HDU4756+Prim

题意简单：去掉最小生成树的某一条边并补上一条，求MaxVal

思路：贪心（借鉴Yamidie的思路。。。）

分别求出最小生成树和次最小生成树，再在这两棵树上求最小生成树

 #include<stdio.h>
 #include<string.h>
 #include<stdlib.h>
 #include<algorithm>
 #include<math.h>
 using namespace std;
 const int maxn = ;
 const int maxm = maxn*maxn;
 const int inf1 = 0x3f3f3f3f;
 const double inf2 = ;

 struct Point {
     double x,y;
 }pnt[ maxn ];
 struct Edge{
     int u,v;
     double val;
     int id;
 }edge[ maxn<< ];
 int cnt_edge;
 double mat[ maxn ][ maxn ];
 double dis[ maxn ];
 bool vis[ maxn ];
 int pre[ maxn ];

 double LenPrim1;
 double LenPrim2;

 int fa[ maxn ],rank[ maxn ];

 int find( int x ){
     if( x==fa[x] ) return x;
     else return fa[ x ] = find( fa[x] );
 }

 void init( int n ){
     for( int i=;i<n;i++ ){
         fa[ i ] = i;
         rank[ i ] = ;
     }
     return ;
 } 

 double dist( int i,int j ){
     return sqrt( (pnt[i].x-pnt[j].x)*(pnt[i].x-pnt[j].x)+(pnt[i].y-pnt[j].y)*(pnt[i].y-pnt[j].y) );
 } 

 int cmp( Edge a,Edge b ){
     return a.val<b.val;
 }    

 void GetMap( int n ){
     for( int i=;i<n;i++ )
         for( int j=;j<n;j++ ){
             mat[i][j] = dist( i,j );
             //printf("mat[%d][%d]=%.3lf\n",i,j,mat[i][j]);
         }
     return ;
 }

 double prim( int n,int Belong ){
     for( int i=;i<n;i++ ){
         dis[ i ] = mat[][i];
         vis[ i ] = false;
         pre[ i ] = ;
     }
     vis[] = true;
     //if( Belong==2 ){
     //    for( int i=0;i<n;i++ )for( int j=0;j<n;j++ )
             //printf("mat[%d][%d]=%.3lf\n",i,j,mat[i][j]);
     //}
     double ans = ;
     for( int i=;i<n;i++ ){
         int id = -;
         double M = inf2;
         for( int j=;j<n;j++ ){
             if( !vis[j] && M>dis[j] ){
                 M = dis[j];
                 id = j;
             }
         }
         if( id==- ) break;
         vis[ id ] = true;
         ans += M;
         edge[ cnt_edge ].u = pre[ id ];
         edge[ cnt_edge ].v = id;
         edge[ cnt_edge ].id = Belong;
         edge[ cnt_edge ].val = mat[ id ][ pre[id] ];
         //printf("u = %d,v = %d\n",edge[cnt_edge].u,edge[cnt_edge].v);
         cnt_edge ++ ;
         for( int j=;j<n;j++ ){
             if( !vis[j] && dis[j]>mat[id][j] ){
                 dis[j] = mat[id][j];
                 pre[ j ] = id;
             }
         }
     }
     return ans;
 }    

 void Deal( int n ){
     for( int i=;i<cnt_edge;i++ ){
         mat[ edge[i].u ][ edge[i].v ] = inf2;
         mat[ edge[i].v ][ edge[i].u ] = inf2;
     }
 }

 double Kruskal( int n,int id ){
     double ans = ;
     init( n );
     int cnt = ;
     for( int i=;i<cnt_edge;i++ ){
         if( i==id ) continue;
         int fx = find( edge[i].u );
         int fy = find( edge[i].v );
         if( fx!=fy ){
             if( rank[ fx ]<rank[ fy ] ){
                 rank[ fy ] += rank[ fx ];
                 fa[ fx ] = fy;
             }
             else {
                 rank[ fx ] += rank[ fy ];
                 fa[ fy ] = fx;
             }
             cnt ++ ;
             ans += edge[i].val;
             if( cnt==n- ) break;
         }
        }
        return ans;
 }

 int main(){
     int T;
     scanf("%d",&T);
     while( T-- ){
         int n;
         double k;
         scanf("%d%lf",&n,&k);
         for( int i=;i<n;i++ )
             scanf("%lf%lf",&pnt[i].x,&pnt[i].y);
         GetMap( n );
         cnt_edge = ;
         LenPrim1 = prim( n, );
         Deal( n );
         LenPrim2 = prim( n, );
         double ans = LenPrim1;
         double temp_ans = ;
         sort( edge,edge+cnt_edge,cmp );
         //printf("cnt_edge = %d\n",cnt_edge);
         for( int i=;i<cnt_edge;i++ ){
             if( edge[i].id== && edge[i].u!= && edge[i].v!= ){
                 temp_ans = Kruskal( n,i );
                 if( temp_ans>ans )
                     ans = temp_ans;
             }
         }
         printf("%.2lf\n",ans*k);
     }
     return ;
 }