1036: [ZJOI2008]树的统计Count - BZOJ

Description

一棵树上有n个节点，编号分别为1到n，每个节点都有一个权值w。我们将以下面的形式来要求你对这棵树完成一些操作： I. CHANGE u t : 把结点u的权值改为t II. QMAX u v: 询问从点u到点v的路径上的节点的最大权值 III. QSUM u v: 询问从点u到点v的路径上的节点的权值和 注意：从点u到点v的路径上的节点包括u和v本身
Input

输入的第一行为一个整数n，表示节点的个数。接下来n – 1行，每行2个整数a和b，表示节点a和节点b之间有一条边相连。接下来n行，每行一个整数，第i行的整数wi表示节点i的权值。接下来1行，为一个整数q，表示操作的总数。接下来q行，每行一个操作，以“CHANGE u t”或者“QMAX u v”或者“QSUM u v”的形式给出。 对于100％的数据，保证1<=n<=30000，0<=q<=200000；中途操作中保证每个节点的权值w在-30000到30000之间。
Output

对于每个“QMAX”或者“QSUM”的操作，每行输出一个整数表示要求输出的结果。
Sample Input
4
1 2
2 3
4 1
4 2 1 3
12
QMAX 3 4
QMAX 3 3
QMAX 3 2
QMAX 2 3
QSUM 3 4
QSUM 2 1
CHANGE 1 5
QMAX 3 4
CHANGE 3 6
QMAX 3 4
QMAX 2 4
QSUM 3 4
Sample Output
4
1
2
2
10
6
5
6
5
16

裸树链剖分，我就不多说了，附入门教程

 const
     maxn=;
 type
     node=record
       son:array[..]of longint;
       sum,max,left,right,mid:longint;
     end;
 var
     n,m,num,tot,xx,ll,rr,goal:longint;
     tree:array[..maxn*]of node;
     first,fa,dep,son,size,w,top,root:array[..maxn]of longint;
     next,last:array[..maxn*]of longint;

 procedure insert(x,y:longint);
 begin
     inc(num);
     last[num]:=y;
     next[num]:=first[x];
     first[x]:=num;
 end;

 procedure dfs1(x,d,f:longint);
 var
     i:longint;
 begin
     dep[x]:=d;
     fa[x]:=f;
     size[x]:=;
     i:=first[x];
     while i<> do
       begin
         if last[i]<>f then
         begin
           dfs1(last[i],d+,x);
           if size[last[i]]>size[son[x]] then son[x]:=last[i];
           inc(size[x],size[last[i]]);
         end;
         i:=next[i];
       end;
 end;

 procedure build(l,r:longint);
 var
     now:longint;
 begin
     inc(tot);
     now:=tot;
     with tree[now] do
       begin
         left:=l;
         right:=r;
         if l=r then exit;
         mid:=(l+r)>>;
         son[]:=tot+;
         build(l,mid);
         son[]:=tot+;
         build(mid+,r);
       end;
 end;

 procedure dfs2(x,t,ww:longint);
 var
     i:longint;
 begin
     w[x]:=ww;
     top[x]:=t;
     if son[x]= then
       begin
         root[x]:=tot+;
         build(,ww);
         exit;
       end
     else
       begin
         dfs2(son[x],t,ww+);
         root[x]:=root[son[x]];
       end;
     i:=first[x];
     while i<> do
       begin
         if (last[i]<>fa[x]) and (last[i]<>son[x]) then dfs2(last[i],last[i],);
         i:=next[i];
       end;
 end;

 procedure change(now:longint);
 begin
     with tree[now] do
       begin
         if left=right then
         begin
           sum:=goal;
           max:=goal;
           exit;
         end;
         if xx<=mid then change(son[])
         else change(son[]);
         if tree[son[]].max>tree[son[]].max then max:=tree[son[]].max
         else max:=tree[son[]].max;
         sum:=tree[son[]].sum+tree[son[]].sum;
       end;
 end;

 function getsum(now:longint):longint;
 begin
     with tree[now] do
       begin
         if (ll<=left) and (rr>=right) then exit(sum);
         if rr<=mid then exit(getsum(son[]));
         if ll>mid then exit(getsum(son[]));
         exit(getsum(son[])+getsum(son[]));
       end;
 end;

 function getmax(now:longint):longint;
 var
     s:longint;
 begin
     with tree[now] do
       begin
         if (ll<=left) and (rr>=right) then exit(max);
         if rr<=mid then exit(getmax(son[]));
         if ll>mid then exit(getmax(son[]));
         getmax:=getmax(son[]);
         s:=getmax(son[]);
         if s>getmax then getmax:=s;
       end;
 end;

 procedure init;
 var
     i,x,y:longint;
 begin
     read(n);
     for i:= to n- do
       begin
         read(x,y);
         insert(x,y);
         insert(y,x);
       end;
     dfs1(,,);
     dfs2(,,);
     for i:= to n do
       begin
         read(goal);
         xx:=w[i];
         change(root[i]);
       end;
 end;

 procedure work;
 var
     i,ans,s,x,y:longint;
     s1,s2:char;
 begin
     read(m);
     for i:= to m do
       begin
         read(s2);
         while s2<>' ' do
           begin
             s1:=s2;
             read(s2);
           end;
         read(x,y);
         case s1 of
           'E':begin
             goal:=y;
             xx:=w[x];
             change(root[x]);
           end;
           'X':begin
             ans:=-;
             while top[x]<>top[y] do
               begin
                 if dep[top[x]]<dep[top[y]] then
                 begin
                   s:=x;x:=y;y:=s;
                 end;
                 ll:=;
                 rr:=w[x];
                 s:=getmax(root[x]);
                 if s>ans then ans:=s;
                 x:=fa[top[x]];
               end;
             if dep[x]<dep[y] then
             begin
               s:=x;x:=y;y:=s;
             end;
             ll:=w[y];
             rr:=w[x];
             s:=getmax(root[x]);
             if s>ans then ans:=s;
             writeln(ans);
           end;
           'M':begin
             ans:=;
             while top[x]<>top[y] do
               begin
                 if dep[top[x]]<dep[top[y]] then
                 begin
                   s:=x;x:=y;y:=s;
                 end;
                 ll:=;
                 rr:=w[x];
                 inc(ans,getsum(root[x]));
                 x:=fa[top[x]];
               end;
             if dep[x]<dep[y] then
             begin
               s:=x;x:=y;y:=s;
             end;
             ll:=w[y];
             rr:=w[x];
             inc(ans,getsum(root[x]));
             writeln(ans);
           end;
         end;
       end;
 end;

 begin
     init;
     work;
 end.