第6章 图
3. 克鲁斯卡尔(Kruskal) 算法
克鲁斯卡尔算法的基本思想是：对一个有n个顶点的无向连通图，将图中的边按权值大小依次选取，若选取的边使生成树不形成回路，则把它加入到树中；若形成回路，则将它舍弃。如此进行下去，直到树中包含有n-1条边为止。(当整个图为连通图时为n-1条边)
根据邻接矩阵存储结构实现Kruskal算法：（邻接链表的实现在前面的博客）
public void Kruskal()
{
bool[,] markers = new bool[NodeNum, NodeNum];
Dictionary<AdjListNode<T>, VexListNode<T>> dic = new Dictionary<AdjListNode<T>, VexListNode<T>>();
while (true)
{
AdjListNode<T> adjNode = null;
VexListNode<T> vexNode = null;
AdjListNode<T> currentAdjNode = null;
VexListNode<T> currentVexNode = null;
for (int j = 0; j < NodeNum; j++)
{
currentVexNode = vexList[j];
currentAdjNode = currentVexNode.FirstAdj;
while (currentAdjNode != null)
{
if (markers[j, currentAdjNode.AdjVexIndex] == false)
{
if (adjNode == null || currentAdjNode.Weight < adjNode.Weight)
{
vexNode = currentVexNode;
adjNode = currentAdjNode;
}
}
currentAdjNode = currentAdjNode.Next;
}
}
if (adjNode == null)
break;
dic.Add(adjNode, vexNode);
markers[IsNode(vexNode.Node), adjNode.AdjVexIndex] = true;
markers[adjNode.AdjVexIndex, IsNode(vexNode.Node)] = true;
bool ifCycle = true;
while (ifCycle)
{
ifCycle = false;
for (int j = 0; j < NodeNum; j++)
{
for (int k = 0; k < NodeNum; k++)
{
if (markers[j, k] == true)
{
for (int m = 0; m < NodeNum; m++)
{
if (m == k)
continue;
if (markers[k, m] == true && markers[j, m] == false)
{
markers[j, m] = true;
markers[m, j] = true;
ifCycle = true;
}
}
}
}
}
}
}
foreach (var i in dic.Keys)
{
Console.WriteLine(dic[i].Node.Value.ToString() + " -> " + i.Weight + " -> " + vexList[i.AdjVexIndex].Node.Value.ToString());
}
}
调用代码:
GraphAdjList<int> adjList = new GraphAdjList<int>(100);
//Inial graph object
GraphNode<int> node1 = new GraphNode<int>(1);
GraphNode<int> node2 = new GraphNode<int>(2);
GraphNode<int> node3 = new GraphNode<int>(3);
GraphNode<int> node4 = new GraphNode<int>(4);
GraphNode<int> node5 = new GraphNode<int>(5);
GraphNode<int> node6 = new GraphNode<int>(6);
GraphNode<int> node7 = new GraphNode<int>(7);
GraphNode<int> node8 = new GraphNode<int>(8);
adjList.SetNode(node1);
adjList.SetNode(node2);
adjList.SetNode(node3);
adjList.SetNode(node4);
adjList.SetNode(node5);
adjList.SetNode(node6);
adjList.SetNode(node7);
adjList.SetNode(node8);
adjList.SetEdge(0, node2, node1, 2);
adjList.SetEdge(1,node1, node3, 4);
adjList.SetEdge(2,node1, node4, 4);
adjList.SetEdge(3, node1, node5, 3);
adjList.SetEdge(4, node2, node3, 3);
adjList.SetEdge(5, node2, node4, 1);
adjList.SetEdge(6, node2, node5, 2);
adjList.SetEdge(7, node3, node4, 4);
adjList.SetEdge(8, node3, node5, 4);
adjList.SetEdge(9, node5, node4, 2);
adjList.SetEdge(10, node6, node7, 3);
adjList.SetEdge(11, node8, node6, 2);
adjList.SetEdge(12, node7, node8, 3);
adjList.Kruskal();
System.Console.ReadKey();
输出为：
2 -> 1 -> 4
2 -> 2 -> 5
2 -> 2 -> 1
8 -> 2 -> 6
2 -> 3 -> 3
6 -> 3 -> 7