最短路径常用算法

 

 

/*Floyd算法求最短路径，图中不能带有“负权回路” */
for (int k = 1; k <= n; k++)
   for (int i = 1; i <= n; i++)
     for (int j = 1; j <= n; j++)
        if (Map[i][j] > Map[i][k] + Map[k][j])
           Map[i][j] = Map[i][k] + Map[k][j];

 

/*Dijkstra算法求最短路径*/
#define inf 99999999
for (int i = 1; i <= n - 1; i++)//n个顶点
{
	//找到离1号顶点最近的点
	min = inf;//inf是无穷大
	for (int j = 1; j <= n; j++)
	{
		if (book[j] == 0 && dis[j] < min)
		{
			min = dis[j];
			u = j;
		}
	}
	book[u] = 1;
	//遍历每一个点
	for (int v = 1; v <= n; v++)
	{
		if (Map[u][v] < inf)
		{
			if (dis[v] > dis[u] + Map[u][v])
				dis[v] = dis[u] + Map[u][v];
		}
	}
}

/*Bellman-Ford算法求最短路径*/
#define inf 99999999
for (int k = 1; k <= n - 1; k++)
{
	//备份dis数组，优化
	for (int i = 1; i <= n; i++)
		bak[i] = dis[i];
	//进行一轮松弛
	for (int i = 1; i <= m; i++)
		if (dis[v[i]] > dis[u[i]] + w[i])
			dis[v[i]] = dis[u[i]] + w[i];
	//检测dis数组是否有更新
	check = 0;
	for(int i=1;i<=n;i++)
		if (bak[i] != dis[i])
		{
			check = 1;
			break;
		}
	if (check == 0)//若没有更新，则提前退出循环
		break;
	
}