1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
| #include<algorithm>
#include<iostream>
#include<iomanip>
#include<cstring>
#include<cstdlib>
#include<climits>
#include<vector>
#include<cstdio>
#include<cmath>
#include<queue>
using namespace std;
inline const int Get_Int() {
int num=0,bj=1;
char x=getchar();
while(x<'0'||x>'9') {
if(x=='-')bj=-1;
x=getchar();
}
while(x>='0'&&x<='9') {
num=num*10+x-'0';
x=getchar();
}
return num*bj;
}
const int maxn=100005;
struct Tree {
int child[2],father;
int size,val;
Tree() {}
Tree(int l,int r,int f,int s,int v):father(f),size(s),val(v) {
child[0]=l;
child[1]=r;
}
};
struct ScapeGoat_Tree {
const double alpha=0.7;
Tree tree[maxn];
int root,size;
#define ls(x) tree[x].child[0]
#define rs(x) tree[x].child[1]
#define fa(x) tree[x].father
#define val(x) tree[x].val
#define size(x) tree[x].size
ScapeGoat_Tree() {
tree[++size]=Tree(0,2,0,2,-INT_MAX);
tree[++size]=Tree(0,0,1,1,INT_MAX);
root=1;
}
bool balance(int index) {
return size(index)*alpha>=max(size(ls(index)),size(rs(index)));
}
bool checkson(int index) {
return rs(fa(index))==index;
}
void push_up(int index) {
size(index)=size(ls(index))+1+size(rs(index));
}
int cnt,a[maxn];
void dfs(int index) {
if(ls(index))dfs(ls(index));
a[++cnt]=index;
if(rs(index))dfs(rs(index));
}
int build(int Left,int Right) {
if(Left>Right)return 0;
int mid=(Left+Right)>>1,pos=a[mid];
ls(pos)=build(Left,mid-1);
rs(pos)=build(mid+1,Right);
fa(ls(pos))=fa(rs(pos))=pos;
push_up(pos);
return pos;
}
void rebuild(int index) {
cnt=0;
dfs(index);
int father=fa(index),side=checkson(index);
int pos=build(1,cnt);
tree[father].child[side]=pos;
fa(pos)=father;
if(index==root)root=pos;
}
void insert(int v) {
int now=root,father=0;
while(now) {
father=now;
size(father)++;
now=tree[now].child[val(now)<=v];
}
tree[now=++size]=Tree(0,0,father,1,v);
if(father)tree[father].child[val(father)<=v]=now;
int pos=0;
for(int i=now; i; i=fa(i))
if(!balance(i))pos=i;
if(pos)rebuild(pos);
}
void remove(int index) {
if(ls(index)&&rs(index)) {
int pre=ls(index);
while(rs(pre))pre=rs(pre);
val(index)=val(pre);
index=pre;
}
int son=ls(index)?ls(index):rs(index),side=checkson(index);
tree[fa(index)].child[side]=son;
fa(son)=fa(index);
for(int i=fa(index); i; i=fa(i))size(i)--;
if(index==root)root=son;
}
int find(int v) {
int now=root;
while(now) {
if(val(now)==v)return now;
else now=tree[now].child[val(now)<v];
}
return -1;
}
int rank(int v) {
int now=root,ans=0;
while(now) {
if(v<=val(now))now=ls(now);
else {
ans+=size(ls(now))+1;
now=rs(now);
}
}
return ans;
}
int kth(int rank) {
rank++;
int now=root;
while(now>0&&rank>=0) {
if(ls(now)&&size(ls(now))>=rank)now=ls(now);
else {
if(rank<=size(ls(now))+1)return now;
rank-=size(ls(now))+1;
now=rs(now);
}
}
return -1;
}
int pre(int num) {
int now=root,ans=-INT_MAX;
while(now) {
if(val(now)<num)ans=max(ans,val(now)),now=rs(now);
else now=ls(now);
}
return ans;
}
int suc(int num) {
int now=root,ans=INT_MAX;
while(now) {
if(val(now)>num)ans=min(ans,val(now)),now=ls(now);
else now=rs(now);
}
return ans;
}
} sgt;
int n;
int main() {
n=Get_Int();
for(int i=1; i<=n; i++) {
int order=Get_Int();
if(order==1)sgt.insert(Get_Int());
if(order==2)sgt.remove(sgt.find(Get_Int()));
if(order==3)printf("%d\n",sgt.rank(Get_Int()));
if(order==4)printf("%d\n",sgt.tree[sgt.kth(Get_Int())].val);
if(order==5)printf("%d\n",sgt.pre(Get_Int()));
if(order==6)printf("%d\n",sgt.suc(Get_Int()));
}
return 0;
}
|
