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本文介绍了一个使用C++实现的Dijkstra最短路径算法。该算法通过定义顶点类、路径类和图类来组织数据，并实现了从指定起点到终点的最短路径计算功能。此外，还提供了从文件中读取图数据的方法。

C++版Dijkstra最短路径算法

/////////////////////////////////////////////////////////////////////////////////////

//file:ShortestPath.h

#ifndef _SHORTESTPATH_H_
#define _SHORTESTPATH_H_

#define MAX_NODES 100
#define INFINITY 100

#include <iostream>
using namespace std;

class Vertex {                 //顶点类
public:
	Vertex(int i = -1) {
		id = i;               //顶点标号 初始化为-1
		known = false;        //打圈的标记 初始化为false
		dist = INFINITY;      //距离 初始化为正无穷
		pred = -1;            //顶点的前一个点 初始化为-1
	}
	int id;     
	bool known;
	int dist;
	int pred;
};

class Path {                  //路径类
public:
	Path() {
		_start = MAX_NODES;       //开始下标 初始化为MAX_NODES
		for(int i = 0; i < MAX_NODES; i++)
			_path[i] = -1;        //初始路径初始化为-1
	}
	int in_path(int item) {       //写入一个路径顶点
		_start--;
		_path[_start] = item;
		return 0;
	}
	int de_path(int& item) {      //输出一个路径顶点
		item = _path[_start];
		_start++;
		return 0;
	}
	bool is_empty() const{
		if(_start == MAX_NODES)    return true;
		else return false;
	}
private:
	int _start;
	int _path[MAX_NODES];
};

class Graph {                    //图类
public:
	Graph() {
		_num_nodes = 0;              //初始化顶点数为0 权值矩阵均为正无穷
		for(int i = 0; i < MAX_NODES; i ++)
			for(int j = 0; j < MAX_NODES; j ++)
				_weight[i][j] = INFINITY;
	}
	int build(string ifile);       //从文件中读取数据建立图
	Path shortest_path(int S, int T);   //计算从S到T的最短路径
private:
	int _num_nodes;            //顶点总数
	Vertex Vex[MAX_NODES];     //顶点的集合
	int _weight[MAX_NODES][MAX_NODES];    //权值矩阵

};

#endif

//////////////////////////////////////////////////////////////////////////////////////

//file:ShortestPath.cpp

#include "ShortestPath.h"
#include <fstream>

int Graph::build(string ifile) {   //从文件数据中创建图
	int i = 0;
	int j = 0;

	ifstream infile(ifile.c_str());
	if(!infile) {
		cout << "Error: Unable to open the input file!" << ifile.c_str() << endl;
		exit(-1);
	}

	infile >> _num_nodes;          //读取节点总数
	while(infile >> i) {
		if(i >= _num_nodes) {
			cout << "The node does not exist!" << endl;
			exit(-1);
		}
		infile >> j;
		if(j >= _num_nodes) {
			cout << "The node does not exist!" << endl;
			exit(-1);
		}
		infile >> _weight[i][j];    //读取权值
	}
	infile.close();

	for(int i = 0; i < _num_nodes; i++) {    //建立顶点
		Vex[i] = Vertex(i);
	}

	return 0;
}

Path Graph::shortest_path(int S, int T) {    //求从S到T的最短路径
	Path path;
	int next = -1;

	if(_num_nodes == 0) {                   //判空
		cout << "The graph is empty!" << endl;
		exit(-1);
	}
	if(S < 0 || T < 0 || S >= _num_nodes || T >= _num_nodes) {    //检查节点是否存在
		cout << "Node S or T does not exist!" << endl;
		exit(-1);
	}

	int current = S;
	Vex[S].dist = 0;

	while(Vex[T].known == false) {
		int smallest_d = INFINITY;
		for(int i = 0; i < _num_nodes; i++) {
			if(Vex[i].known == false) {
				if(Vex[current].dist + _weight[current][i] < Vex[i].dist) {
					Vex[i].dist = Vex[current].dist + _weight[current][i];
					Vex[i].pred = current;
				}
				if(Vex[i].dist < smallest_d) {
					smallest_d = Vex[i].dist;
					next = i;
				}
			}
		}

		current = next;
		Vex[current].known =true;
	}

	path.in_path(T);   //将路径存入path

	current = T;
	while(current != S) {
		path.in_path(Vex[current].pred);
		current = Vex[current].pred;
	}

	return path;
}

//////////////////////////////////////////////////////////////////////////////////////

//file:main.cpp

#include "ShortestPath.h"

ostream& operator<<(ostream& out, Path& path) {  //重载输出运算符
	int item = -1;

	while(!path.is_empty()) {
		path.de_path(item);
		out << "-->" << item;
	}
	return out;
}

int main() {
	int S = 0;
	int T = 6;
	string file_name = "data.txt";

	Graph G;  

	G.build(file_name); 

	Path path; 
	path = G.shortest_path(S, T);
	
	cout << path;


 return 0;

}

//////////////////////////////////////////////////////////////////////////////////////