通信网Project之——单源单宿最短路问题

最主要的Vertex类：

#ifndef VERTEX_H
#define VERTEX_H

#include <climits>
#include <cstddef>
#define INF INT_MAX

class Vertex
{
public:
	int ID;
	Vertex* parent;
	int d;

	Vertex(int id) : ID(id), d(INF), parent(NULL){}
};

#endif

接下来是Edge类：

#ifndef EDGE_H
#define EDGE_H

#include "vertex.h"

class Edge
{
private:
	float weight;
	float capacity;
	float passrate;

public:
	int id;
	Vertex* tail;
	Vertex* head;
	/******** constructor *******/
	Edge(int ID, Vertex& t, Vertex& h, float wght = 1,
			float cap = 1, float pssrt = 1) :
		id(ID), head(&h), tail(&t), weight(wght),
		capacity(cap), passrate(pssrt) {}

	/********** The ID **********/
	void setId(int ID)
	{
		id = ID;
	}
	int getId()
	{
		return id;
	}

	/********* The vertex ********/
	void setTail(Vertex& v)
	{
		tail = &v;
	}
	void setHead(Vertex& v)
	{
		head = &v;
	}

	/******** Other method *******/
	void setWeight(const float w)
	{
		weight = w;
	}
	float getWeight()
	{
		return weight;
	}
	float getCapacity()
	{
		return capacity;
	}
	float getPassRate()
	{
		return passrate;
	}

};

#endif

当然还有路问题须要的Path类：

#ifndef PATH_H
#define PATH_H

#include <list>
#include "vertex.h"

class Path : std::list<Vertex*>
{
public:
	Path(Vertex& tail);

	void print();
};

#endif

这是Path类的实现：

#include "path.h"
#include <iostream>
#include "vertex.h"
#include <list>

using namespace std;

Path::Path(Vertex& tail)
{
	Vertex* temp = &tail;
	while (temp->parent != NULL)
	{
		push_back(temp);
		temp = temp->parent;
	}
	push_back(temp);
}

void Path::print()
{
	reverse();
	list<Vertex*>::iterator it;
	it = begin();
	cout << "Vertex " << (*it)->ID;
	it++;
	for (; it != end(); it++)
		cout << " -> Vertex " << (*it)->ID;
}

下来就是最重要也是最复杂的Graph类了！

#ifndef GRAPH_H
#define GRAPH_H

#include <map>
#include "edge.h"
#include "vertex.h"
#include "path.h"
#include <set>
#include <list>

class Graph
{
	std::map<int, Vertex*> vertexMap;
	// The map: vertex and its incident edge.
	std::map<Vertex*, std::list<Edge*> > incMap;
	std::set<Edge*> edgeList;
	std::list<Vertex*> notMarkedVertex;
	bool fromFile;
	Path* path;

	void update(Vertex* v);

public:
	/********** constructor *********/
	Graph(): fromFile(false){}
	Graph(const char* inputFileName);
	Graph(std::list<Edge*>& edge);
	~Graph();

	/*********** size info **********/
	int getNumVertex()
	{
		return vertexMap.size();
	}
	int getNumEdge()
	{
		return edgeList.size();
	}

	void print();
	void addEdge(Edge& edge);
	void dijkstra(int s, int d);
	void dijkstra(Vertex& s, Vertex& d);
};

#endif

下来是实现：

#include "graph.h"
#include <iostream>
#include <fstream>
#include <map>
#include <set>
#include <list>
#include <string>
#include <cstdlib>

using namespace std;

Graph::Graph(const char* inputFileName)
{
	fromFile = true;
	ifstream in(inputFileName);

	string s;
	getline(in, s);
	getline(in, s);

	while (in.good())
	{
		int id, tail, head;
		float weight, capacity, passrate;
		in >> id >> tail >> head
		   >> weight >> capacity >> passrate;
		map<int, Vertex*>::iterator it;
		it = vertexMap.find(tail);

		Vertex *t;
		Vertex *h;

		if (it == vertexMap.end())
			t = new Vertex(tail);
		else
			t = it->second;

		it = vertexMap.find(head);
		if (it == vertexMap.end())
			h = new Vertex(head);
		else
			h = it->second;

		Edge* e = new Edge(id, *t, *h, weight, capacity, passrate);
		addEdge(*e);
	}
}

Graph::Graph(list<Edge*>& edge)
{
	list<Edge*>::iterator it;
	for (it = edge.begin(); it != edge.end(); it++)
		addEdge(**it);
	fromFile = false;
}

void Graph::addEdge(Edge& edge)
{
	edgeList.insert(&edge);
	vertexMap.insert(pair<int, Vertex*>(edge.tail->ID, edge.tail));
	vertexMap.insert(pair<int, Vertex*>(edge.head->ID, edge.head));

	if (incMap.find(edge.tail) == incMap.end())
	{
		list<Edge*>* l = new list<Edge*>(1, &edge);
		incMap.insert(pair<Vertex*, list<Edge*> >(edge.tail, *l));
	}
	else
		incMap.find(edge.tail)->second.push_back(&edge);
}

void Graph::print()
{
	map<Vertex*, list<Edge*> >::iterator it;
	list<Edge*>::iterator it2;
	for (it = incMap.begin(); it != incMap.end(); it++)
	{
		cout << "Vertex " << it->first->ID << endl;
		for (it2 = it->second.begin();
			 it2 != it->second.end();
			 it2++)
			cout << "\tEdge " << (*it2)->id << " to Vertex "
				 << (*it2)->head->ID << endl;
	}
}

Graph::~Graph()
{
	if (fromFile)
	{
		set<Edge*>::iterator it;
		for (it = edgeList.begin();
			 it != edgeList.end();
			 it++)
			delete *it;

		map<int, Vertex*>::iterator it2;
		for (it2 = vertexMap.begin();
			 it2 != vertexMap.end();
			 it2++)
		delete it2->second;
	}
}

bool comp(Vertex* a, Vertex* b)
{
	return a->d < b->d;
}

void Graph::update(Vertex* v)
{
	list<Edge*> inc = incMap[v];
	if (inc.size() == 0)
	{
		cerr << "No out degree!" << endl;
		exit(EXIT_FAILURE);
	}

	list<Edge*>::iterator it;
	for (it = inc.begin(); it != inc.end(); it++)
	{
		int d = v->d + (*it)->getWeight();
		if ((*it)->head->d > d)
		{
			(*it)->head->parent = v;
			(*it)->head->d = d;
		}
	}
}

void Graph::dijkstra(int sid, int did)
{
	Vertex* s = vertexMap[sid];
	Vertex* temp;
	s->d = 0;

	map<int, Vertex*>::iterator it;
	for (it = vertexMap.begin();
		 it != vertexMap.end();
		 it++)
		if (it->second->ID != sid)
			notMarkedVertex.push_back(it->second);
	update(s);

	do
	{
		notMarkedVertex.sort(comp);
		temp = notMarkedVertex.front();
		notMarkedVertex.pop_front();
		if (temp->ID == did)
			break;
		update(temp);
	}while(!notMarkedVertex.empty());

	path = new Path(*vertexMap[did]);
	path->print();
}

void Graph::dijkstra(Vertex& s, Vertex& d)
{
	dijkstra(s.ID, d.ID);
}

眼下的工作就是这些了。

以下是一个測试程序：

test.cpp:

#include <iostream>
#include "graph.h"
#include "path.h"

using namespace std;

int main()
{
	Graph graph("InputFile.txt");
	graph.print();

	cout << "Please input the s and d: ";
	int s, d;
	cin >> s >> d;
	graph.dijkstra(s, d);

	return 0;
}

还有InputFile.txt 的内容：

n 7
e 9
1 1 2 1 20 0.8
2 2 3 5 30 0.8
3 3 6 6 22 0.6
4 7 6 5 22 0.4
5 1 7 3 20 0.2
6 5 6 2 20 0.3
7 3 5 1 20 0.5
8 4 5 6 20 0.6
9 2 4 2 20 0.7

最后是执行结果了！