最小生成树<lct>

题解：

lct动态维护最小生成树

每次加边时若这两个之间不连通，那么直接连接

如果这两个点联通，那么就找到这条边上的最大值

如果这个大于当前边，就替换掉

但是需要注意的是lct只能维护点，不能维护边

所以可以把边弄成点

代码：

#include <bits/stdc++.h>
using namespace std;
#define ll long long
#define maxn 500000
ll n,m,num,root,data[maxn],fa[maxn],
leftson[maxn],rightson[maxn];
ll v[maxn],aa[maxn],bb[maxn];
bool rev[maxn];
void down(ll x)
{
  if (!rev[x]) return;
  swap(leftson[x],rightson[x]); rev[x]=0;
  rev[leftson[x]]^=1; rev[rightson[x]]^=1; 
}
int se(int x,int y,int z)
{
  if (v[x]>=v[y]&&v[x]>=v[z]) return(x);
  else if (v[y]>=v[x]&&v[y]>=v[z]) return(y);
  else return(z);
}
void updata(ll x)
{
    down(x);
    data[x]=se(x,data[leftson[x]],data[rightson[x]]);
}
void pushr(ll x)
{
  rev[x]^=1;
}
bool pd(ll x)
{
  ll y=fa[x];
  if (leftson[y]!=x&&rightson[y]!=x) return(false);
  else return(true);
}
void rotate(ll x,ll y)
{
  ll father=fa[x];
  if (y==1)
  {
    rightson[father]=leftson[x];
    if (leftson[x]) fa[leftson[x]]=father;
  } else
  {
    leftson[father]=rightson[x];
    if (rightson[x]) fa[rightson[x]]=father;
  }
  fa[x]=fa[father];
  if (pd(father))
  {
    if (leftson[fa[father]]==father) 
      leftson[fa[father]]=x; else
      rightson[fa[father]]=x;
  }
  fa[father]=x;
  if (y==1) leftson[x]=father; else rightson[x]=father;
  updata(father); updata(x);
}
void dfs(ll x)
{
  if (pd(x)) dfs(fa[x]);
  down(x);
}
void splay(ll x)
{
  dfs(x);
  ll father=fa[x];
  while (pd(x))
  {
    if (!pd(father))
    {
      if (x==leftson[father]) rotate(x,2);
      else rotate(x,1);
    } else
    {
      if (father==leftson[fa[father]])
      {
        if (x==leftson[father]) 
          rotate(father,2),rotate(x,2);
        else rotate(x,1),rotate(x,2);
      } else
      {
        if (x==rightson[father])
          rotate(father,1),rotate(x,1);
        else rotate(x,2),rotate(x,1);
      }
    }
    father=fa[x];
  }
}
void access(ll x)
{
  for (ll y=0;x;y=x,x=fa[x])
    splay(x),rightson[x]=y,updata(x);
}
void makeroot(ll x)
{
  access(x);
  splay(x);
  pushr(x);
}
ll findroot(ll x)
{
  access(x);
  splay(x);
  while (leftson[x]) x=leftson[x];
  return x;
}
void split(ll x,ll y)
{
  makeroot(x);
  access(y);
  splay(y);
}
void link(ll x,ll y)
{
  makeroot(x);
  if (findroot(y)!=x) fa[x]=y;
}
void cut(ll x,ll y)
{
  makeroot(x);
  split(x,y);
  fa[x]=leftson[y]=0;
}
int main()
{
  freopen("noip.in","r",stdin);
  freopen("noip.out","w",stdout);
  cin>>n>>m;
  int c,d,e;
  int cnt=0,num=0;
  for (int i=1;i<=m;i++)
  {
      cin>>c>>d>>e;
      makeroot(c);
    if (findroot(d)==c)
    { 
        split(c,d);
        int d1=data[d];
        if (v[d1]>e)
        {
          cut(aa[d1],d1); cut(bb[d1],d1); num-=(v[d1]-e);
          link(c,i+n); link(i+n,d); v[i+n]=e;
          aa[i+n]=c; bb[i+n]=d;
        }
      } else
      {
        cnt++; link(c,i+n); link(i+n,d); v[i+n]=e;
        aa[i+n]=c; bb[i+n]=d; num+=e;
    }
  }
  cout<<num;
  return 0;
}