1036: [ZJOI2008]树的统计Count

Time Limit: 10 Sec Memory Limit: 162 MB
Submit: 7496 Solved: 3078
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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

HINT

Source

树的分治

题解：phile神犇推荐的链剖模板题，一直不知道为啥挂掉，急死掉= =，最后发现居然把inline去掉就A了QAQ，逗我= =

事实证明——（引用phile神犇的原话）黑科技不可滥用TT

 type

     point=^node;

     node=record

                g:longint;

                next:point;

     end;

 var

    i,j,k,l,m,n,tot,root:longint;a1:int64;

    a:array[..] of point;ch:char;

    d,e:array[..] of int64;

    len,son,siz,top,list,f,num,anum:array[..] of longint;

    c:array[..,..] of longint;

 function min(x,y:longint):longint;

          begin

               if x<y then min:=x else min:=y;

          end;

 function max(x,y:longint):longint;

          begin

               if x>y then max:=x else max:=y;

          end;

 procedure swap(var x,y:longint);

           var z:longint;

           begin

                z:=x;x:=y;y:=z;

           end;

 procedure add(x,y:longint);

           var p:point;

           begin

                new(p);p^.g:=y;p^.next:=a[x];a[x]:=p;

           end;

 procedure dfs(y,x:longint);

           var p:point;

           begin

                c[,x]:=y;siz[x]:=;len[x]:=len[y]+;son[x]:=;

                p:=a[x];

                while p<>nil do

                      begin

                           if p^.g<>y then

                              begin

                                   dfs(x,p^.g);

                                   inc(siz[x],siz[p^.g]);

                                   if (son[x]=) or (siz[p^.g]>siz[son[x]]) then son[x]:=p^.g;

                              end;

                           p:=p^.next;

                      end;

           end;

 procedure dfs2(y,x,z:longint);

           var p:point;

           begin

                top[x]:=z;inc(tot);num[x]:=tot;anum[tot]:=x;

                if son[x]<> then dfs2(x,son[x],z);p:=a[x];

                while p<>nil do

                      begin

                           if (p^.g<>y) and (p^.g<>son[x]) then dfs2(x,p^.g,p^.g);

                           p:=p^.next;

                      end;

           end;

 procedure built(z,x,y:longint);

           begin

                if x=y then

                   begin

                        list[x]:=z;

                        d[z]:=f[anum[x]];

                        e[z]:=d[z];

                   end

                else

                    begin

                         built(z*,x ,(x+y) div );

                         built(z*+,(x+y) div +,y);

                         d[z]:=d[z*]+d[z*+];

                         if e[z*+]>e[z*] then e[z]:=e[z*+] else e[z]:=e[z*];

                    end;

           end;

 procedure change(x:longint;y:int64);

          begin

               x:=list[x];d[x]:=y;e[x]:=y;x:=x div ;

               while x> do

                     begin

                          d[x]:=d[x*]+d[x*+];

                          if e[x*+]>e[x*] then e[x]:=e[x*+] else e[x]:=e[x*];

                          x:=x div ;

                     end;

          end;

 function sum(z,x,y,l,r:longint):int64;

          begin

               if l>r then exit();

               if (x=l) and (y=r) then exit(d[z]);

               exit(sum(z*,x,(x+y) div ,l,min(r,(x+y) div ))+sum(z*+,(x+y) div +,y,max((x+y) div +,l),r));

          end;

 function getmax(z,x,y,l,r:longint):int64;

          var a1,a2:int64;

          begin

               if l>r then exit(-maxlongint*maxlongint);

               if (x=l) and (y=r) then exit(e[z]);

               a1:=getmax(z*,x,(x+y) div ,l,min(r,(x+y) div ));

               a2:=getmax(z*+,(x+y) div +,y,max((x+y) div +,l),r);

               if a1>a2 then exit(a1) else exit(a2);

          end;

 function getup(x,y:longint):longint;

          var i:longint;

          begin

               i:=;

               while y> do

                     begin

                          if odd(y) then x:=c[i,x];

                          inc(i);y:=y div ;

                     end;

               exit(x);

          end;

 function getcom(x,y:longint):longint;

          var i:longint;

          begin

               if len[x]<len[y] then swap(x,y);

               x:=getup(x,len[x]-len[y]);

               if x=y then exit(x);

               for i:=trunc(round(ln(len[x])/ln())) downto  do

                   if c[i,x]<>c[i,y] then

                      begin

                           x:=c[i,x];

                           y:=c[i,y];

                      end;

               exit(c[,x]);

          end;

 procedure treechange(x:longint;y:int64);

           begin

                change(num[x],y);

           end;

 function treesum(x,y:longint):int64;

           var i,z:longint;

           begin

                z:=getcom(x,y);treesum:=;

                repeat

                      if len[top[x]]<len[z] then i:=z else i:=top[x];

                      inc(treesum,sum(,,n,num[i],num[x]));

                      if i=z then break;

                      x:=c[,i];

                until false;

                repeat

                      if len[top[y]]<len[z] then i:=z else i:=top[y];

                      inc(treesum,sum(,,n,num[i],num[y]));

                      if i=z then break;

                      y:=c[,i];

                until false;

                dec(treesum,sum(,,n,num[z],num[z]));

           end;

 function treemax(x,y:longint):int64;

          var i,z:longint;a1:int64;

          begin

               treemax:=-maxlongint*maxlongint;

               z:=getcom(x,y);

               repeat

                     if len[top[x]]<len[z] then i:=z else i:=top[x];

                     a1:=getmax(,,n,num[i],num[x]);

                     if a1>treemax then treemax:=a1;

                     if i=z then break;

                     x:=c[,i];

               until false;

               repeat

                     if len[top[y]]<len[z] then i:=z else i:=top[y];

                     a1:=getmax(,,n,num[i],num[y]);

                     if a1>treemax then treemax:=a1;

                     if i=z then break;

                     y:=c[,i];

               until false;

          end;

 begin

      readln(n);

      for i:= to n do a[i]:=nil;

      for i:= to n- do

          begin

               readln(j,k);

               add(j,k);add(k,j);

          end;

      for i:= to n do read(f[i]);readln;

      root:=random(n)+;dfs(,root);dfs2(,root,root);

      for i:= to trunc(round(ln(n)/ln()))+ do

          for j:= to n do

              c[i,j]:=c[i-,c[i-,j]];

      built(,,n);

      readln(m);

      for i:= to m do

          begin

               read(ch,ch);

               case upcase(ch) of

                    'M':begin

                             readln(ch,ch,j,k);

                             writeln(treemax(j,k));

                    end;

                    'S':begin

                             readln(ch,ch,j,k);

                             writeln(treesum(j,k));

                    end;

                    'H':begin

                             readln(ch,ch,ch,ch,j,a1);

                             treechange(j,a1);

                    end;

               end;

          end;

      readln;

 end.