bzoj2209 2329

括号序列的经典做法
把(看成1，）看成-1
匹配的括号序列即任意前缀和都非负
我们先解决静态的问题，给定一段括号序列求最少修改次数
我们先找出最大后缀和a和最小前缀和b
之间一定可以不相交
显然a+|b|个括号是未匹配的
显然修改即为(|b|+1) div 2+(a+1) div 2;
由于序列的变化，我们用splay维护
由于涉及到括号反转我们还要维护左最大和右最小
然后就没了
这个是bzoj2329的代码

 var son:array[..,..] of longint;
     laz,lmax,rmax,lmin,rmin,size,sum,a,fa:array[..] of longint;
     cha,rev:array[..] of boolean;
     root,i,n,m,x,y,z,w:longint;
     ch:char;
     s:string;

 function min(a,b:longint):longint;
   begin
     if a>b then exit(b) else exit(a);
   end;

 function max(a,b:longint):longint;
   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 get(var a,b:longint);
   var c:longint;
   begin
     c:=a;
     a:=-b;
     b:=-c;
   end;

 procedure update(x:longint);
   var l,r:longint;
   begin
     l:=son[x,];
     r:=son[x,];
     size[x]:=size[l]+size[r]+;
     sum[x]:=sum[l]+sum[r]+a[x];
     lmax[x]:=max(lmax[l],sum[l]+a[x]+lmax[r]);
     rmax[x]:=max(rmax[r],sum[r]+a[x]+rmax[l]);
     lmin[x]:=min(lmin[l],sum[l]+a[x]+lmin[r]);
     rmin[x]:=min(rmin[r],sum[r]+a[x]+rmin[l]);
   end;

 procedure replace(x,w:longint);
   begin
     a[x]:=w;
     laz[x]:=w;
     cha[x]:=false;
     if w=- then
     begin
       sum[x]:=-size[x];
       lmax[x]:=;
       rmax[x]:=;
       lmin[x]:=sum[x];
       rmin[x]:=sum[x];
     end
     else begin
       sum[x]:=size[x];
       lmax[x]:=sum[x];
       rmax[x]:=sum[x];
       lmin[x]:=;
       rmin[x]:=;
     end;
   end;

 procedure reverse(x:longint);
   begin
     swap(son[x,],son[x,]);
     swap(lmax[x],rmax[x]);
     swap(lmin[x],rmin[x]);
     rev[x]:=not rev[x];
   end;

 procedure change(x:longint);
   begin
     a[x]:=-a[x];
     sum[x]:=-sum[x];
     get(lmax[x],lmin[x]);
     get(rmax[x],rmin[x]);
     cha[x]:=not cha[x];
   end;

 procedure push(x:longint);
   var l,r:longint;
   begin
     l:=son[x,];
     r:=son[x,];
     if laz[x]<> then
     begin
       if l<>- then replace(l,laz[x]);
       if r<>- then replace(r,laz[x]);
       laz[x]:=;
     end;
     if cha[x] then
     begin
       if l<>- then change(l);
       if r<>- then change(r);
       cha[x]:=false;
     end;
     if rev[x] then
     begin
       if l<>- then reverse(l);
       if r<>- then reverse(r);
       rev[x]:=false;
     end;
   end;

 function find(k:longint):longint;
   var p:longint;
   begin
     p:=root;
     while true do
     begin
       push(p);
       if size[son[p,]]+=k then exit(p);
       if size[son[p,]]+>k then p:=son[p,]
       else begin
         k:=k-size[son[p,]]-;
         p:=son[p,];
       end;
     end;
   end;

 procedure rotate(x,w:longint);
   var y:longint;
   begin
     y:=fa[x];
     push(x);
     if fa[y]=- then root:=x
     else begin
       if son[fa[y],]=y then son[fa[y],]:=x
       else son[fa[y],]:=x;
     end;
     fa[x]:=fa[y];
     son[y,-w]:=son[x,w];
     if son[x,w]<>- then fa[son[x,w]]:=y;
     son[x,w]:=y;
     fa[y]:=x;
     update(y);
   end;

 procedure splay(x,f:longint);
   var y:longint;
   begin
     while fa[x]<>f do
     begin
       y:=fa[x];
       if fa[y]=f then
       begin
         if son[y,]=x then rotate(x,)
         else rotate(x,);
       end
       else begin
         if son[fa[y],]=y then
         begin
           if son[y,]=x then rotate(y,) else rotate(x,);
           rotate(x,);
         end
         else begin
           if son[y,]=x then rotate(x,) else rotate(y,);
           rotate(x,);
         end;
       end;
     end;
     update(x);
   end;

 function getrange(x,y:longint):longint;
   begin
     x:=find(x);
     y:=find(y+);
     splay(x,-);
     splay(y,x);
     exit(son[y,]);
   end;

 function build(l,r:longint):longint;
   var m:longint;
   begin
     m:=(l+r) shr ;
     build:=m;
     if l<=m- then
     begin
       son[m,]:=build(l,m-);
       fa[son[m,]]:=m;
     end;
     if m+<=r then
     begin
       son[m,]:=build(m+,r);
       fa[son[m,]]:=m;
     end;
     update(m);
   end;

 begin
   fillchar(fa,sizeof(fa),);
   fillchar(son,sizeof(son),);
   readln(n,m);
   for i:= to n do
   begin
     read(ch);
     if ch='(' then a[i]:= else a[i]:=-;
   end;
   readln;
   root:=build(,n+);
   for i:= to m do
   begin
     read(ch);
     s:='';
     while ch<>' ' do
     begin
       s:=s+ch;
       read(ch);
     end;
     read(x,y);
     z:=getrange(x,y);
     if s='Query' then
       writeln((abs(lmin[z])+) div +(rmax[z]+) div )
     else if s='Invert' then
     begin
       if laz[z]= then change(z)
       else replace(z,-laz[z]);
     end
     else if s='Swap' then
       reverse(z)
     else if s='Replace' then
     begin
       read(ch);
       while not((ch='(') or (ch=')')) do read(ch);
       if ch='(' then w:=
       else w:=-;
       replace(z,w);
     end;
     readln;
   end;
 end.