平衡树-有/无旋Treap
有旋Treap
可以在普通二叉搜索树的基础上保持优秀log复杂度
代码里有较为详细的注释
所以，话不多说，放代码qwq
#include<iostream>
using namespace std;
#define lid d[id].l
#define rid d[id].r
int cnt_tree,ans;
struct Treap{
int l,r; //左孩子，右孩子
int siz; //大小
int cnt; //重复元素数量
int rank; //随机出来的优先度
int val; //值
}d[100005];
void Update_size(int id){//更新大小
d[id].siz=d[id].cnt+d[lid].siz+d[rid].siz;
}
void lrotate(int &id){
/* 左旋：也就是让右子节点变成根节点
* A C
* / \ / \
* B C ----> A E
* / \ / \
* D E B D
*/
int t=d[id].r; //记录右孩子
d[id].r=d[t].l; //A的右孩子改为C的左孩子
d[t].l=id; //C的左孩子改为A
d[t].siz=d[id].siz;//传递size
Update_size(id);//更新A的size
id=t;//换根
}
void rrotate(int &id){
/* 右旋：也就是让左子节点变成根节点
* A C
* / \ / \
* B C <---- A E
* / \ / \
* D E B D
*/
int t=d[id].l;//同上
d[id].l=d[t].r;
d[t].r=id;
d[t].siz=d[id].siz;
Update_size(id);
id=t;
}
void insert(int &id,int val){
if(!id){ //没有点新建点
id=++cnt_tree;
d[id].rank=rand();
d[id].siz=1;
d[id].cnt=1;
d[id].val=val;
return;
}
d[id].siz++; //大小++
if(val==d[id].val){
d[id].cnt++; //值相同，直接扔进去
}
else if(val<d[id].val){
insert(lid,val); //增加在左孩子里
if(d[lid].rank<d[id].rank){
rrotate(id); //为满足小根堆性质(上方优先度低于下方)，需要右旋
}
}
else{
insert(rid,val); //同上
if(d[rid].rank<d[id].rank){
lrotate(id);
}
}
}
//用bool，0为未删点，1为删点
bool del(int &id,int val){
if(!val) return false; //如果没有点，不需要修改，所以return false
if(val==d[id].val){ //如果相等
if(d[id].cnt>1){ //有重复元素则直接删除
d[id].cnt--;
d[id].siz--;
return true;
}
if(lid==0 || rid==0){ //只有一个孩子，或没有孩子，不存在内讧，故直接赋值
id=lid+rid;
return true;
}
else if(d[lid].rank<d[rid].rank){ //删完还要满足小根堆，故右旋
rrotate(id);
return del(id,val); //删点
}
else{
lrotate(id);
return del(id,val);
}
}
else if(val<d[id].val){
bool dele=del(lid,val); //点在左孩子，记录是否成功删点
if(dele) d[id].siz--;
return dele;
}
else{
bool dele=del(rid,val);
if(dele) d[id].siz--;
return dele;
}
}
int Query_Rank(int id,int val){ //查询排名
if(!id) return 0; //若 定义排名为比当前数小的数的个数+1 则此处应该为return 1;
if(val==d[id].val) return d[lid].siz+1; //仅比所有左侧节点大
else if(val<d[id].val) return Query_Rank(lid,val); //点在左孩子
else return d[lid].siz+d[id].cnt+Query_Rank(rid,val); //1.比所有左节点大，2.比该节点的所有重复元素大，3.点在右孩子
}
int Query_Num(int id,int val){ //查询排名为val的节点值
if(!id) return 0;
if(val<=d[lid].siz) return Query_Num(lid,val); //节点在左孩子
else if(val>d[lid].siz+d[id].cnt) return Query_Num(rid,val-d[lid].siz-d[id].cnt); //!节点在右孩子，但排名在右孩子里应减小
else return d[id].val; //不在左，不在右，就只能在自己里了呗awa
}
void Query_Pre(int id,int val){ //查询前驱
if(!id) return; //类似二分查找
if(val>d[id].val){ //!别弄反了
ans=id;
Query_Pre(rid,val);
}
else{
Query_Pre(lid,val);
}
}
void Query_Sub(int id,int val){
if(!id) return;
if(val<d[id].val){ //!别弄反了
ans=id;
Query_Sub(lid,val);
}
else{
Query_Sub(rid,val);
}
}
int main(){
ios::sync_with_stdio(false),cin.tie(0),cout.tie(0);
int n,root=0;
cin>>n;
for(int i=1;i<=n;i++){
int op,x;
cin>>op>>x;
if(op==1){
insert(root,x);
}
if(op==2){
del(root,x);
}
if(op==3){
cout<<Query_Rank(root,x)<<"\n";
}
if(op==4){
cout<<Query_Num(root,x)<<"\n";
}
if(op==5){
ans=0;
Query_Pre(root,x);
cout<<d[ans].val<<"\n";
}
if(op==6){
ans=0;
Query_Sub(root,x);
cout<<d[ans].val<<"\n";
}
}
}
无旋Treap(FHQ)
#include <iostream>
#include <cstring>
#include <algorithm>
#include <bitset>
#include <vector>
#include <set>
#include <queue>
#include <cmath>
#include <map>
#include <cassert>
#include <bitset>
#include <cstdio>
#include <climits>
#include <iomanip>
using namespace std;
#define lid ch[id][0]
#define rid ch[id][1]
#define emp emplace_back
#define pb push_back
#define fi first
#define se second
#define IL inline
#define reg register
#define endl '\n'
#define IL inline
#define LF 1
#define RF 0
const int M = 20000 + 7, N = 100000 + 7, mod = 10007, B = 300; // !!!!!!!!
// #define int long long
using pii = pair <int, int>;
using ll = long long;
using ld = long double;
using ull = unsigned long long;
using I = __int128;
using uIt = __uint128_t;
int root;
class FHQ
{
public :
int rnk[N], val[N], siz[N], ch[N][2], tot;
int New(int k)
{
++tot;
rnk[tot] = rand();
val[tot] = k;
siz[tot] = 1;
return tot;
}
void PushUp(int id)
{
siz[id] = siz[lid] + siz[rid] + 1;
}
void Split(int id, int k, int &x, int &y)
{
if (!id) return (x = 0, y = 0), void();
if (k < val[id])
{
y = id;
Split(ch[y][0], k, x, ch[y][0]);
}
else
{
x = id;
Split(ch[x][1], k, ch[x][1], y);
}
PushUp(id);
}
int Merge(int x, int y)
{
if (!x || !y) return x | y;
if (rnk[x] < rnk[y])
{
ch[x][1] = Merge(ch[x][1], y);
PushUp(x);
return x;
}
else
{
ch[y][0] = Merge(x, ch[y][0]);
PushUp(y);
return y;
}
}
void Insert(int k)
{
int x, y, z;
Split(root, k, x, y);
z = New(k);
root = Merge(Merge(x, z), y);
}
void Del(int k)
{
int x, y, z;
Split(root, k, x, z);
Split(x, k - 1, x, y);
y = Merge(ch[y][0], ch[y][1]);
root = Merge(Merge(x, y), z);
}
int Find_K(int id, int k)
{
if (k <= siz[lid]) return Find_K(lid, k);
if (k == siz[lid] + 1) return id;
return Find_K(rid, k - siz[lid] - 1);
}
int Find_Val(int k)
{
int x, y;
Split(root, k - 1, x, y);
int p = siz[x] + 1;
root = Merge(x, y);
return p;
}
int Find_Pre(int k)
{
int x, y;
Split(root, k - 1, x, y);
int p = Find_K(x, siz[x]);
root = Merge(x, y);
return p;
}
int Find_Sub(int k)
{
int x, y;
Split(root, k, x, y);
int p = Find_K(y, 1);
root = Merge(x, y);
return p;
}
}T;
int main()
{
// freopen("data.in", "r", stdin); freopen("data.out", "w", stdout);
ios :: sync_with_stdio(false), cin.tie(0), cout.tie(0);
int n; cin >> n;
while (n--)
{
int op, x; cin >> op >> x;
if (op == 1) T.Insert(x);
if (op == 2) T.Del(x);
if (op == 3) cout << T.Find_Val(x) << '\n';
if (op == 4) cout << T.val[T.Find_K(root, x)] << '\n';
if (op == 5) cout << T.val[T.Find_Pre(x)] << '\n';
if (op == 6) cout << T.val[T.Find_Sub(x)] << '\n';
}
return 0;
}
维护区间信息
#include <iostream>
#include <cstring>
#include <algorithm>
#include <bitset>
#include <vector>
#include <set>
#include <queue>
#include <cmath>
#include <map>
#include <cassert>
#include <bitset>
#include <cstdio>
#include <climits>
#include <iomanip>
using namespace std;
#define lid ch[id][0]
#define rid ch[id][1]
#define emp emplace_back
#define pb push_back
#define fi first
#define se second
#define IL inline
#define reg register
#define endl '\n'
#define IL inline
#define LF 1
#define RF 0
const int M = 20000 + 7, N = 100000 + 7, mod = 10007, B = 300; // !!!!!!!!
// #define int long long
using pii = pair <int, int>;
using ll = long long;
using ld = long double;
using ull = unsigned long long;
using I = __int128;
using uIt = __uint128_t;
int root;
class FHQ
{
public :
int tag[N], siz[N], rnk[N], tot, ch[N][2], val[N];
void PushUp(int id) {siz[id] = siz[lid] + siz[rid] + 1;}
void PushDown(int id)
{
if (tag[id])
{
swap(lid, rid);
if (lid) tag[lid] ^= 1;
if (rid) tag[rid] ^= 1;
tag[id] = 0;
}
}
void Split(int id, int k, int &x, int &y)
{
if (!id) return (x = y = 0), void();
PushDown(id);
if (k <= siz[ch[id][0]])
{
y = id;
Split(ch[y][0], k, x, ch[y][0]);
PushUp(y);
}
else
{
x = id;
Split(ch[x][1], k - siz[ch[id][0]] - 1, ch[x][1], y);
PushUp(x);
}
}
int Merge(int x, int y)
{
if (!x || !y) return x | y;
PushDown(x), PushDown(y);
if (rnk[x] > rnk[y])
{
ch[x][1] = Merge(ch[x][1], y);
PushUp(x);
return x;
}
else
{
ch[y][0] = Merge(x, ch[y][0]);
PushUp(y);
return y;
}
}
void Reverse(int l, int r)
{
int x, y, z;
Split(root, l - 1, x, y);
Split(y, r - l + 1, y, z);
tag[y] ^= 1;
root = Merge(Merge(x, y), z);
}
void print(int id)
{
PushDown(id);
if (lid) print(lid);
cout << val[id] << ' ';
if (rid) print(rid);
}
}T;
int rnk[N], sta[N], top;
int main()
{
srand(time(NULL));
// freopen("data.in", "r", stdin); freopen("data.out", "w", stdout);
ios :: sync_with_stdio(false), cin.tie(0), cout.tie(0);
int n; cin >> n;
for (int i = 1; i <= n; i++) T.rnk[i] = rand(), T.val[i] = i, T.siz[i] = 1;
for (int i = 1; i <= n; i++)
{
int k = top;
while (k && T.rnk[sta[k]] < T.rnk[i]) k--;
if (k) T.ch[sta[k]][1] = i;
if (k < top) T.ch[i][0] = sta[k + 1];
sta[++k] = i;
top = k;
}
root = sta[1];
int m; cin >> m;
for (int i = 1; i <= m; i++)
{
int l, r; cin >> l >> r;
T.Reverse(l, r);
}
T.print(root);
return 0;
}
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