算法思路:求最小生成树,用maxx[i][j]来表示最小生成树中i到j的最大边权,求完后,直接枚举所有不在最小生成树中的边,替换最大边权的边,更新答案
bool vis[maxn],used[maxn][maxn];
int n,dis[maxn],pre[maxn],maxx[maxn][maxn],cost[maxn][maxn];
int Prim()
{
int ans=inf,tot=0;
memset ( vis , false , sizeof(vis) );
memset ( maxx , 0 , sizeof(maxx) );
memset ( used , false , sizeof(used) );
vis[0] = true;
pre[0] = -1;
for ( int i=1 ; i<n ; i++ )
dis[i] = cost[0][i],pre[i] = 0;
dis[0] = 0;
while ( true )
{
int minc = inf,p = -1;
for ( int i=0 ; i<n ; i++ )
if ( !vis[i]&&dis[i]<minc )
minc = dis[i],p = i;
if ( p==-1 ) break;
tot += minc;
vis[p] = true;
used[p][pre[p]] = used[pre[p]][p] = true;
for ( int i=0 ; i<n ; i++ )
{
if ( vis[i]&&i!=p )
maxx[i][p] = maxx[p][i] = Max( maxx[i][pre[p]] , dis[p] );
if ( !vis[i]&&dis[i]>cost[p][i] )
dis[i] = cost[p][i],pre[i] = p;
}
}
for ( int i=0 ; i<n ; i++ )
for ( int j=i+1 ; j<n ; j++ )
if ( !used[i][j] ) ans = Min ( ans , tot-maxx[i][j]+cost[i][j] );
return ans;
}