算法模板——平衡树Treap

实现功能如下——1. 插入x数
2. 删除x数(若有多个相同的数，因只删除一个)
3. 查询x数的排名(若有多个相同的数，因输出最小的排名)
4. 查询排名为x的数
5. 求x的前驱(前驱定义为小于x，且最大的数)
6. 求x的后继(后继定义为大于x，且最小的数)

本程序的实现原理为Treap平衡树

详见BZOJ3224

 var
    i,j,k,l,m,n,head,ts:longint;f1:text;
    a,b,fix,lef,rig:array[..] of longint;
 procedure lt(var x:longint);inline;
           var f,r:longint;
           begin
                if (x=) or (rig[x]=) then exit;
                f:=x;r:=rig[x];
                b[r]:=b[f];
                b[f]:=b[lef[f]]++b[LEF[R]];
                rig[f]:=lef[r];
                lef[r]:=f;
                x:=r;
           end;
 procedure rt(var x:longint);inline;
           var f,l:longint;
           begin
                if (x=) or (lef[x]=) then exit;
                f:=x;l:=lef[x];
                b[l]:=b[f];
                b[f]:=b[rig[f]]++b[rig[l]];
                lef[f]:=rig[l];
                rig[l]:=f;
                x:=l;
           end;
 FUNCTION max(x,y:longint):longint;inline;
          begin
               if x>y then max:=x else max:=y;
          end;
 function min(x,y:longint):longint;inline;
          begin
               if x<y then min:=x else min:=y;
          end;
 procedure ins(var head:longint;x:longint);
           begin
                if head= then
                   begin
                        head:=x;
                        exit;
                   end;
                if a[x]<a[head] then
                   begin
                        ins(lef[head],x);
                        b[head]:=b[lef[head]]+b[rig[head]]+;
                        if fix[lef[head]]<fix[head] then rt(head);
                   end
                else
                    begin
                         ins(rig[head],x);
                         b[head]:=b[lef[head]]+b[rig[head]]+;
                         if fix[rig[head]]<fix[head] then lt(head);
                    end;
           end;
 function getp(head,x:longint):longint;
          begin
               if head= then exit();
               if a[head]=x then exit(head);
               if a[head]>x then exit(getp(lef[head],x)) else exit(getp(rig[head],x));
          end;
 procedure del(var head:longint);
           var i,j,k,l,f,r:longint;
           begin
                if head= then exit;
                if (lef[head]=) then
                   begin
                        b[head]:=b[rig[head]];
                        head:=rig[head];
                        exit;
                   end;
                if rig[head]= then
                   begin
                        b[head]:=b[lef[head]];
                        head:=lef[head];
                        exit;
                   end;
                if fix[lef[head]]>fix[rig[head]] then
                   begin
                        lt(head);
                        del(lef[head]);
                        b[head]:=b[lef[head]]+b[rig[head]]+;
                   end
                else
                    begin
                         rt(head);
                         del(rig[head]);
                         b[head]:=b[lef[head]]+b[rig[head]]+;
                    end;
           end;
 procedure det(var head,x:longint);
           begin
                if head= then exit;
                if x=head then
                   begin
                        del(head);
                        b[head]:=b[lef[head]]+b[rig[head]]+;
                        exit;
                   end;
                if lef[head]=x then
                   begin
                        del(lef[head]);
                        b[head]:=b[lef[head]]+b[rig[head]]+;
                        exit;
                   end;
                if rig[head]=x then
                   begin
                        del(rig[head]);
                        b[head]:=b[lef[head]]+b[rig[head]]+;
                        exit;
                   end;
                if a[x]<a[head] then det(lef[head],x) else det(rig[head],x);
                b[head]:=b[lef[head]]+b[rig[head]]+;
           end;
 procedure showoff(head:longint);
           begin
                if head= then exit;
                showoff(lef[head]);
                write(a[head],' ');
                showoff(rig[head]);
           end;
 function getrank(head,x:longint):longint;
          var k:longint;
          begin
               if head= then exit(-);
               if x=a[head] then   //亲们注意了，就是这个地方坑了我好久啊啊啊啊啊啊
                  begin
                       k:=getrank(lef[head],x);
                       if k=- then exit(b[lef[head]]+) else exit(k);
                  end
               else
                   begin
                        if x<a[head] then
                           begin
                                exit(getrank(lef[head],x));
                           end
                        else
                            begin
                                 k:=getrank(rig[head],x);
                                 if k=- then exit(-) else exit(b[lef[head]]++k);
                            end;
                   end;
          end;
 function rankget(head,x:longint):longint;
          begin
               if head= then exit(maxlongint);
               if (b[lef[head]]+)=x then exit(a[head]);
               if (b[lef[head]]+)<x then exit(rankget(rig[head],x--b[lef[head]])) else exit(rankget(lef[head],x))
          end;
 function getsuc(head,x:longint):longint;
          begin
               if (head=) then exit(+maxlongint);
               if (a[head]<=x) then exit(getsuc(rig[head],x)) else exit(min(a[head],getsuc(lef[head],x)));
          end;
 function getpre(head,x:longint):longint;
          begin
               if (head=) then exit(-maxlongint);
               if (a[head]>=x) then exit(getpre(lef[head],x)) else exit(max(a[head],getpre(rig[head],x)));
          end;

 begin
      m:=;head:=;
      randomize;
      readln(n);
      for i:= to  n do
          begin
               read(l);
               case l of
                    :begin
                           readln(j);
                           inc(m);
                           a[m]:=j;
                           fix[m]:=random(maxlongint);
                           lef[m]:=;rig[m]:=;b[m]:=;
                           ins(head,m);
                    end;
                    :begin
                           readln(j);
                           k:=getp(head,j);
                           det(head,k);
                           l:=;
                    end;
                    :BEGIN
                           readln(j);
                           k:=getrank(head,j);
                           writeln(k);
                    end;
                    :begin
                           readln(j);
                           writeln(rankget(head,j));
                    end;
                    :begin
                           readln(j);
                           writeln(getpre(head,j));
                    end;
                    :begin
                           readln(j);
                           writeln(getsuc(head,j));
                    end;
               end;

               l:=;
          end;
          readln;
 end.