cf 609E.Minimum spanning tree for each edge

最小生成树，lca（树链剖分（太难搞，不会写））

问存在这条边的最小生成树，2种情况。1.这条边在原始最小生成树上。2.加上这条半形成一个环（加上），那么就找原来这条边2端点间的最大边就好（减去）。（sum+val-max）

（代码冗长）

 #include<bits/stdc++.h>
 #define LL long long
 #define  N 100005
 using namespace std;
 inline int ra()
 {
     int x=,f=; char ch=getchar();
     while (ch<'' || ch>'') {if (ch=='-') f=-; ch=getchar();}
     while (ch>='' && ch<='') {x=x*+ch-''; ch=getchar();}
     return x*f;
 }
 struct node{
     int x,y,id,v;
 }a[N<<];
 struct data{
     int to,next,v;
 }e[N<<];
 int n,m,deep[N<<],fa[N<<][];
 int father[N<<],cnt;
 LL sum;
 int mx[N<<][],head[N<<];
 bool vis[N<<];
 void insert(int x, int y, int v)
 {
     e[++cnt].next=head[x];
     e[cnt].to=y;
     e[cnt].v=v;
     head[x]=cnt;
 }
 int find(int x)
 {
     return father[x]==x?x:father[x]=find(father[x]);
 }
 bool cmp(node a, node b)
 {
     return a.v<b.v;
 }
 bool cmpid(node a, node b)
 {
     return a.id<b.id;
 }
 void dfs(int x, int f)
 {
     for (int i=; i<=; i++)
     {
         fa[x][i]=fa[fa[x][i-]][i-];
         mx[x][i]=max(mx[x][i-],mx[fa[x][i-]][i-]);
     }
     for (int i=head[x];i;i=e[i].next)
     {
         if (e[i].to==f) continue;
         fa[e[i].to][]=x;
         mx[e[i].to][]=e[i].v;
         deep[e[i].to]=deep[x]+;
         dfs(e[i].to,x);
     }
 }
 int getans(int x, int y)
 {
     int ans=;
     if (deep[x]<deep[y]) swap(x,y);
     int t=deep[x]-deep[y];
     for (int i=; i<=; i++)
         if (t&(<<i)) ans=max(ans,mx[x][i]),x=fa[x][i];
     for (int i=; i>=; i--)
         if (fa[x][i]!=fa[y][i])
         {
             ans=max(ans,max(mx[x][i],mx[y][i]));
             x=fa[x][i]; y=fa[y][i];
         }
     if (x!=y) return max(ans,max(mx[x][],mx[y][]));
     return ans;
 }
 int main()
 {
     n=ra(); m=ra();
     for (int i=; i<=m; i++)
     {
         int x=ra(),y=ra(),v=ra();
         a[i].x=x; a[i].y=y; a[i].v=v; a[i].id=i;
     }
     sort(a+,a+m+,cmp); int tot=;
     for (int i=; i<=n; i++) father[i]=i;
     for (int i=; i<=m; i++)
     {
         int q=find(a[i].x),p=find(a[i].y);
         if (p!=q)
         {
             vis[a[i].id]=;
             father[p]=q;
             sum+=a[i].v;
             tot++;
             insert(a[i].x,a[i].y,a[i].v);
             insert(a[i].y,a[i].x,a[i].v);
     //        cout<<a[i].x<<"   "<<a[i].y<<"    "<<a[i].v<<endl;
         }
         if (tot==n-) break;
     }
     dfs(,);
     sort(a+,a+m+,cmpid);
     for (int i=; i<=m; i++)
     {
         if (vis[i]) printf("%I64d\n",sum);
         else {
             cout<<sum+(LL)a[i].v-(LL)getans(a[i].x,a[i].y)<<endl;
         //    cout<<getans(a[i].x,a[i].y);while (1);
         }
     }
     return ;
 }