{
assert(vertex < size( ));
return labels[vertex];
// Returns only a copy of the label
}
template <class Item>
std::set<size_t> graph<Item>::neighbors(size_t vertex) const
// Library facilities used: cassert, cstdlib, set
{
std::set<size_t> answer;
size_t i;
assert(vertex < size( ));
for (i = 0; i < size( ); ++i)
{
if (edges[vertex][i])
answer.insert(i);
}
return answer;
}
template <class Item>
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void graph<Item>::remove_edge(size_t source, size_t target)
// Library facilities used: cassert, cstdlib
{
assert(source < size( ));
assert(target < size( ));
edges[source][target] = false;
}
}
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Exercise 2
// FILE: searches.h (part of namespace main_savitch_15)
// This file provides three template functions for searching graphs
// from the graph template class of graph.h
//
// template <class Process, class Item, class SizeType>
// void rec_dfs(Process f, graph<Item>& g, SizeType v, bool marked[])
// Precondition: g is a labeled graph that is being traversed by a
// depth-first search. For each vertex x, marked[x] is true if x has
// already been visited by this search, otherwise marked[x] is false.
// The vertex v is an unmakred vertex that the search has just arrived at.
// Postcondition: the depth-first search of g has been continued
// through vertex v and beyond to all the vertices that can be reached
// from v via a path of unmarked vertices. The function f has been
// applied to the labe of each vertex visited by the search, and each
// such vertex x has also been marked by setting marked[x] to true.
//
// template <class Process, class Item, class SizeType>
// void depth_first(Process f, graph<Item>& g, SizeType start)
// Precondion: start is a vertex number of the labeled graph g.
// Postcondition: A depth-first search of g has been executed,
// starting at the start vertex. The function f has been applied to the
// label of each vertex visited by the search.
//
// template <class Process, class Item, class SizeType>
// void breadth_first(Process f, graph<Item>& g, SizeType start)
// Precondition: start is a vertex number of the labeled graph g.
// Postcondition: A breadth-first search of g has been executed,
// starting at the start vertex. The function f has been applied to the
// label of each vertex visited by the search.
#ifndef SEARCHES_H
#define SEARCHES_H
#include "graph.h"
namespace main_savitch_15
{
template <class Process, class Item, class SizeType>
void rec_dfs(Process f, graph<Item>& g, SizeType v, bool marked[]);
template <class Process, class Item, class SizeType>
void depth_first(Process f, graph<Item>& g, SizeType start);
template <class Process, class Item, class SizeType>
void breadth_first(Process f, graph<Item>& g, SizeType start);
}
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#include "searches.template" // Include the implementation.
#endif
// FILE: searches.template
// From Chapter 15 of Data Structures and Other Objects (Second Edition)
//
________________________________________________________________________
//
// This file has been modified to work with Microsoft Visual C++ 6.0,
// as described in www.cs.colorado.edu/~main/vc6.html
//
________________________________________________________________________
//
// TEMPLATE FUNCTIONS IMPLEMENTED: rec_dfs, depth_first, and breadth_first.
// Please see searches.h for documentation of these functions.
// This file is included at the bottom of searches.h, and should not be
// separately compiled.
#include <algorithm>
#include <cassert>
#include <cstdlib>
#include <queue>
#include <set>
#include "graph.h"
namespace main_savitch_15
{
template <class Process, class Item, class SizeType>
void rec_dfs(Process f, graph<Item>& g, SizeType v, bool marked[])
// Precondition: g is a labeled graph that is being traversed by a
// depth-first search. For each vertex x, marked[x] is true if x has
// already been visited by this search, otherwise marked[x] is false.
// The vertex v is an unmakred vertex that the search has just arrived at.
// Postcondition: the depth-first search of g has been continued
// through vertex v and beyond to all the vertices that can be reached
// from v via a path of unmarked vertices. The function f has been
// applied to the labe of each vertex visited by the search, and each
// such vertex x has also been marked by setting marked[x] to true.
// Library facilities used: cstdlib, graph.h, set
{
std::set<size_t> connections = g.neighbors(v);
std::set<size_t>::iterator it;
marked[v] = true; // Mark vertex v
f(g[v]);
// Process the label of vertex v with the function f
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// Traverse all the neighbors, looking for unmarked vertices:
for (it = connections.begin( ); it != connections.end( ); ++it)
{
if (!marked[*it])
rec_dfs(f, g, *it, marked);
}
}
template <class Process, class Item, class SizeType>
void depth_first(Process f, graph<Item>& g, SizeType start)
// Precondion: start is a vertex number of the labeled graph g.
// Postcondition: A depth-first search of g has been executed,
// starting at the start vertex. The function f has been applied to the
// label of each vertex visited by the search.
// Library facilities used: algorithm, cassert, graph.h
{
bool marked[g.MAXIMUM];
assert(start < g.size( ));
std::fill_n(marked, g.size( ), false);
rec_dfs(f, g, start, marked);
}
template <class Process, class Item, class SizeType>
void breadth_first(Process f, graph<Item>& g, SizeType start)
// Precondition: start is a vertex number of the labeled graph g.
// Postcondition: A breadth-first search of g has been executed,
// starting at the start vertex. The function f has been applied to the
// label of each vertex visited by the search.
// Library facilities used: algorithm, cassert, cstdlib, graph.h, queue
{
bool marked[g.MAXIMUM];
std::set<size_t> connections;
std::set<size_t>::iterator it;
std::queue<size_t> vertex_queue;
assert(start < g.size( ));
std::fill_n(marked, g.size( ), false);
marked[start] = true;
f(g[start]);
vertex_queue.push(start);
do
{
connections = g.neighbors(vertex_queue.front( ));
vertex_queue.pop( );
// Mark and process the unmarked neighbors,
// and place them in the queue.
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for (it = connections.begin( ); it != connections.end( ); ++it)
{
if (!marked[*it])
{
marked[*it] = true;
f(g[*it]);
vertex_queue.push(*it);
}
}
}
while (!vertex_queue.empty( ));
}
}
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