bzoj4127

肯定是树链剖分+线段树，关键是怎么维护

绝对值和这个东西显然不能简单的合并标记

因为对于负数，加之后绝对值和是变小的

那我们考虑对负数和非负数数分别维护

下面的问题就是经过操作如果负数变成了正数怎么办

注意每次加的都是正数，这意味着这样的变化最多发生n次，

每个数发生这种变化，我们就用push到底即可，这样最多nlogn的

所以我们只要在维护一个区间最大负数即可

 const inf=;
 type node=record
        po,next:longint;
      end;
      link=record
        s0,s1,mx:int64;
        s:longint;
      end;

 var tree:array[..*] of link;
     lazy:array[..*] of int64;
     e:array[..*] of node;
     top,fa,a,b,c,d,p,s:array[..] of longint;
     t,i,x,y,ch,z,len,n,m:longint;

 function max(a,b:int64):int64;
   begin
     if a>b then exit(a) else exit(b);
   end;

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

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

 procedure dfs1(x:longint);
   var i,y:longint;
   begin
     i:=p[x];
     s[x]:=;
     while i<> do
     begin
       y:=e[i].po;
       if s[y]= then
       begin
         fa[y]:=x;
         d[y]:=d[x]+;
         dfs1(y);
         s[x]:=s[x]+s[y];
       end;
       i:=e[i].next;
     end;
   end;

 procedure dfs2(x:longint);
   var q,i,y:longint;
   begin
     inc(t);
     c[x]:=t;
     b[t]:=x;
     i:=p[x];
     q:=;
     while i<> do
     begin
       y:=e[i].po;
       if c[y]= then
         if s[y]>s[q] then q:=y;
       i:=e[i].next;
     end;
     if q<> then
     begin
       top[q]:=top[x];
       dfs2(q);
     end;
     i:=p[x];
     while i<> do
     begin
       y:=e[i].po;
       if c[y]= then
       begin
         top[y]:=y;
         dfs2(y);
       end;
       i:=e[i].next;
     end;
   end;

 procedure update(i:longint);
   begin
     tree[i].s0:=tree[i*].s0+tree[i*+].s0;
     tree[i].s1:=tree[i*].s1+tree[i*+].s1;
     tree[i].s:=tree[i*].s+tree[i*+].s;
     tree[i].mx:=max(tree[i*].mx,tree[i*+].mx);
   end;

 procedure build(i,l,r:longint);
   var m:longint;
   begin
     if l=r then
     begin
       if a[b[l]]>= then
       begin
         tree[i].s0:=a[b[l]];
         tree[i].s:=;
         tree[i].mx:=-inf;
       end
       else begin
         tree[i].s1:=a[b[l]];
         tree[i].mx:=a[b[l]];
       end;
     end
     else begin
       m:=(l+r) shr ;
       build(i*,l,m);
       build(i*+,m+,r);
       update(i);
     end;
   end;

 procedure modi(i,len:longint; z:int64);
   begin
     inc(lazy[i],z);
     inc(tree[i].mx,z);
     inc(tree[i].s0,int64(tree[i].s)*z);
     inc(tree[i].s1,int64(len-tree[i].s)*z);
   end;

 procedure push(i,l,r:longint);
   var m:longint;
   begin
     m:=(l+r) shr ;
     modi(i*,m-l+,lazy[i]);
     modi(i*+,r-m,lazy[i]);
     lazy[i]:=;
   end;

 procedure down(i,l,r:longint);
   var m:longint;
   begin
     if l=r then
     begin
       tree[i].s0:=tree[i].mx;
       tree[i].s:=;
       tree[i].mx:=-inf;
       tree[i].s1:=;
     end
     else begin
       m:=(l+r) shr ;
       if lazy[i]<> then push(i,l,r);
       if tree[i*].mx>= then down(i*,l,m);
       if tree[i*+].mx>= then down(i*+,m+,r);
       update(i);
     end;
   end;

 procedure ins(i,l,r,x,y:longint);
   var m:longint;
   begin
     if (x<=l) and (y>=r) then
     begin
       if tree[i].mx+z>= then
       begin
         inc(lazy[i],z);
         inc(tree[i].mx,z);
         down(i,l,r);
       end
       else modi(i,r-l+,z);
     end
     else begin
       if lazy[i]<> then push(i,l,r);
       m:=(l+r) shr ;
       if x<=m then ins(i*,l,m,x,y);
       if y>m then ins(i*+,m+,r,x,y);
       update(i);
     end;
   end;

 function get(i,l,r,x,y:longint):int64;
   var m:longint;
       s:int64;

   begin
     if (x<=l) and (y>=r) then exit(tree[i].s0+abs(tree[i].s1))
     else begin
       if lazy[i]<> then push(i,l,r);
       m:=(l+r) shr ;
       s:=;
       if x<=m then s:=s+get(i*,l,m,x,y);
       if y>m then s:=s+get(i*+,m+,r,x,y);
       exit(s);
     end;
   end;

 procedure work(x,y:longint);
   var f1,f2:longint;
   begin
     f1:=top[x];
     f2:=top[y];
     while f1<>f2 do
     begin
       if d[f1]>=d[f2] then
       begin
         ins(,,n,c[f1],c[x]);
         x:=fa[f1];
         f1:=top[x];
       end
       else begin
         ins(,,n,c[f2],c[y]);
         y:=fa[f2];
         f2:=top[y];
       end;
     end;
     if c[x]>c[y] then swap(x,y);
     ins(,,n,c[x],c[y]);
   end;

 function ask(x,y:longint):int64;
   var f1,f2:longint;
   begin
     ask:=;
     f1:=top[x];
     f2:=top[y];
     while f1<>f2 do
     begin
       if d[f1]>=d[f2] then
       begin
         ask:=ask+get(,,n,c[f1],c[x]);
         x:=fa[f1];
         f1:=top[x];
       end
       else begin
         ask:=ask+get(,,n,c[f2],c[y]);
         y:=fa[f2];
         f2:=top[y];
       end;
     end;
     if c[x]>c[y] then swap(x,y);
     ask:=ask+get(,,n,c[x],c[y]);
   end;

 begin
   readln(n,m);
   for i:= to n do
     read(a[i]);
   for i:= to n- do
   begin
     readln(x,y);
     add(x,y);
     add(y,x);
   end;
   dfs1();
   top[]:=;
   dfs2();
   build(,,n);
   for i:= to m do
   begin
     read(ch,x,y);
     if ch= then
     begin
       readln(z);
       work(x,y);
     end
     else begin
       readln;
       writeln(ask(x,y));
     end;
   end;
 end.