# 伸展树

{% hint style="success" %}
[洛谷 P3369 【模板】普通平衡树](https://www.luogu.com.cn/problem/P3369)
{% endhint %}

```cpp
#include <bits/stdc++.h>

using namespace std;
using ll = long long;
using p = pair<int, int>;
const int maxn(1e5 + 10);
int idx, root;

struct node {
    int val;
    int siz, cnt;
    int fa, ch[2];
} tree[maxn];

template<typename T = int>
inline const T read()
{
    T x = 0, f = 1;
    char ch = getchar();
    while (ch < '0' || ch > '9') {
        if (ch == '-') f = -1;
        ch = getchar();
    }
    while (ch >= '0' && ch <= '9') {
        x = (x << 3) + (x << 1) + ch - '0';
        ch = getchar();
    }
    return x * f;
}

template<typename T>
inline void write(T x, bool ln)
{
    if (x < 0) {
        putchar('-');
        x = -x;
    }
    if (x > 9) write(x / 10, false);
    putchar(x % 10 + '0');
    if (ln) putchar(10);
}

inline int new_node(int val)
{
    ++idx;
    tree[idx].val = val;
    tree[idx].siz = tree[idx].cnt = 1;
    return idx;
}

inline bool get_rel(int cur, int fa)
{
    return tree[fa].ch[1] == cur;
}

inline void connect(int cur, int fa, int rel)
{
    tree[fa].ch[rel] = cur;
    tree[cur].fa = fa;
}

inline void push_up(int cur)
{
    tree[cur].siz = tree[tree[cur].ch[0]].siz + tree[tree[cur].ch[1]].siz + tree[cur].cnt;
}

inline void rotate(int cur)
{
    int fa = tree[cur].fa;
    int gf = tree[fa].fa;
    bool rel = get_rel(cur, fa);
    connect(tree[cur].ch[rel ^ 1], fa, rel);
    connect(cur, gf, get_rel(fa, gf));
    connect(fa, cur, rel ^ 1);
    push_up(fa);
    push_up(cur);
}

inline void splaying(int cur, int top)
{
    while (tree[cur].fa not_eq top) {
        int fa = tree[cur].fa;
        int gf = tree[fa].fa;
        if (gf not_eq top) {
            get_rel(cur, fa) ^ get_rel(fa, gf) ? rotate(cur) : rotate(fa);
        }
        rotate(cur);
    }
    if (not top) {
        root = cur;
    }
}

inline void insert(int val)
{
    int cur = root, fa = 0;
    while (cur and tree[cur].val not_eq val) {
        fa = cur;
        cur = tree[cur].ch[val > tree[cur].val];
    }
    if (cur) {
        ++tree[cur].cnt;
        ++tree[cur].siz;
    } else {
        cur = new_node(val);
        connect(cur, fa, val > tree[fa].val);
    }
    splaying(cur, 0);
}

inline void remove(int val)
{
    int cur = root, fa = 0;
    while (tree[cur].val not_eq val) {
        fa = cur;
        cur = tree[cur].ch[val > tree[cur].val];
    }
    splaying(cur, 0);
    if (tree[cur].cnt > 1) {
        --tree[cur].cnt;
        --tree[cur].siz;
    } else if (tree[cur].ch[1]) {
        int nxt = tree[cur].ch[1];
        while (tree[nxt].ch[0]) {
            nxt = tree[nxt].ch[0];
        }
        splaying(nxt, cur);
        connect(tree[cur].ch[0], nxt, 0);
        root = nxt;
        tree[root].fa = 0;
        push_up(root);
    } else {
        root = tree[cur].ch[0];
        tree[root].fa = 0;
    }
}

inline int get_rank(int val)
{
    int cur = root, rank = 1;
    while (cur) {
        if (tree[cur].val == val) {
            rank += tree[tree[cur].ch[0]].siz;
            splaying(cur, 0);
            break;
        } else if (val < tree[cur].val) {
            cur = tree[cur].ch[0];
        } else {
            rank += tree[tree[cur].ch[0]].siz + tree[cur].cnt;
            cur = tree[cur].ch[1];
        }
    }
    return rank;
}

inline int get_val(int rank)
{
    int cur = root;
    while (cur) {
        int size_l = tree[tree[cur].ch[0]].siz;
        if (size_l + 1 <= rank and rank <= size_l + tree[cur].cnt) {
            splaying(cur, 0);
            break;
        } else if (size_l >= rank) {
            cur = tree[cur].ch[0];
        } else {
            rank -= size_l + tree[cur].cnt;
            cur = tree[cur].ch[1];
        }
    }
    return tree[cur].val;
}

inline int get_prev(int val)
{
    return get_val(get_rank(val) - 1);
}

inline int get_next(int val)
{
    return get_val(get_rank(val + 1));
}

int main()
{
#ifdef ONLINE_JUDGE
#else
    freopen("input.txt", "r", stdin);
#endif
    int n = read();
    while (n--) {
        int op = read(), x = read();
        if (op == 1) {
            insert(x);
        } else if (op == 2) {
            remove(x);
        } else if (op == 3) {
            write(get_rank(x), true);
        } else if (op == 4) {
            write(get_val(x), true);
        } else if (op == 5) {
            write(get_prev(x), true);
        } else {
            write(get_next(x), true);
        }
    }
    return 0;
}
```

{% hint style="success" %}
[洛谷 P3391 【模板】文艺平衡树](https://www.luogu.com.cn/problem/P3391)
{% endhint %}

```cpp
#include <bits/stdc++.h>

using namespace std;
using ll = long long;
using p = pair<int, int>;
const int maxn(1e5 + 10);
int idx, root;

struct node {
    int val, siz;
    int fa, ch[2];
    bool rev;
} tree[maxn];

template<typename T = int>
inline const T read()
{
    T x = 0, f = 1;
    char ch = getchar();
    while (ch < '0' || ch > '9') {
        if (ch == '-') f = -1;
        ch = getchar();
    }
    while (ch >= '0' && ch <= '9') {
        x = (x << 3) + (x << 1) + ch - '0';
        ch = getchar();
    }
    return x * f;
}

template<typename T>
inline void write(T x, char c)
{
    if (x < 0) {
        putchar('-');
        x = -x;
    }
    if (x > 9) write(x / 10, false);
    putchar(x % 10 + '0');
    if (c) putchar(c);
}

inline int new_node(int val)
{
    ++idx;
    tree[idx].val = val;
    tree[idx].siz = 1;
    return idx;
}

inline void push_up(int cur)
{
    tree[cur].siz = tree[tree[cur].ch[0]].siz + tree[tree[cur].ch[1]].siz + 1;
}

inline void push_down(int cur)
{
    if (tree[cur].rev) {
        swap(tree[cur].ch[0], tree[cur].ch[1]);
        tree[tree[cur].ch[0]].rev ^= 1;
        tree[tree[cur].ch[1]].rev ^= 1;
        tree[cur].rev = false;
    }
}

inline int get_rel(int cur, int fa)
{
    return tree[fa].ch[1] == cur;
}

inline void connect(int cur, int fa, bool rel)
{
    tree[fa].ch[rel] = cur;
    tree[cur].fa = fa;
}

inline void rotate(int cur)
{
    int fa = tree[cur].fa;
    int gf = tree[fa].fa;
    bool rel = get_rel(cur, fa);
    connect(tree[cur].ch[rel ^ 1], fa, rel);
    connect(cur, gf, get_rel(fa, gf));
    connect(fa, cur, rel ^ 1);
    push_up(fa);
    push_up(cur);
}

inline void splaying(int cur, int top)
{
    while (tree[cur].fa not_eq top) {
        int fa = tree[cur].fa;
        int gf = tree[fa].fa;
        if (gf not_eq top) {
            get_rel(cur, fa) ^ get_rel(fa, gf) ? rotate(cur) : rotate(fa);
        }
        rotate(cur);
    }
    if (not top) {
        root = cur;
    }
}

inline void insert(int val)
{
    int cur = root, fa = 0;
    while (cur) {
        fa = cur;
        cur = tree[cur].ch[val > tree[cur].val];
    }
    cur = new_node(val);
    connect(cur, fa, val > tree[fa].val);
    splaying(cur, 0);
}

inline int get_id(int pos)
{
    int cur = root;
    while (cur) {
        push_down(cur);
        if (tree[tree[cur].ch[0]].siz >= pos) {
            cur = tree[cur].ch[0];
        } else if (tree[tree[cur].ch[0]].siz + 1 == pos) {
            return cur;
        } else {
            pos -= tree[tree[cur].ch[0]].siz + 1;
            cur = tree[cur].ch[1];
        }
    }
    return cur;
}

inline void reverse(int l, int r)
{
    int x = get_id(l - 1);
    int y = get_id(r + 1);
    splaying(x, 0);
    splaying(y, x);
    tree[tree[y].ch[0]].rev ^= 1;
}

void dfs(int cur, int n)
{
    if (not cur) return;
    push_down(cur);
    dfs(tree[cur].ch[0], n);
    if (tree[cur].val >= 1 and tree[cur].val <= n) {
        write(tree[cur].val, ' ');
    }
    dfs(tree[cur].ch[1], n);
}

int main()
{
#ifdef ONLINE_JUDGE
#else
    freopen("input.txt", "r", stdin);
#endif
    int n = read(), m = read();
    for (int i = 0; i <= n + 1; ++i) {
        insert(i);
    }
    while (m--) {
        int l = read() + 1, r = read() + 1;
        reverse(l, r);
    }
    dfs(root, n);
    return 0;
}
```


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