1036: [ZJOI2008]树的统计Count

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

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const
    maxn=30010;
type
    node=record
      son:array[0..1]of longint;
      sum,max,left,right,mid:longint;
    end;
var
    n,m,num,tot,xx,ll,rr,goal:longint;
    tree:array[0..maxn*2]of node;
    first,fa,dep,son,size,w,top,root:array[0..maxn]of longint;
    next,last:array[0..maxn*2]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]:=1;
    i:=first[x];
    while i<>0 do
      begin
        if last[i]<>f then
        begin
          dfs1(last[i],d+1,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)>>1;
        son[0]:=tot+1;
        build(l,mid);
        son[1]:=tot+1;
        build(mid+1,r);
      end;
end;

procedure dfs2(x,t,ww:longint);
var
    i:longint;
begin
    w[x]:=ww;
    top[x]:=t;
    if son[x]=0 then
      begin
        root[x]:=tot+1;
        build(1,ww);
        exit;
      end
    else
      begin
        dfs2(son[x],t,ww+1);
        root[x]:=root[son[x]];
      end;
    i:=first[x];
    while i<>0 do
      begin
        if (last[i]<>fa[x]) and (last[i]<>son[x]) then dfs2(last[i],last[i],1);
        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[0])
        else change(son[1]);
        if tree[son[0]].max>tree[son[1]].max then max:=tree[son[0]].max
        else max:=tree[son[1]].max;
        sum:=tree[son[0]].sum+tree[son[1]].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[0]));
        if ll>mid then exit(getsum(son[1]));
        exit(getsum(son[0])+getsum(son[1]));
      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[0]));
        if ll>mid then exit(getmax(son[1]));
        getmax:=getmax(son[0]);
        s:=getmax(son[1]);
        if s>getmax then getmax:=s;
      end;
end;

procedure init;
var
    i,x,y:longint;
begin
    read(n);
    for i:=1 to n-1 do
      begin
        read(x,y);
        insert(x,y);
        insert(y,x);
      end;
    dfs1(1,1,0);
    dfs2(1,1,1);
    for i:=1 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:=1 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:=-300000;
            while top[x]<>top[y] do
              begin
                if dep[top[x]]<dep[top[y]] then
                begin
                  s:=x;x:=y;y:=s;
                end;
                ll:=1;
                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:=0;
            while top[x]<>top[y] do
              begin
                if dep[top[x]]<dep[top[y]] then
                begin
                  s:=x;x:=y;y:=s;
                end;
                ll:=1;
                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.