次小生成树

次小生成树

http://acm.cs.ecnu.edu.cn/problem.php?problemid=2165
找了个次小生成树的题目做一做。

方法是先找出最小生成树，然后依次添加每条在原图中，而不在MST上的边，然后删除
形成的环上的最大边（先通过dfs预处理求出MST上任意点之间的最大边权），这样
形成了一棵新树，找出所有添加删除形成的secondary minimum spanning tree就OK了！

#include  < stdio.h >
#include < string .h >
#define  INF 2139062143
int  m,n,min_dif,flag,lowcost[ 501 ],map[ 501 ][ 501 ],mst_map[ 501 ][ 501 ],
    s[ 501 ],pre[ 501 ],max_val[ 501 ][ 501 ],vis[ 501 ];
void  dfs( int  sta, int  t, int  max){
     for ( int  i = 1 ;i <= n;i ++ ){
         if ( ! vis[i]  &&  mst_map[t][i] != INF){
            vis[i] = 1 ;
             int  tmp = max;
             if (mst_map[t][i] > max) max = mst_map[t][i];
             if (max > max_val[sta][i]) max_val[sta][i] = max_val[i][sta] = max;
            dfs(sta,i,max);
            max = tmp;
        }
    }

}
int  main(){
     while (scanf( " %d%d " , & n, & m) != EOF){
        memset(map, 127 , sizeof (map));
        memset(mst_map, 127 , sizeof (mst_map));
        memset(lowcost, 127 , sizeof (lowcost));
        memset(s, 0 , sizeof (s));
        memset(pre, 0 , sizeof (pre));
        memset(max_val, 128 , sizeof (max_val));
         int  i,j,idx,min_mst = 0 ,mincost,a,b,c;
         for (i = 1 ;i <= m;i ++ ){
            scanf( " %d%d%d " , & a, & b, & c);
            map[a][b] = map[b][a] = c;
        }
         // prim algorithm
        lowcost[ 1 ] = 0 ;
         for (i = 1 ;i <= n;i ++ ){
            mincost = INF;
             for (j = 1 ;j <= n;j ++ )
                 if ( ! s[j]  &&  lowcost[j] < mincost){
                    mincost = lowcost[j];
                    idx = j;
                }
            s[idx] = 1 ;
            min_mst += mincost;
            mst_map[idx][pre[idx]] = mst_map[pre[idx]][idx] = map[pre[idx]][idx];
             for (j = 1 ;j <= n;j ++ ){
                 if ( ! s[j]  &&  map[idx][j] < lowcost[j]){
                    lowcost[j] = map[idx][j];
                    pre[j] = idx;
                }
            }
        }
         // calc max_val[i][j] 
         for (i = 1 ;i <= n;i ++ ){
            memset(vis, 0 , sizeof (vis));
            vis[i] = 1 ;
            dfs(i,i, - INF);
        }
         // for each edge excluded int the MST
         // try to get secondary minimum spanning tree
        min_dif = INF;flag = 0 ;
         for (i = 1 ;i <= n;i ++ ){
             for (j = i + 1 ;j <= n;j ++ ){
                 if (mst_map[i][j] == INF  &&  map[i][j] != INF){
                    flag = 1 ; // mark if there's s new tree
                     if (map[i][j] - max_val[i][j] < min_dif) min_dif = map[i][j] - max_val[i][j];
                }
            }    
        }
         if ( ! flag) printf( " %d -1\n " ,min_mst);
         else  printf( " %d %d\n " ,min_mst,min_mst + min_dif);
    }
     return   0 ;
}