Dijkstra算法C++实现的坑

1.整体思路

理清算法->设计程序->搭好框架->填充细节->简单测试->详细测试

2.无穷大问题

假设输入的邻接矩阵中，每点与自己的权值为0，不邻接的两点权值为MAX，MAX被宏定义为一个非常大但不容易溢出的整数。

3.多维动态数组传参问题

受编译器原理的限制，C/C++将多维动态数组作为函数参数传递是非常麻烦的，比如邻接矩阵。

#include<iostream>
using namespace std;


#define MAX 50000

void printPath(int path[], int n,int s,int t)
{
    if (t == s) 
        cout << s; 
    else 
    { 
        printPath(path, n, s, path[t]); 
        cout << "->"<<t;
    }

}
/*
仅适用于无负权的图
distance是目前算出的s到某点的距离数组，path是从s到某点v的最短路径中，v的上一节点
初始化将distance全部赋为正无穷，之后从s点开始，进行缩短操作，
此后选择未进行缩短的点中distance最小者进行缩短，直至所有点都完成了缩短操作
*/
int main()
{
    /*-----------------------声明与定义--------------------*/
    int n  =7, s = 0, t = 0, i, distS2T;
    int G[7][7] =
    {   0,4,5,6,MAX,MAX,MAX,
        4,0,3,MAX,1,MAX,MAX,
        5,3,0,MAX,MAX,2,MAX,
        6,MAX,MAX,0,2,MAX,MAX,
        MAX,1,MAX,2,0,MAX,4,
        MAX,MAX,2,MAX,MAX,0,3,
        MAX,MAX,MAX,MAX,4,3,0
    };
    int *known = new int[n](), *distance = new int[n],*path = new int[n];

    //如果s到某点距离已经确定了(该点已经被用于relax过了)，则known为1，否则为0
    //disFromS[]数组是s到各点的最短距离.
    //---------------------------------赋初值-------------------------------
    for (i = 0; i < n; i++)      
    {
        distance[i] = MAX;
    }
    distance[s] = 0;
    path[s] = s;
    

    //------循环：选择unknown的点中dis最小的进行缩短操作，直到所有点全部为known------
    
    while (1)  //there's stil unknown vertex
    {
        
        i = 0;
        while (known[i] == 1 && i<n) 
            i++;//find the first unknown vertex
        if (i >= n) break; //if all vertices are known ,end the algorithm
        int v = i;
        for (; i < n; i++)  //find the unknown vertex with the min distance
        {
            if (!known[i] && distance[v] > distance[i]) v = i;
        }

        //relax(minPos);  modify dis and parent
        for (i = 0; i < n; i++)
        {
            //for each unknown vertex i, 
            if (known[i]) continue;
            if (distance[i] > distance[v] + G[v][i])
            {
                distance[i] = distance[v] + G[v][i];
                path[i] = v;
            }
        }
        known[v] = 1;
    }

    //--------------输出&释放内存----------------------
    distS2T = distance[t];
    cout << distS2T<<endl;
    for (i = 0; i < n;i++)
        cout << path[i] << " ";
    cout << endl;
    for (i = 0; i < n; i++)
        cout << distance[i]<<" ";
    cout << endl;
    printPath(path, n, 0, 6);

    delete[] known;
    delete[] distance;
    delete[] path;
    while (1);
    return 0;

}