20190428

Author: Del-te

最小生成树两种算法.cpp

@@ -0,0 +1,157 @@
+#include <iostream>
+#include <vector>
+#include <queue>
+#include <algorithm>
+using namespace std;
+#define INF 0x3f3f3f3f   
+#define VertexData int  //顶点数据
+#define UINT  int
+#define vexCounts 6  //顶点数量
+char vextex[] = { 'A', 'B', 'C', 'D', 'E', 'F' };
+struct node 
+{
+    VertexData data;
+    int lowestcost;
+}closedge[vexCounts]; //Prim算法中的辅助信息
+typedef struct 
+{
+    VertexData u;
+    VertexData v;
+    int cost;  //边的代价
+}Arc;  //原始图的边信息
+void AdjMatrix(int adjMat[][vexCounts])  //邻接矩阵表示法
+{
+    for (int i = 0; i < vexCounts; i++)   //初始化邻接矩阵
+        for (int j = 0; j < vexCounts; j++)
+        {
+            adjMat[i][j] = INF;
+        }
+    adjMat[0][1] = 6; adjMat[0][2] = 1; adjMat[0][3] = 5;
+    adjMat[1][0] = 6; adjMat[1][2] = 5; adjMat[1][4] = 3;
+    adjMat[2][0] = 1; adjMat[2][1] = 5; adjMat[2][3] = 5; adjMat[2][4] = 6; adjMat[2][5] = 4;
+    adjMat[3][0] = 5; adjMat[3][2] = 5; adjMat[3][5] = 2;
+    adjMat[4][1] = 3; adjMat[4][2] = 6; adjMat[4][5] = 6;
+    adjMat[5][2] = 4; adjMat[5][3] = 2; adjMat[5][4] = 6;
+}
+int Minmum(struct node * closedge)  //返回最小代价边
+{
+    int min = INF;
+    int index = -1;
+    for (int i = 0; i < vexCounts;i++)
+    {
+        if (closedge[i].lowestcost < min && closedge[i].lowestcost !=0)
+        {
+            min = closedge[i].lowestcost;
+            index = i;
+        }
+    }
+    return index;
+}
+void MiniSpanTree_Prim(int adjMat[][vexCounts], VertexData s)
+{
+    for (int i = 0; i < vexCounts;i++)
+    {
+        closedge[i].lowestcost = INF;
+    }      
+    closedge[s].data = s;      //从顶点s开始
+    closedge[s].lowestcost = 0;
+    for (int i = 0; i < vexCounts;i++)  //初始化辅助数组
+    {
+        if (i != s)
+        {
+            closedge[i].data = s;
+            closedge[i].lowestcost = adjMat[s][i];
+        }
+    }
+    for (int e = 1; e <= vexCounts -1; e++)  //n-1条边时退出
+    {
+        int k = Minmum(closedge);  //选择最小代价边
+        cout << vextex[closedge[k].data] << "--" << vextex[k] << endl;//加入到最小生成树
+        closedge[k].lowestcost = 0; //代价置为0
+        for (int i = 0; i < vexCounts;i++)  //更新v中顶点最小代价边信息
+        {
+            if ( adjMat[k][i] < closedge[i].lowestcost)
+            {
+                closedge[i].data = k;
+                closedge[i].lowestcost = adjMat[k][i];
+            }
+        }
+    }
+}
+void ReadArc(int  adjMat[][vexCounts],vector<Arc> &vertexArc) //保存图的边代价信息
+{
+    Arc * temp = NULL;
+    for (int i = 0; i < vexCounts;i++)
+    {
+        for (int j = 0; j < i; j++)
+        {
+            if (adjMat[i][j]!=INF)
+            {
+                temp = new Arc;
+                temp->u = i;
+                temp->v = j;
+                temp->cost = adjMat[i][j];
+                vertexArc.push_back(*temp);
+            }
+        }
+    }
+}
+bool compare(Arc  A, Arc  B)
+{
+    return A.cost < B.cost ? true : false;
+}
+bool FindTree(VertexData u, VertexData v,vector<vector<VertexData> > &Tree)
+{
+    int index_u = INF;
+    int index_v = INF;
+    for (int i = 0; i < Tree.size();i++)  //检查u,v分别属于哪颗树
+    {
+        if (find(Tree[i].begin(), Tree[i].end(), u) != Tree[i].end())
+            index_u = i;
+        if (find(Tree[i].begin(), Tree[i].end(), v) != Tree[i].end())
+            index_v = i;
+    }
+ 
+    if (index_u != index_v)   //u,v不在一颗树上，合并两颗树
+    {
+        for (int i = 0; i < Tree[index_v].size();i++)
+        {
+            Tree[index_u].push_back(Tree[index_v][i]);
+        }
+        Tree[index_v].clear();
+        return true;
+    }
+    return false;
+}
+void MiniSpanTree_Kruskal(int adjMat[][vexCounts])
+{
+    vector<Arc> vertexArc;
+    ReadArc(adjMat, vertexArc);//读取边信息
+    sort(vertexArc.begin(), vertexArc.end(), compare);//边按从小到大排序
+    vector<vector<VertexData> > Tree(vexCounts); //6棵独立树
+    for (int i = 0; i < vexCounts; i++)
+    {
+        Tree[i].push_back(i);  //初始化6棵独立树的信息
+    }
+    for (int i = 0; i < vertexArc.size(); i++)//依次从小到大取最小代价边
+    {
+        VertexData u = vertexArc[i].u;  
+        VertexData v = vertexArc[i].v;
+        if (FindTree(u, v, Tree))//检查此边的两个顶点是否在一颗树内
+        {
+            cout << vextex[u] << "---" << vextex[v] << endl;//把此边加入到最小生成树中
+        }   
+    }
+}
+ 
+int main()
+{
+    int  adjMat[vexCounts][vexCounts] = { 0 };
+    AdjMatrix(adjMat);   //邻接矩阵
+    cout << "Prim :" << endl;
+    MiniSpanTree_Prim(adjMat,0); //Prim算法，从顶点0开始.
+    cout << "-------------" << endl << "Kruskal:" << endl;
+    MiniSpanTree_Kruskal(adjMat);//Kruskal算法
+    system("pause");
+    return 0;
+}