【源代码】C++数据结构算法（十二）图与最短路径

日常说明：首先博主也是菜鸟一枚，有错误欢迎大家指正。另外本博客所有的代码博主编写后均调试
通过。重要提醒！！！！博主使用的是VS2017，如果有低版本的小伙伴
最好新建空项目将此代码复制上去。
更多算法请关注我的算法专栏https://blog.csdn.net/column/details/20417.html
运行截图：

SPath.h

#pragma once
#pragma once
#pragma once
#include<stack>
#include<iomanip>
#include<iostream>
using namespace std;
#define max_v_num 100
#define INFINITY 10000
#define max 100
typedef int Boolean;
Boolean visited[max];

template <class T>
class Mgraph
{
public:
    Mgraph(int vexs_num, int edge_num);
    void SPath(Mgraph<T>graph, int start);
    int weight(int i, int j);
    stack<char> stack_vexs;
    //private:
    int vexs_num, edge_num;
    T vexs[max_v_num];
    int arc[max_v_num][max_v_num];
    int pre[6];
};

template<class T>
Mgraph<T>::Mgraph(int vexs_num, int edge_num)
{
    this->vexs_num = vexs_num;
    this->edge_num = edge_num;
    cout << "请输入各顶点：";
    for (int i = 0; i < vexs_num; i++)
    {
        cin >> vexs[i];
    }
    for (int i = 0; i < vexs_num; i++)  //邻接矩阵初始化
    {
        for (int j = 0; j < edge_num; j++)
        {
            this->arc[i][j] = INFINITY;
        }
    }
    cout << "请输入邻接矩阵下标i,j以及权值：" << endl;
    for (int k = 0; k < edge_num; k++)   //写入邻接矩阵元素
    {

        int i, j;
        int w;
        cin >> i >> j >> w;
        arc[i][j] = w;
    }
}

template<class T>
void Mgraph<T>::SPath(Mgraph<T>graph, int start)
{
    int temp[max];
    int pose = 0;
    int k ;
    int pre[6] = { -1,-1,-1,-1,-1,-1 };
    /*pre[0]=start;*/
    for (int i = 0; i < graph.vexs_num; i++)
    {
        visited[i] = false;
        if (i != start)
        {
            temp[i] = graph.arc[start][i];
            if (graph.arc[start][i] != INFINITY)
            {
                pre[i] = 0;
            }   
        }
    }
    visited[start] = true;
    for (int i = 0; i < graph.vexs_num - 1; i++)
    {
        int min_weight = 1000;
        for (int j = 0; j < graph.vexs_num; j++)
        {
            if (!visited[j] && temp[j]<min_weight)
            {
                min_weight = temp[j];
                /*k = pose;*/
                pose = j;
            }
        }
        /*pre[pose] = k;*/
    /*  if (!visited[pose])
        {
             pre[k] = pose ;
             k = pose;
        }*/
        visited[pose] = true;
        for (int j = 0; j < graph.vexs_num; j++)
        {
            if (/*!visited[j] && */temp[j]>graph.arc[pose][j] + min_weight)
            {
                temp[j] = graph.arc[pose][j] + min_weight;
                pre[j] = pose;
            }
        }
    }
    /*cout << graph.vexs[start]<<" ";*/
    for (int i = 1; i < graph.vexs_num; i++)
    {
        int n = 0;
        int j = i;
        while (pre[j] != -1)
        {
            n = pre[j];
            if (stack_vexs.empty())
            {
                stack_vexs.push(graph.vexs[j]);
            }
            stack_vexs.push(graph.vexs[n]);
            j = pre[j];
        }
        while (!stack_vexs.empty())
        {
            char gettop;
            gettop = stack_vexs.top();
            stack_vexs.pop();
            cout << gettop<<" ";
        }
        cout << endl;
    }
}

template<class T>
int Mgraph<T>::weight(int i, int j)
{
    return  arc[i][j];
}

SPath.cpp

#include "SPath.h"



int main()
{
    int vexs_num, edge_num;
    cout << "请输入顶点数和边数:";
    cin >> vexs_num >> edge_num;
    Mgraph<char>Graph(vexs_num, edge_num);
    cout << "输出邻接矩阵：" << endl;
    for (int i = 0; i < Graph.vexs_num; i++)
    {
        for (int j = 0; j < Graph.vexs_num; j++)
        {
            int w;
            w = Graph.weight(i, j);
            if (w == INFINITY)
            {
                cout << setw(6) << "∞";
            }
            else cout << setw(6) << w;
        }
        cout << endl;
    }
    cout << endl;
    cout << "最短路径：";
    Graph.SPath(Graph, 0);
    return 0;
}