万恶的平衡树
作者：互联网
以普通平衡树为例
有旋Treap
#include <iostream>
#include <cstdlib>
using namespace std;
inline int in(){
int x = 0;
bool f = 1;
char c = getchar();
while(c > '9' || c < '0'){
if(c == '-') f = 0;
c = getchar();
}
while(c <= '9' && c >= '0'){
x = (x << 1) + (x << 3) + (c ^ 48);
c = getchar();
}
if(f) return x;
else return -x;
}
const int N = 1e5+10;
const int inf = 0x7fffffff;
struct treap{
int l,r;//左右子树
int val;//关键码
int dat;//权值
int sz;//子树大小
int cnt;//相同的关键码的个数,插入++,删除--,减为0删除该节点
}a[N];
int n,tot,root;
inline int New(int val){
a[++tot].val = val;
a[tot].dat = rand();
a[tot].cnt = a[tot].sz = 1;
return tot;
}
inline void update(int rt){
a[rt].sz = a[a[rt].l].sz + a[a[rt].r].sz + a[rt].cnt;
}
inline void build(){
New(-inf);
New(inf);
root = 1;
a[1].r = 2;
update(root);
}
inline void zag(int &rt){//左旋
int x = a[rt].r;
a[rt].r = a[x].l;
a[x].l = rt;
rt = x;
update(a[rt].l);
update(rt);
}
inline void zig(int &rt){//右旋
int x = a[rt].l;
a[rt].l = a[x].r;
a[x].r = rt;
rt = x;
update(a[rt].r);
update(rt);
}
inline void insert(int &rt,int val){
if(!rt){
rt = New(val);
return;
}
if(val == a[rt].val){
a[rt].cnt++;
update(rt);
return;
}
if(a[rt].val < val){
insert(a[rt].r,val);
if(a[rt].dat < a[a[rt].r].dat) zag(rt);//不满足堆性质,左旋
}else{
insert(a[rt].l,val);
if(a[rt].dat < a[a[rt].l].dat) zig(rt);//右旋
}
update(rt);
}
inline void dlt(int &rt,int val){
if(!rt) return;
if(a[rt].val == val){
if(a[rt].cnt > 1){
a[rt].cnt--;
update(rt);
return;
}
if(a[rt].l || a[rt].r){//如果不是叶子节点,转下去
if(!a[rt].r || a[a[rt].l].dat > a[a[rt].r].dat){
zig(rt);
dlt(a[rt].r,val);
}else{
zag(rt);
dlt(a[rt].l,val);
}
update(rt);
}else rt = 0;
return;
}
if(val < a[rt].val) dlt(a[rt].l,val);
else dlt(a[rt].r,val);
update(rt);
}
inline int gtr(int rt,int val){
if(!rt) return 0;
if(val == a[rt].val) return a[a[rt].l].sz + 1;
if(val < a[rt].val) return gtr(a[rt].l,val);
else return gtr(a[rt].r,val) + a[a[rt].l].sz + a[rt].cnt;
}
inline int gtv(int rt,int rank){
if(!rt) return 0;
if(a[a[rt].l].sz >= rank) return gtv(a[rt].l,rank);
else if(a[a[rt].l].sz + a[rt].cnt >= rank) return a[rt].val;
else return gtv(a[rt].r,rank-a[a[rt].l].sz-a[rt].cnt);
}
inline int gtp(int val){
int ans = 1;//a[1].val = -inf
int rt = root;
while(rt){
if(val == a[rt].val){
if(a[rt].l){
rt = a[rt].l;
while(a[rt].r) rt = a[rt].r;
ans = rt;
}
break;
}
if(a[rt].val < val && a[rt].val > a[ans].val) ans = rt;
if(val < a[rt].val) rt = a[rt].l;
else rt = a[rt].r;
}
return a[ans].val;
}
inline int gtn(int val){
int ans = 2;//a[2].val = inf
int rt = root;
while(rt){
if(val == a[rt].val){
if(a[rt].r){
rt = a[rt].r;
while(a[rt].l) rt = a[rt].l;
ans = rt;
}
break;
}
if(a[rt].val > val && a[rt].val < a[ans].val) ans = rt;
if(val < a[rt].val) rt = a[rt].l;
else rt = a[rt].r;
}
return a[ans].val;
}
int main(){
build();
n = in();
int opt,x;
while(n--){
opt = in();
x = in();
if(opt == 1) insert(root,x);
else if(opt == 2) dlt(root,x);
else if(opt == 3) printf("%d\n",gtr(root,x)-1);
else if(opt == 4) printf("%d\n",gtv(root,x+1));
else if(opt == 5) printf("%d\n",gtp(x));
else if(opt == 6) printf("%d\n",gtn(x));
}
return 0;
}Splay
#include <iostream>
#include <cstdlib>
#define fa(x) a[x].fa
#define ls(x) a[x].ch[0]
#define rs(x) a[x].ch[1]
#define sz(x) a[x].sz
#define cnt(x) a[x].cnt
#define val(x) a[x].val
using namespace std;
inline int in(){
int x = 0;
bool f = 1;
char c = getchar();
while(c > '9' || c < '0'){
if(c == '-') f = 0;
c = getchar();
}
while(c <= '9' && c >= '0'){
x = (x << 1) + (x << 3) + (c ^ 48);
c = getchar();
}
if(f) return x;
else return -x;
}
const int N = 1e5+100;
const int inf = 0x7ffffff;
struct splay{
int fa;
int ch[2];
int val;
int cnt;
int sz;
}a[N];
int n,tot,root,ans;
inline void update(int rt){
sz(rt) = sz(ls(rt)) + sz(rs(rt)) + cnt(rt);
}
inline bool get(int rt){
return rt == rs(fa(rt));
}
inline void clear(int rt){
fa(rt) = val(rt) = cnt(rt) = sz(rt) = ls(rt) = rs(rt) = 0;
}
inline void rotate(int rt){
int f = fa(rt);
int pa = fa(f);
int cnt = get(rt);
a[f].ch[cnt] = a[rt].ch[cnt^1];
if(a[rt].ch[cnt^1]) fa(a[rt].ch[cnt^1]) = f;
a[rt].ch[cnt^1] = f;
fa(f) = rt;
fa(rt) = pa;
if(pa) a[pa].ch[f == rs(pa)] = rt;
update(rt);
update(f);
}
inline void splay(int rt){
for(int f = fa(rt);f = fa(rt),f;rotate(rt))
if(fa(f)) rotate(get(rt) == get(f) ? f : rt);
root = rt;
}
inline void insert(int val){
if(!root){
val(++tot) = val;
cnt(tot) = 1;
root = tot;
update(root);
return;
}
int rt = root,f = 0;
while(1){
if(val(rt) == val){
cnt(rt)++;
update(rt);
update(f);
splay(rt);
break;
}
f = rt;
rt = a[rt].ch[val(rt) < val];
if(!rt){
val(++tot) = val;
cnt(tot) = 1;
fa(tot) = f;
a[f].ch[val(f) < val] = tot;
update(tot);
update(f);
splay(tot);
break;
}
}
}
inline int rk(int val){//查询val的排名
int res = 0,cnt = root;
while(1){
if(val < val(cnt)) cnt = ls(cnt);
else{
res += sz(ls(cnt));
if(val == val(cnt)){
splay(cnt);
return res + 1;
}
res += cnt(cnt);
cnt = rs(cnt);
}
}
}
inline int kth(int k){//查询排名为k的数
int cnt = root;
while(1){
if(ls(cnt) && k <= sz(ls(cnt))) cnt = ls(cnt);
else{
k -= cnt(cnt) + sz(ls(cnt));
if(k <= 0){
splay(cnt);
return val(cnt);
}
cnt = rs(cnt);
}
}
}
inline int pre(){
int cnt = ls(root);
if(!cnt) return cnt;
while(rs(cnt)) cnt = rs(cnt);
splay(cnt);
return cnt;
}
inline int nxt(){
int cnt = rs(root);
if(!cnt) return cnt;
while(ls(cnt)) cnt = ls(cnt);
splay(cnt);
return cnt;
}
inline void dlt(int val){
rk(val);
if(cnt(root) > 1){
cnt(root)--;
update(root);
return;
}
if(!ls(root) && !rs(root)){
clear(root);
root = 0;
return;
}
if(!ls(root)){
int cnt = root;
root = rs(root);
fa(root) = 0;
clear(cnt);
return;
}
if(!rs(root)){
int cnt = root;
root = ls(root);
fa(root) = 0;
clear(cnt);
return;
}
int cnt = root;
int x = pre();
fa(rs(cnt)) = x;
rs(x) = rs(cnt);
clear(cnt);
update(root);
}
int main(){
n = in();
int x,opt;
for(int i = 1;i <= n;++i){
opt = in();
x = in();
if(opt == 1) insert(x);
if(opt == 2) dlt(x);
if(opt == 3) printf("%d\n",rk(x));
if(opt == 4) printf("%d\n",kth(x));
if(opt == 5){
insert(x);
printf("%d\n",val(pre()));
dlt(x);
}
if(opt == 6){
insert(x);
printf("%d\n",val(nxt()));
dlt(x);
}
}
return 0;
}裂开。。。。。TAT
标签：rt,万恶,cnt,return,val,int,平衡,root 来源： https://www.cnblogs.com/Kamisato-Ayaka/p/16388089.html