[BZOJ3224] Tyvj 1728 普通平衡树

传送门

http://www.lydsy.com/JudgeOnline/problem.php?id=3224

题目大意

支持以下操作

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)

题解

平衡树模板题

const
maxn=100005;
var
w:array[-1..maxn,1..6]of longint;
i,j,k:longint;
n,sum,root,a,b:longint;
procedure print(a:longint);
var i:longint;
begin
if w[a,1]<>-1 then print(w[a,1]);
for i:=1 to w[a,5] do write(w[a,6],' ');
if w[a,2]<>-1 then print(w[a,2]);
if a=root then writeln;
end;

procedure rotate(a,kind:longint);
var b,unkind:longint;
begin
b:=w[a,3]; unkind:=kind xor 3;
w[a,4]:=w[b,4]; dec(w[b,4],w[a,5]+w[w[a,kind],4]);
w[b,kind]:=w[a,unkind];
w[w[a,unkind],3]:=b;
w[a,unkind]:=b;
w[a,3]:=w[b,3];
w[b,3]:=a;
if w[a,3]<>-1
then
if w[w[a,3],1]=b
then w[w[a,3],1]:=a
else w[w[a,3],2]:=a;
end;

procedure splay(a,goal:longint);
var b,kind,unkind:longint;
begin
while w[a,3]<>goal do
begin
b:=w[a,3];
if w[b,1]=a then kind:=1 else kind:=2; unkind:=kind xor 3;
if w[b,3]=goal then rotate(a,kind)
else
if w[w[b,3],kind]=b
then begin rotate(b,kind); rotate(a,kind); end
else begin rotate(a,kind); rotate(a,unkind); end;
end;
if goal=-1 then root:=a;
end;

procedure init(a:longint);
var tt,fa,kind:longint;
begin
tt:=root;
while tt<>-1 do
begin
inc(w[tt,4]);
if w[tt,6]=a then break;
fa:=tt;
if a<w[tt,6]
then begin kind:=1; tt:=w[tt,1]; end
else begin kind:=2; tt:=w[tt,2]; end;
end;
if w[tt,6]=a
then inc(w[tt,5])
else begin inc(sum); w[sum,1]:=-1; w[sum,2]:=-1; w[sum,3]:=fa; w[sum,4]:=1; w[sum,5]:=1; w[sum,6]:=a; w[fa,kind]:=sum; tt:=sum; end;
splay(tt,-1);
end;

function getmax(a:longint):longint;
var tt:longint;
begin
tt:=a;
while w[tt,2]<>-1 do
tt:=w[tt,2];
exit(tt);
end;

function getmin(a:longint):longint;
var tt:longint;
begin
tt:=a;
while w[tt,1]<>-1 do
tt:=w[tt,1];
exit(tt);
end;

procedure del(a:longint);
var tt:longint;
begin
tt:=root;
while w[tt,6]<>a do
if a<w[tt,6]
then tt:=w[tt,1]
else tt:=w[tt,2];
splay(tt,-1);
if w[root,5]=1
then
begin
splay(getmax(w[root,1]),root);
w[w[root,1],2]:=w[root,2]; w[w[root,1],4]:=w[root,4]-1; root:=w[root,1]; w[w[root,2],3]:=root; w[root,3]:=-1;
end
else
begin dec(w[root,5]); dec(w[root,4]); end;
end;

function getrank(a:longint):longint;
var tt:longint;
begin
tt:=root;
while w[tt,6]<>a do
if a<w[tt,6]
then tt:=w[tt,1]
else tt:=w[tt,2];
splay(tt,-1);
exit(w[w[tt,1],4]);
end;

function getkth(a:longint):longint;
var tt:longint;
begin
tt:=root;
while (a<=w[w[tt,1],4])or(a>w[w[tt,1],4]+w[tt,5]) do
if a<=w[w[tt,1],4]
then tt:=w[tt,1]
else begin dec(a,w[w[tt,1],4]+w[tt,5]); tt:=w[tt,2]; end;
exit(w[tt,6]);
end;

begin
readln(n); sum:=2; root:=2;
w[1,1]:=-1; w[1,2]:=-1; w[1,3]:=2; w[1,4]:=1; w[1,5]:=1; w[1,6]:=-1000000005;
w[2,1]:=1; w[2,2]:=-1; w[2,3]:=-1; w[2,4]:=2; w[2,5]:=1; w[2,6]:=1000000005;
for i:=1 to n do
begin
readln(a,b);
case a of
1:begin init(b); end;
2:begin del(b); end;
3:begin writeln(getrank(b)); end;
4:begin writeln(getkth(b+1)); end;
5:begin init(b); writeln(w[getmax(w[root,1]),6]); del(b); end;
6:begin init(b); writeln(w[getmin(w[root,2]),6]); del(b); end;
end;
end;
end.