迪杰斯特拉算法

最近一直带两个考研学生的《数据结构》，正好讲到图这一章，顺便实现了一下迪杰斯特拉算法。

#include"stdafx.h"
#include <iostream>

using namespace std;
const int MAXSIZE = 10;
const int INF = 99999;//当作最大值
typedef struct VertexNode{
    int Index;//点的编号默认为从1开始
    char info;
};

typedef struct MGraph{
    int edges[MAXSIZE][MAXSIZE];
    VertexNode nodes[MAXSIZE];
    int n, e;
};
//构建一个用邻接矩阵存储的图
void CreateMGraph(MGraph& g,int n,int e);
//迪杰斯特拉算法求图的最短路径
void DijkStra(MGraph& g, int v, int dist[], int path[]);
//输出该最短路径
void PrintRoad(int path[],int v);

void main(void)
{
    MGraph g;
    int dist[MAXSIZE];
    int path[MAXSIZE];
    CreateMGraph(g, 7, 12);
    DijkStra(g, 1, dist, path);
    PrintRoad(path, 7);
}

void CreateMGraph(MGraph& g, int n,int e)
{
    g.n = n;
    g.e = e;
    int vertex1, vertex2;
    int value;
    for (int i = 1; i <= n; ++i)
    {
        g.nodes[i].Index = i;
    }

    for (int i = 1; i <= g.n; ++i)
    for (int j = 1; j <= g.n; ++j)
    {
        g.edges[i][j] = INF;
    }
    
    for (int j = 1; j <= e; j++)
    {
        cout << "请输入边的两个点，中间以空格隔开
";
        cin >> vertex1 >> vertex2;
        cout << "请输入该边的权值
";
        cin >> value;
        g.edges[vertex1][vertex2] = value;
    }
}

void DijkStra(MGraph& g, int v,int dist[], int path[])
{
    int i, j, min, u;
    int visited[MAXSIZE];
    for (i = 1; i <= g.n; ++i)
    {
        if (g.edges[v][i] < INF)
        {
            dist[i] = g.edges[v][i];
            path[i] = v;
        }
        else
        {
            dist[i] = -1;
            path[i] = -1;
        }

        visited[i] = 0;
    }
    visited[v] = 1;
    for (i = 1; i <= g.n; ++i)
    {
        min = INF;
        for (j = 1; j <= g.n;++j)
        if (visited[j] == 0 && dist[j] < min)
        {
            min = dist[j];
            u = j;
        }
        visited[u] = 1;
        for (j = 1; j <= g.n; ++j)
        {
            if (visited[j] == 0 && dist[j] > g.edges[u][j] + dist[u])
            {
                dist[j] = g.edges[u][j] + dist[u];
                path[j] = u;
            }
        }
    }
}

void PrintRoad(int path[],int v)
{
    int stack[MAXSIZE], top = -1;
    while (path[v]!= -1)
    {
        stack[++top] = v;
        v = path[v];
    }
    stack[++top] = v;
    while (top != -1)
    {
        cout << stack[top--] << " ";
    }
    cout << endl;
}