bzoj1267 3784

双倍经验题
像这种方案太多不能全部求出来但求前k大一般有这样一个思路
将所有方案无重复不漏的分为若干类，每个类的元素满足单调性，然后我们用堆维护就行了！
对于这道题，可以想到用树的分治来处理路径，当处理根为x时
我们处理当前的子树每个点i和之前的子树上的组成的路径，
我们完全可以把访问顺序状态记录成一条链（状态是nlogn规模不会爆）
当前子树的每个点i在链上都有一段连续的可选区间，这个区间的点和i构成一条过根x的路径
这样链上的每个点就代表了一类路径
很明显，我们就可以noi超级钢琴的做法来解决，st表预处理+堆维护

 type way=record
        po,num,next:longint;
      end;
      node=record
        l,r,s,t:longint;
      end;

 var e:array[..] of way;
     h:array[..] of node;
     w:array[..,..] of longint;
     d:array[..] of longint;
     a:array[..] of longint;
     q:array[..,..] of longint;
     f,p,s:array[..] of longint;
     v:array[..] of boolean;
     l,r,root,len,t,tot,i,n,k,x,y,z,j:longint;
     m:node;

 function max(a,b:longint):longint;
   begin
     if a>b then exit(a) else exit(b);
   end;

 function mx(x,y:longint):longint;
   begin
     if a[x]>a[y] then exit(x) else exit(y);
   end;

 function ask(x,y:longint):longint;
   var k:longint;
   begin
     k:=trunc(ln(y-x+)/ln());
     exit(mx(w[x,k],w[y-d[k]+,k]));
   end;

 procedure swap(var a,b:node);
   var c:node;
   begin
     c:=a;
     a:=b;
     b:=c;
   end;

 procedure add(x,y,z:longint);
   begin
     inc(len);
     e[len].po:=y;
     e[len].num:=z;
     e[len].next:=p[x];
     p[x]:=len;
   end;

 procedure up(i:longint);
   var j:longint;
   begin
     j:=i shr ;
     while j> do
     begin
       if a[h[j].s]+a[h[j].t]<a[h[i].s]+a[h[i].t] then
       begin
         swap(h[i],h[j]);
         i:=j;
         j:=j shr ;
       end
       else break;
     end;
   end;

 procedure sift(i:longint);
   var j:longint;
   begin
     j:=i shl ;
     while j<=t do
     begin
       if (j<t) and (a[h[j+].s]+a[h[j+].t]>a[h[j].s]+a[h[j].t]) then inc(j);
       if a[h[j].s]+a[h[j].t]>a[h[i].s]+a[h[i].t] then
       begin
         swap(h[i],h[j]);
         i:=j;
         j:=j shl ;
       end
       else break;
     end;
   end;

 procedure getroot(x,fa:longint);
   var i,y:longint;
   begin
     s[x]:=;
     f[x]:=;
     i:=p[x];
     while i<> do
     begin
       y:=e[i].po;
       if (y<>fa) and not v[y] then
       begin
         getroot(y,x);
         s[x]:=s[x]+s[y];
         f[x]:=max(f[x],s[y]);
       end;
       i:=e[i].next;
     end;
     f[x]:=max(f[x],tot-s[x]);
     if f[x]<f[root] then root:=x;
   end;

 procedure get(x,fa,len:longint);
   var i,y:longint;
   begin
     inc(t);
     a[t]:=len;
     q[t,]:=l; q[t,]:=r;
     i:=p[x];
     while i<> do
     begin
       y:=e[i].po;
       if (y<>fa) and not v[y] then get(y,x,len+e[i].num);
       i:=e[i].next;
     end;
   end;

 procedure work(x:longint);
   var i,y:longint;
   begin
     v[x]:=true;
     i:=p[x];
     inc(t);
     l:=t;
     r:=t;
     q[t,]:=l; q[t,]:=r;
     while i<> do
     begin
       y:=e[i].po;
       if not v[y] then
       begin
         r:=t;
         get(y,x,e[i].num);
       end;
       i:=e[i].next;
     end;
     i:=p[x];
     while i<> do
     begin
       y:=e[i].po;
       if not v[y] then
       begin
         root:=;
         tot:=s[y];
         getroot(y,);
         work(root);
       end;
       i:=e[i].next;
     end;
   end;

 begin
   readln(n,k);
   for i:= to n- do
   begin
     readln(x,y,z);
     add(x,y,z);
     add(y,x,z);
   end;
   f[]:=;
   tot:=n;
   getroot(,);
   work(root);
   tot:=trunc(ln(t)/ln());
   d[]:=;
   for i:= to tot do
     d[i]:=d[i-]*;

   for i:= to t do
     w[i,]:=i;
   for j:= to tot do
     for i:= to t do
       if i+d[j]-<=t then
         w[i,j]:=mx(w[i,j-],w[i+d[j-],j-])
       else break;

   tot:=t; t:=;
   for i:= to tot do
   begin
     inc(t);
     with h[t] do
     begin
       l:=q[i,]; r:=q[i,];
       s:=i;
       t:=ask(l,r);
     end;
     up(t);
   end;
   for i:= to k do
   begin
     writeln(a[h[].s]+a[h[].t]);
     swap(h[],h[t]);
     m:=h[t];
     dec(t);
     sift();
     if m.t>m.l then
     begin
       inc(t);
       with h[t] do
       begin
         l:=m.l; r:=m.t-;
         s:=m.s;
         t:=ask(l,r);
       end;
       up(t);
     end;
     if m.t<m.r then
     begin
       inc(t);
       with h[t] do
       begin
         l:=m.t+; r:=m.r;
         s:=m.s;
         t:=ask(l,r);
       end;
       up(t);
     end;
   end;
 end.