dijkstra 求最短路径

dijkstra算法写起来很容易，但是理解，证明它的正确性却不容易。

#include"Graph.h"
#include<assert.h>
#include<iostream>
#include<fstream>
#include<limits>
using namespace std;

const int MAX=std::numeric_limits<int>:: max();

int main()
{
	ifstream cin("input.txt");
	int vertex_num=5;
	Graph<char,int> myGraph(vertex_num);
	myGraph.Init(cin);
	//myGraph.RandInit();
	int *visited=new int[vertex_num];
	int *dis=new int[vertex_num];
	int *output=new int[vertex_num];
	visited[0]=1;
	output[0]=0;
	for(int i=1;i<vertex_num;i++)
	{
		dis[i]=myGraph.getWeight(0,i);
		visited[i]=0;
		output[i]=0;
	}
	for(int i=1;i<vertex_num;i++)
	{
		int min=MAX;
		int min_index=-1;
		for(int j=0;j<vertex_num;j++)
		{
			if(visited[j]==0&&dis[j]<min)
			{
				min=dis[j];
				min_index=j;
			}
		}
		visited[min_index]=1;
		for(int j=0;j<vertex_num;j++)
		{
			int temp_weight;
			if(visited[j]==0&&(temp_weight=myGraph.getWeight(min_index,j))<MAX&&dis[j]>dis[min_index]+temp_weight)
			{
				dis[j]=dis[min_index]+temp_weight;
				output[j]=min_index;
			}
		}
	}
	for(int i=1;i<vertex_num;i++)
	{
		int j=i;
		cout<<j<<"到0的路径是长度:"<<dis[j]<<"路径是:";
		while(j!=0)
		{
			cout<<j<<" ";
			j=output[j];
			
		}
		cout<<0<<endl;
	}
	return 0;
}