【POJ3237】Tree（树链剖分）

题意：在一棵N个节点，有边权的树上维护以下操作：

1：单边修改，将第X条边的边权修改成Y

2：区间取反，将点X与Y在树上路径中的所有边边权取反

3：区间询问最大值，询问X到Y树上路径中边权最大值

n<=10000 CAS<=20

思路：做了2天，改出来的一刻全身都萎掉了

边权转点权，点权就是它到父亲的边的边权，加一些反向标记

取反的标记TAG下传时不能直接赋值为-1，而是将原先的标记取反

多组数据时倍增数组，深度也需要清零

树链剖分不能取第一条边，需要+1

 const oo=;
 var t:array[..]of record
                           min,max,tag:longint;
                          end;
     f:array[..,..]of longint;
     head,vet,next,dep,tid,id,flag,
     len,son,size,top,a,b,c,d,g,h:array[..]of longint;
     n,m,i,tot,x,y,k,v,cas,time,z,s,tmp,fuhao:longint;
     ch:string;

 function min(x,y:longint):longint;
 begin
  if x<y then exit(x);
  exit(y);
 end;

 function max(x,y:longint):longint;
 begin
  if x>y then exit(x);
  exit(y);
 end;

 procedure add(a,b,c:longint);
 begin
  inc(tot);
  next[tot]:=head[a];
  vet[tot]:=b;
  len[tot]:=c;
  head[a]:=tot;
 end;

 procedure dfs(u:longint);
 var e,v,i,t:longint;
 begin
  for i:= to  do
  begin
   if dep[u]<(<<i) then break;
   f[u,i]:=f[f[u,i-],i-];
  end;
  e:=head[u]; flag[u]:=; size[u]:=; son[u]:=; t:=;
  while e<> do
  begin
   v:=vet[e];
   if flag[v]= then
   begin
    dep[v]:=dep[u]+;
    f[v,]:=u;
    dfs(v);
    size[u]:=size[u]+size[v];
    if size[v]>t then
    begin
     t:=size[v]; son[u]:=v;
    end;
   end;
   e:=next[e];
  end;
 end;

 procedure swap(var x,y:longint);
 var t:longint;
 begin
  t:=x; x:=y; y:=t;
 end;

 function lca(x,y:longint):longint;
 var i,d:longint;
 begin
  if dep[x]<dep[y] then swap(x,y);
  d:=dep[x]-dep[y];
  for i:= to  do
   if d and (<<i)> then x:=f[x,i];
  for i:= downto  do
   if f[x,i]<>f[y,i] then
   begin
    x:=f[x,i]; y:=f[y,i];
   end;
  if x=y then exit(x);
  exit(f[x,]);
 end;

 procedure pushdown(l,r,p:longint);
 var mid,tmp,t1,t2:longint;
 begin
  tmp:=t[p].tag;
  if (l=r)or(tmp=) then exit;
  t[p].tag:=;
  t1:=t[p<<].min; t2:=t[p<<].max;
  t[p<<].max:=-t1; t[p<<].min:=-t2;
  t1:=t[p<<+].min; t2:=t[p<<+].max;
  t[p<<+].max:=-t1; t[p<<+].min:=-t2;
  t[p<<].tag:=--t[p<<].tag; t[p<<+].tag:=--t[p<<+].tag;

 end;

 procedure pushup(p:longint);
 begin
  t[p].min:=min(t[p<<].min,t[p<<+].min);
  t[p].max:=max(t[p<<].max,t[p<<+].max);
 end;

 procedure change(l,r,x,v,p:longint);
 var mid:longint;
 begin
  pushdown(l,r,p);
  if (l=x)and(r=x) then
  begin
   t[p].min:=v; t[p].max:=v;
  // t[p].tag:=v;
   exit;
  end;
  mid:=(l+r)>>;
  if x<=mid then change(l,mid,x,v,p<<)
   else change(mid+,r,x,v,p<<+);
  pushup(p);
 end;

 procedure dfs2(u,ance:longint);
 var e,v:longint;
 begin
  flag[u]:=; inc(time); tid[u]:=time; id[time]:=u; top[u]:=ance;
  if son[u]> then dfs2(son[u],ance);
  e:=head[u];
  while e<> do
  begin
   v:=vet[e];
   if flag[v]= then dfs2(v,v);
   e:=next[e];
  end;
 end;

 procedure build(l,r,p:longint);
 var mid:longint;
 begin
  if l=r then
  begin
   if h[id[l]]>oo then
   begin
    t[p].min:=oo; t[p].max:=-oo;
   end
    else begin t[p].min:=h[id[l]]; t[p].max:=h[id[l]]; end;
   t[p].tag:=;
   exit;
  end;
  mid:=(l+r)>>;
  build(l,mid,p<<);
  build(mid+,r,p<<+);
  pushup(p);
 end;

 function query(l,r,x,y,p:longint):longint;
 var mid,t1,t2:longint;
 begin
  pushdown(l,r,p);
  if (l>=x)and(r<=y) then exit(t[p].max);
  mid:=(l+r)>>; query:=-oo;
  if x<=mid then query:=max(query,query(l,mid,x,y,p<<));
  if y>mid then query:=max(query,query(mid+,r,x,y,p<<+));
  pushup(p);
 end;

 procedure negate(l,r,x,y,p:longint);
 var mid,t1,t2:longint;
 begin
  pushdown(l,r,p);
  if (l>=x)and(r<=y) then
  begin
   t1:=t[p].min; t2:=t[p].max;
   t[p].min:=-t2; t[p].max:=-t1;
   t[p].tag:=-;
   exit;
  end;
  mid:=(l+r)>>;
  if x<=mid then negate(l,mid,x,y,p<<);
  if y>mid then negate(mid+,r,x,y,p<<+);
  pushup(p);
 end;

 procedure ngt(x,y:longint);
 var q:longint;
 begin
  q:=lca(x,y);
  while top[x]<>top[q] do
  begin
   negate(,n,tid[top[x]],tid[x],);
   x:=f[top[x],];
  end;
  if tid[q]+<=tid[x] then negate(,n,tid[q]+,tid[x],);
  while top[y]<>top[q] do
  begin
   negate(,n,tid[top[y]],tid[y],);
   y:=f[top[y],];
  end;
  if tid[q]+<=tid[y] then negate(,n,tid[q]+,tid[y],);
 end;

 function ask(x,y:longint):longint;
 var q:longint;
 begin
  q:=lca(x,y);
  ask:=-oo;
  while top[x]<>top[q] do
  begin
   ask:=max(ask,query(,n,tid[top[x]],tid[x],));
   x:=f[top[x],];
  end;
  if tid[q]+<=tid[x] then ask:=max(ask,query(,n,tid[q]+,tid[x],));
  while top[y]<>top[q] do
  begin
   ask:=max(ask,query(,n,tid[top[y]],tid[y],));
   y:=f[top[y],];
  end;
  if tid[q]+<=tid[y] then ask:=max(ask,query(,n,tid[q]+,tid[y],));
 end;

 begin
  assign(input,'tree.in'); reset(input);
  assign(output,'poj3237.out'); rewrite(output);
  readln(cas);
  for v:= to cas do
  begin
   readln(n);
   fillchar(head,sizeof(head),); tot:=; time:=;
   fillchar(flag,sizeof(flag),);
   fillchar(d,sizeof(d),); fillchar(g,sizeof(g),);
   fillchar(h,sizeof(h),$7f); fillchar(dep,sizeof(dep),);
   fillchar(f,sizeof(f),); fillchar(tid,sizeof(tid),);
   fillchar(id,sizeof(id),);
   for i:= to n<< do
   begin
    t[i].min:=oo; t[i].max:=-oo; t[i].tag:=;
   end;
   for i:= to n- do
   begin
    readln(a[i],b[i],c[i]);
    add(a[i],b[i],c[i]);
    add(b[i],a[i],c[i]);
   end;

   dfs();
   fillchar(flag,sizeof(flag),);
   dfs2(,);
   for i:= to n- do
   begin
    if dep[a[i]]<dep[b[i]] then tmp:=b[i]
     else tmp:=a[i];
    d[i]:=tmp; g[tmp]:=i; h[tmp]:=c[i];
   end;
  // h[]:=; d[n]:=; g[]:=n;
   build(,n,);
   while true do
   begin
    readln(ch); x:=; y:=; k:=length(ch);
    if ch[]='D' then break; s:=; fuhao:=;
    for i:= to k do
    begin
     if ch[i]=' ' then begin inc(s); continue; end;
     if (s=)and(ch[i]<>' ') then x:=x*+ord(ch[i])-ord('');
     if (s=)and(ch[i]<>' ') then
     begin
      if ch[i]='-' then begin fuhao:=-; continue; end
       else y:=y*+ord(ch[i])-ord('');
     end;
    end;
    if ch[]='C' then change(,n,tid[d[x]],fuhao*y,);
    if ch[]='N' then ngt(x,y);
    if ch[]='Q' then
    begin
     writeln(ask(x,y));
     //writeln;
    end;
   end;
  end;
  close(input);
  close(output);
 end.