DS图--最小生成树

题目描述

根据输入创建无向网。分别用Prim算法和Kruskal算法构建最小生成树。（假设：输入数据的最小生成树唯一。）

输入

顶点数n

n个顶点

边数m

m条边信息,格式为：顶点1 顶点2 权值

Prim算法的起点v

输出

输出最小生成树的权值之和

对两种算法，按树的生长顺序，输出边信息(Kruskal中边顶点按数组序号升序输出)

样例输入

6

v1 v2 v3 v4 v5 v6

10

v1 v2 6

v1 v3 1

v1 v4 5

v2 v3 5

v2 v5 3

v3 v4 5

v3 v5 6

v3 v6 4

v4 v6 2

v5 v6 6

v1

样例输出

15

prim:

v1 v3 1

v3 v6 4

v6 v4 2

v3 v2 5

v2 v5 3

kruskal:

v1 v3 1

v4 v6 2

v2 v5 3

v3 v6 4

v2 v3 5

 

 普里姆算法更新lowcost数组的值

#include<iostream>
using namespace std;
struct{
   string adjvex;
   int lowcost;
}closedge[];
class MGraph
{
public:
    int graph[][],graph1[][];
    int n,len; //n 是节点个数 len是边的数
    int visited[],low[];
    string *q;//存节点
    string start;
    int startpos;
    MGraph(){};
    void SetMGraph()
    {
        int i,j;
        cin>>n;
        for(i=;i<;i++)
            for(j=;j<;j++)
            {
                graph[i][j]=; //将每个权值置为最大
                graph1[i][j]=;
            }

        q=new string[n];
        for(i=;i<n;i++)
            cin>>q[i];
        cin>>len;
        for(i=;i<=len;i++)
        {
            string ch1,ch2;
            int weight;
            cin>>ch1>>ch2>>weight;
            int loc1,loc2;
            for(j=;j<n;j++)
            {
                if(q[j]==ch1)
                    loc1=j;
                if(q[j]==ch2)
                    loc2=j;
            }
            graph1[loc1][loc2]=graph[loc1][loc2]=weight;
            graph1[loc1][loc2]=graph[loc2][loc1]=weight;//无向图
        }
        cin>>start;
        for(i=;i<n;i++)
            if(q[i]==start)
                startpos=i;
    }
    void prim()
    {
        int i,j;
        for(i=;i<=n;i++)
            visited[i]=;
        visited[startpos]=;
        int min;
        for(i=;i<n;i++)
        {
            min=;
            for(j=;j<n;j++)
            {
                if(graph[i][j]<min)
                {
                    min=graph[i][j];
                    closedge[i].adjvex=q[j];
                    closedge[i].lowcost=min;
                }
            }
        }
        string s3;
        string *e1,*e2;
        int *w3;
        e1=new string[];
        e2=new string[];
        w3=new int[];
        int index,k=;
        for(i=;i<n;i++)
        {
            min=;
            for(j=;j<n;j++)
            {
                if(!visited[j])
                    continue;
                else
                {
                    if(min>closedge[j].lowcost)
                    {
                        min=closedge[j].lowcost;
                        s3=closedge[j].adjvex;
                        index=j;
                    }
                }
            }
            e1[k]=q[index];e2[k]=s3,w3[k++]=min;
            for(int g=;g<n;g++)
            {
                if(q[g]==s3)
                {
                    visited[g]=;
//                    graph[index][g]=99999;
//                    graph[g][index]=99999;
                    break;
                }
            }
            for(int g=;g<n;g++)
            {
                min=;
                for(int m=;m<n;m++)
                {
                    if(min>graph[g][m] && visited[m]==)
                    {
                        min=graph[g][m];
                        closedge[g].adjvex=q[m];
                        closedge[g].lowcost=min;
                    }
                }
            }
        }
        int weight=;
        for(i=;i<k-;i++)
        {
            weight+=w3[i];
        }
        cout<<weight<<endl;
        cout<<"prim:"<<endl;
        for(i=;i<k-;i++)
            cout<<e1[i]<<" "<<e2[i]<<" "<<w3[i]<<endl;
    }
    void kruskal()
    {
        cout<<"kruskal:"<<endl;
        int *uni=new int[n];
        for(int i=;i<n;i++)
        {
            uni[i]=i;
        }
        for(int i=;i<n-;i++)
        {
            int min=;int x,y;
            for(int j=;j<n;j++)
            {
                for(int l=;l<n;l++)
                {
                    if(j==l)
                        continue;
                    if(uni[j]==uni[l])
                        continue;
                    else
                    {
                        if(min>graph1[j][l])
                        {
                            min=graph1[j][l];
                            x=j;y=l;
                        }

                    }
                }
            }
            graph1[x][y]=;graph1[y][x]=;
            if(x>y)
                int k;k=x;x=y;y=k;

            for(int i=;i<n;i++)
            {
                if(uni[i]==uni[y]&&i!=y) uni[i]=uni[x];
            }
            uni[y]=uni[x];
            cout<<q[x]<<" "<<q[y]<<" "<<min<<endl;
        }
    }
    void show()
    {
        int i,j;
        for(i=;i<n;i++)
        {
            for(j=;j<n;j++)
                cout<<graph[i][j]<<" ";
            cout<<endl;
        }
    }
};
int main()
{
    MGraph m,M;
    m.SetMGraph();
    m.prim();
    m.kruskal();
}