深度优先遍历求最短路径

给出一个地图，求顶点 1 到顶点 5 的最短路径

Code:

#include 
#include 
#include 

#define INF 999999

int book[101], e[101][101];
int n;
int min = 9999999;
int path[100];       /// 用来保存路径

void dfs(int cur, int dis)
{
	int i;
	if(n == cur)
	{

        for(i = 1; i <= n; i++)     /// 输出所有可能的路径
        {
            if(path[i])
            {

                printf("%d ", path[i]);
            }
        }
        printf("\t%d\n", dis);

        if(min > dis)
        {
            min = dis;
        }
        return;
	}

	for (i = 1; i <= n; ++i)
	{
		if(e[cur][i] != INF && book[i] == 0)
		{
			book[i] = 1;
			path[i] = i;
			dfs(i, dis+e[cur][i]);
			book[i] = 0;         /// 之前一部探索完毕后,取消对城市 i 的标记以便另一条路径选择顶点
			path[i] = 0;
		}
	}

}

int main(int argc, char const *argv[])
{
	int i, j, a, b, c, m;
    scanf("%d %d", &n, &m);
   	for (i = 1; i <= n; ++i)
   	{
   		for (j = 1; j <= n; ++j)
   		{
   			if(i == j)
   			{
   				e[i][j] = 0;
   			}
   			else
   			{
   				e[i][j] = INF;
   			}
   		}
   	}

   	for(i = 1; i <= m; ++i)
   	{

   		scanf("%d %d %d", &a, &b, &c);
		e[a][b] = c;
   	}


   	book[1] = 1;
   	path[1] = 1;
   	dfs(1, 0);
   	printf("%d\n", min);

   	system("pause");
	return 0;
}

处理无向图和处理有向图基本是一模一样， 只是无向图初始化的邻接矩阵应该是对称的.

求图上两点之间的最短路径除了有深度优先搜索以外，还可以使用广度优先搜索、Floyd、Bellman-Ford、Dijkstra等.