POJ 2485 Highways（最小生成树）

    不知该说好事成双，还是该说有些问题本质是一样的。用Kruskal做完前面那个题目，这个之前没有被解决的Kruskal题也轻易地搞定了。同样是开始的时候用Kruskal出问题，改用Prim过了POJ，现在回过头来用Kruskal算法做，也好，又过了。发出来，或许也会有像我这样曾经被这个问题搞郁闷的朋友。问题抽象一个下就是求Kruskal算法中最后加入的那条边的长度，同样是Prim算法中加入的边的最长的那条。

Kruskal算法C++源代码：

#include <iostream>
#include <algorithm>
using namespace std;
//也就是用Kruskal方法求最短路径时最后加入的那条边
typedef struct Edge{
    int x, y, dis;
};
Edge highway[250001];
bool flag[501];
int nodeSet[501];

bool compare(Edge a, Edge b)
{
    return (a.dis < b.dis);
}
int main()
{
    int tcase, n;
    cin>>tcase;
    while(tcase--){
        scanf("%d", &n);
        int tag = 1;
        for(int i = 1; i <= n; i++){
            nodeSet[i] = i;
            for(int j = 1; j <= n; j++){
                highway[tag].x = i;
                highway[tag].y = j;
                scanf("%d", &highway[tag].dis);
                tag++;
            }
        }
        sort(highway+1, highway+tag, compare);
        memset(flag, 0, sizeof(flag));
        tag = n+1;
        int edgeNum = 0;
        while(edgeNum < n-1){
            if((!flag[highway[tag].x]) && (!flag[highway[tag].y])){
                flag[highway[tag].x] = true;
                flag[highway[tag].y] = true;
                edgeNum++;
                nodeSet[highway[tag].x] = nodeSet[highway[tag].y];
            }else if((!flag[highway[tag].x]) && (flag[highway[tag].y])){
                flag[highway[tag].x] = true;
                edgeNum++;
                nodeSet[highway[tag].x] = nodeSet[highway[tag].y];
            }else if((!flag[highway[tag].y]) && (flag[highway[tag].x])){
                flag[highway[tag].y] = true;
                edgeNum++;
                nodeSet[highway[tag].y] = nodeSet[highway[tag].x];
            }else{
                if(nodeSet[highway[tag].x] != nodeSet[highway[tag].y]){
                    edgeNum++;
                    int tmp = nodeSet[highway[tag].x];
                    for(int i = 1; i <= n; i++)
                        if(nodeSet[i] == tmp)
                            nodeSet[i] = nodeSet[highway[tag].y];
                }
            }
            tag++;
        }
        cout<<highway[tag-1].dis<<endl;
    }
    return 0;
}

 

 

<!---->#include  < iostream >
#include  < algorithm >
using   namespace  std;
// 也就是用Kruskal方法求最短路径时最后加入的那条边
typedef  struct  Edge{
     int  x, y, dis;
};
Edge highway[ 250001 ];
bool  flag[ 501 ];
int  nodeSet[ 501 ];

bool  compare(Edge a, Edge b)
{
     return  (a.dis  <  b.dis);
}
int  main()
{
     int  tcase, n;
    cin >> tcase;
     while (tcase -- ){
        scanf( " %d " ,  & n);
         int  tag  =   1 ;
         for ( int  i  =   1 ; i  <=  n; i ++ ){
            nodeSet[i]  =  i;
             for ( int  j  =   1 ; j  <=  n; j ++ ){
                highway[tag].x  =  i;
                highway[tag].y  =  j;
                scanf( " %d " ,  & highway[tag].dis);
                tag ++ ;
            }
        }
        sort(highway + 1 , highway + tag, compare);
        memset(flag,  0 ,  sizeof (flag));
        tag  =  n + 1 ;
         int  edgeNum  =   0 ;
         while (edgeNum  <  n - 1 ){
             if (( ! flag[highway[tag].x])  &&  ( ! flag[highway[tag].y])){
                flag[highway[tag].x]  =   true ;
                flag[highway[tag].y]  =   true ;
                edgeNum ++ ;
                nodeSet[highway[tag].x]  =  nodeSet[highway[tag].y];
            } else   if (( ! flag[highway[tag].x])  &&  (flag[highway[tag].y])){
                flag[highway[tag].x]  =   true ;
                edgeNum ++ ;
                nodeSet[highway[tag].x]  =  nodeSet[highway[tag].y];
            } else   if (( ! flag[highway[tag].y])  &&  (flag[highway[tag].x])){
                flag[highway[tag].y]  =   true ;
                edgeNum ++ ;
                nodeSet[highway[tag].y]  =  nodeSet[highway[tag].x];
            } else {
                 if (nodeSet[highway[tag].x]  !=  nodeSet[highway[tag].y]){
                    edgeNum ++ ;
                     int  tmp  =  nodeSet[highway[tag].x];
                     for ( int  i  =   1 ; i  <=  n; i ++ )
                         if (nodeSet[i]  ==  tmp)
                            nodeSet[i]  =  nodeSet[highway[tag].y];
                }
            }
            tag ++ ;
        }
        cout << highway[tag - 1 ].dis << endl;
    }
     return   0 ;
}

Prim算法C++源代码：

#include <iostream>
using namespace std;

int highway[501][501];
int lowcost[501], n;

int prim()
{ 
    for(int i = 1; i <= n; i++)
        lowcost[i] = highway[1][i];
    int ans = 0, nextVex, minEdge;
    for(int i = 1; i < n; i++){
        minEdge = 999999999;
        nextVex = 1;
        for(int j = 1; j <= n; j++){
            if((lowcost[j] < minEdge) && (lowcost[j] > 0)){
                minEdge = lowcost[j];
                nextVex = j;	
            }
        }
        if(minEdge > ans)
            ans = minEdge;
        lowcost[nextVex] = 0;
        for(int j = 1; j <= n; j++){
            if(lowcost[j] > highway[nextVex][j]){
                lowcost[j] = highway[nextVex][j];
            }
        }
    }
    return ans;
}
int main()
{
    int tcase;
    scanf("%d", &tcase);
    while(tcase--)
    {
        scanf("%d", &n);	
        for(int i = 1; i <= n; i++)
            for(int j = 1; j <= n; j++)
                scanf("%d", &highway[i][j]);
        printf("%d\n", prim());
    }
    return 0;
}

  <!---->#include  < iostream >
using   namespace  std;

int  highway[ 501 ][ 501 ];
int  lowcost[ 501 ], n;

int  prim()
{ 
     for ( int  i  =   1 ; i  <=  n; i ++ )
        lowcost[i]  =  highway[ 1 ][i];
     int  ans  =   0 , nextVex, minEdge;
     for ( int  i  =   1 ; i  <  n; i ++ ){
        minEdge  =   999999999 ;
        nextVex  =   1 ;
         for ( int  j  =   1 ; j  <=  n; j ++ ){
             if ((lowcost[j]  <  minEdge)  &&  (lowcost[j]  >   0 )){
                minEdge  =  lowcost[j];
                nextVex  =  j;    
            }
        }
         if (minEdge  >  ans)
            ans  =  minEdge;
        lowcost[nextVex]  =   0 ;
         for ( int  j  =   1 ; j  <=  n; j ++ ){
             if (lowcost[j]  >  highway[nextVex][j]){
                lowcost[j]  =  highway[nextVex][j];
            }
        }
    }
     return  ans;
}
int  main()
{
     int  tcase;
    scanf( " %d " ,  & tcase);
     while (tcase -- )
    {
        scanf( " %d " ,  & n);    
         for ( int  i  =   1 ; i  <=  n; i ++ )
             for ( int  j  =   1 ; j  <=  n; j ++ )
                scanf( " %d " ,  & highway[i][j]);
        printf( " %d\n " , prim());
    }
     return   0 ;
}