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;
}