mirror of
https://github.com/This-weiyuqing/DSAndOS.git
synced 2026-10-17 18:55:44 +08:00
126 lines
4.3 KiB
C++
126 lines
4.3 KiB
C++
//算法6.9 克鲁斯卡尔算法
|
|
|
|
#include <iostream>
|
|
using namespace std;
|
|
|
|
typedef char VerTexType; //假设顶点的数据类型为字符型
|
|
typedef int ArcType;
|
|
#define MVNum 100 //最大顶点数
|
|
#define MaxInt 32767 //表示极大值，即∞
|
|
|
|
//----------------图的邻接矩阵---------------------
|
|
typedef struct{
|
|
VerTexType vexs[MVNum]; //顶点表
|
|
ArcType arcs[MVNum][MVNum]; //邻接矩阵
|
|
int vexnum,arcnum; //图的当前点数和边数
|
|
}AMGraph;
|
|
|
|
//辅助数组Edges的定义
|
|
struct{
|
|
VerTexType Head; //边的始点
|
|
VerTexType Tail; //边的终点
|
|
ArcType lowcost; //边上的权值
|
|
}Edge[(MVNum * (MVNum - 1)) / 2];
|
|
|
|
int Vexset[MVNum]; //辅助数组Vexset的定义
|
|
|
|
int LocateVex(AMGraph G , VerTexType v){
|
|
//确定点v在G中的位置
|
|
for(int i = 0; i < G.vexnum; ++i)
|
|
if(G.vexs[i] == v)
|
|
return i;
|
|
return -1;
|
|
}//LocateVex
|
|
|
|
void CreateUDN(AMGraph &G){
|
|
//采用邻接矩阵表示法，创建无向网G
|
|
int i , j , k;
|
|
cout <<"请输入总顶点数，总边数，以空格隔开:";
|
|
cin >> G.vexnum >> G.arcnum; //输入总顶点数，总边数
|
|
cout << endl;
|
|
|
|
cout << "输入点的名称，如a" << endl;
|
|
|
|
for(i = 0; i < G.vexnum; ++i){
|
|
cout << "请输入第" << (i+1) << "个点的名称:";
|
|
cin >> G.vexs[i]; //依次输入点的信息
|
|
}
|
|
cout << endl;
|
|
for(i = 0; i < G.vexnum; ++i) //初始化邻接矩阵，边的权值均置为极大值MaxInt
|
|
for(j = 0; j < G.vexnum; ++j)
|
|
G.arcs[i][j] = MaxInt;
|
|
cout << "输入边依附的顶点及权值，如a b 6" << endl;
|
|
for(k = 0; k < G.arcnum;++k){ //构造邻接矩阵
|
|
VerTexType v1 , v2;
|
|
ArcType w;
|
|
cout << "请输入第" << (k + 1) << "条边依附的顶点及权值:";
|
|
cin >> v1 >> v2 >> w; //输入一条边依附的顶点及权值
|
|
i = LocateVex(G, v1); j = LocateVex(G, v2); //确定v1和v2在G中的位置，即顶点数组的下标
|
|
G.arcs[i][j] = w; //边<v1, v2>的权值置为w
|
|
G.arcs[j][i] = G.arcs[i][j]; //置<v1, v2>的对称边<v2, v1>的权值为w
|
|
Edge[k].lowcost = w;
|
|
Edge[k].Head = v1;
|
|
Edge[k].Tail = v2;
|
|
}//for
|
|
}//CreateUDN
|
|
|
|
//----------冒泡排序-------------------
|
|
void Sort(AMGraph G){
|
|
int m = G.arcnum - 2;
|
|
int flag = 1;
|
|
while((m > 0) && flag == 1){
|
|
flag = 0;
|
|
for(int j = 0 ; j <= m ; j++){
|
|
if(Edge[j].lowcost > Edge[j+ 1].lowcost){
|
|
flag = 1;
|
|
|
|
VerTexType temp_Head = Edge[j].Head;
|
|
Edge[j].Head = Edge[j+ 1].Head;
|
|
Edge[j + 1].Head = temp_Head;
|
|
|
|
|
|
VerTexType temp_Tail = Edge[j].Tail;
|
|
Edge[j].Tail = Edge[j+ 1].Tail;
|
|
Edge[j + 1].Tail = temp_Tail;
|
|
|
|
ArcType temp_lowcost = Edge[j].lowcost;
|
|
Edge[j].lowcost = Edge[j+ 1].lowcost;
|
|
Edge[j + 1].lowcost = temp_lowcost;
|
|
}//if
|
|
}//for
|
|
--m;
|
|
}//while
|
|
}//Sort
|
|
|
|
void MiniSpanTree_Kruskal(AMGraph G){
|
|
//无向网G以邻接矩阵形式存储，构造G的最小生成树T，输出T的各条边
|
|
int i , j , v1 , v2 , vs1 , vs2;
|
|
Sort(G); //将数组Edge中的元素按权值从小到大排序
|
|
for(i = 0; i < G.vexnum; ++i) //辅助数组，表示各顶点自成一个连通分量
|
|
Vexset[i] = i;
|
|
for(i = 0; i < G.arcnum; ++i){
|
|
//依次查看排好序的数组Edge中的边是否在同一连通分量上
|
|
v1 =LocateVex(G, Edge[i].Head); //v1为边的始点Head的下标
|
|
v2 =LocateVex(G, Edge[i].Tail); //v2为边的终点Tail的下标
|
|
vs1 = Vexset[v1]; //获取边Edge[i]的始点所在的连通分量vs1
|
|
vs2 = Vexset[v2]; //获取边Edge[i]的终点所在的连通分量vs2
|
|
if(vs1 != vs2){ //边的两个顶点分属不同的连通分量
|
|
cout << Edge[i].Head << "-->" << Edge[i].Tail << endl; //输出此边
|
|
for(j = 0; j < G.vexnum; ++j) //合并vs1和vs2两个分量，即两个集合统一编号
|
|
if(Vexset[j] == vs2) Vexset[j] = vs1; //集合编号为vs2的都改为vs1
|
|
}//if
|
|
}//for
|
|
}//MiniSpanTree_Kruskal
|
|
|
|
void main(){
|
|
cout << "************算法6.9 克鲁斯卡尔算法**************" << endl << endl;
|
|
AMGraph G;
|
|
CreateUDN(G);
|
|
|
|
cout <<endl;
|
|
cout << "*****无向网G创建完成！*****" << endl;
|
|
|
|
cout <<endl;
|
|
MiniSpanTree_Kruskal(G);
|
|
}///main
|