算法笔记--Splay && Link-Cut-Tree && fhq _treap

Splay

参考：https://tiger0132.blog.luogu.org/slay-notes

普通模板：

const int N = 1e5 + 10;
int ch[N][2], val[N], cnt[N], fa[N], sz[N], lazy[N], ncnt = 0, rt = 0;
int n, m;
inline int ck(int x) {
    return ch[fa[x]][1] == x;
}
inline void push_up(int x) {
    sz[x] = sz[ch[x][0]] + sz[ch[x][1]] + cnt[x];
}
///区间反转
inline void push_down(int x) {
    if(lazy[x]) {
        swap(ch[x][0], ch[x][1]);
        lazy[ch[x][0]] ^= 1;
        lazy[ch[x][1]] ^= 1;
        lazy[x] = 0;
    }
}
void Rotate(int x) {
    int y = fa[x], z = fa[y];
    push_down(y), push_down(x);///区间反转
    int k = ck(x), w = ch[x][k^1];
    ch[y][k] = w, fa[w] = y;
    ch[z][ck(y)] = x, fa[x] = z;
    ch[x][k^1] = y, fa[y] = x;
    push_up(y), push_up(x);
}
void Splay(int x, int goal = 0) {
    push_down(x);///区间反转
    while(fa[x] != goal) {
        int y = fa[x], z = fa[y];
        if(z != goal) {
            if(ck(x) == ck(y)) Rotate(y);
            else Rotate(x);
        }
        Rotate(x);
    }
    if(!goal) rt = x;
}
void Find(int x) {
    if(!rt) return ;
    int cur = rt;
    while(ch[cur][x>val[cur]] && x != val[cur]) cur = ch[cur][x>val[cur]];
    Splay(cur);
}
void Insert(int x) {
    int cur = rt, p = 0;
    while(cur && val[cur] != x) {
        p = cur;
        cur = ch[cur][x>val[cur]];
    }
    if(cur) cnt[cur]++;
    else {
        cur = ++ncnt;
        if(p) ch[p][x>val[p]] = cur;
        fa[cur] = p;
        ch[cur][0] = ch[cur][1] = 0;
        val[cur] = x;
        cnt[cur] = sz[cur] = 1;
    }
    Splay(cur);
}
int Kth(int k) {
    int cur = rt;
    while(true) {
        push_down(cur); ///区间反转
        if(ch[cur][0] && k <= sz[ch[cur][0]]) cur = ch[cur][0];
        else if(k > sz[ch[cur][0]] + cnt[cur]) k -=sz[ch[cur][0]] + cnt[cur], cur = ch[cur][1];
        else return cur;
    }
}
inline int get_min(int x) {
    while(x && ch[x][0]) x = ch[x][0];
    return x;
}
inline int get_max(int x) {
    while(x && ch[x][1]) x = ch[x][1];
    return x;
}
int Pre(int x) {
    Find(x);
    if(val[rt] < x) return rt;
    int cur = ch[rt][0];
    while(ch[cur][1]) cur = ch[cur][1];
    return cur;
}
int Succ(int x) {
    Find(x);
    if(val[rt] > x) return rt;
    int cur = ch[rt][1];
    while(ch[cur][0]) cur = ch[cur][0];
    return cur;
}
void Remove(int x) {
    int last = Pre(x), next = Succ(x);
    Splay(last), Splay(next, last);
    int del = ch[next][0];
    if(cnt[del] > 1) cnt[del]--, Splay(del);
    else ch[next][0] = 0, push_up(next), push_up(last);
}
///区间反转
void Reverse(int l, int r) {
    int x = Kth(l), y = Kth(r+2);
    Splay(x), Splay(y, x);
    lazy[ch[y][0]] ^= 1;
}
void Output(int x) {
    push_down(x);
    if(ch[x][0]) Output(ch[x][0]);
    if(1 <= val[x] && val[x] <= n) printf("%d ", val[x]);
    if(ch[x][1]) Output(ch[x][1]);
}
void delete_root() {
    if(ch[rt][1]) {
        int cur = ch[rt][1];
        while(cur && ch[cur][0]) cur = ch[cur][0];
        Splay(cur, rt);
        ch[cur][0] = ch[rt][0];
        fa[ch[cur][0]] = cur;
        rt = cur;
    }
    else rt = ch[rt][0];
    fa[rt] = 0;
    if(rt) push_up(rt);
}
inline int NewNode(int x) {
    int cur;
    if(q.empty()) cur = ++ncnt;
    else cur = q.front(), q.pop();
    ///初始化
    ch[cur][0] = ch[cur][1] = fa[cur] = lazy[cur] = 0;
    val[cur] = x;
    sz[cur] = cnt[cur] = 1;
    return cur;
}
void Recycle(int x) {
    if(ch[x][0]) Recycle(ch[x][0]);
    if(ch[x][1]) Recycle(ch[x][1]);
    if(x) q.push(x);
}
int build(int l, int r, int *a) {
    if(l > r) return 0;
    int mid = l+r >> 1, cur = NewNode(a[mid]);
    if(l == r) return cur;
    if(ch[cur][0] = build(l, mid-1, a)) fa[ch[cur][0]] = cur;
    if(ch[cur][1] = build(mid+1, r, a)) fa[ch[cur][1]] = cur;
    push_up(cur);
    return cur;
}
inline void init() {
    ncnt = rt = ch[0][0] = ch[0][1] = fa[0] = sz[0] = cnt[0] = val[0] = lazy[0] = 0;
}

按排名插入模板（常数较小？？？也许以前的方法写搓了）：

inline void Newnode(int &cur, int f, int a) {
    cur = ++ncnt;
    fa[cur] = f;
    val[cur] = a;
    ch[cur][0] = ch[cur][1] = 0;
    sz[cur] = cnt[cur] = 1;
}
void Insert(int x, int y) {
    int p = 0;
    if(!rt) {
        Newnode(rt, 0, y);
        return ;
    }
    if(!x) {
        p = rt;
        sz[p]++;
        while(ch[p][0]) p = ch[p][0], sz[p]++;
        Newnode(ch[p][0], p, y);
        Splay(ch[p][0]);
        return ;
    }
    int u = Kth(x);
    Splay(u);
    Newnode(rt, 0, y);
    ch[rt][1] = ch[u][1];
    fa[ch[rt][1]] = rt;
    ch[u][1] = 0;
    ch[rt][0] = u;
    fa[u] = rt;
    push_up(u), push_up(rt);
}

例题：

P3369 【模板】普通平衡树 

代码：

#pragma GCC optimize(2)
#pragma GCC optimize(3)
#pragma GCC optimize(4)
#include<bits/stdc++.h>
using namespace std;
#define y1 y11
#define fi first
#define se second
#define pi acos(-1.0)
#define LL long long
//#define mp make_pair
#define pb push_back
#define ls rt<<1, l, m
#define rs rt<<1|1, m+1, r
#define ULL unsigned LL
#define pll pair<LL, LL>
#define pli pair<LL, int>
#define pii pair<int, int>
#define piii pair<pii, int>
#define pdd pair<double, double>
#define mem(a, b) memset(a, b, sizeof(a))
#define debug(x) cerr << #x << " = " << x << "\n";
#define fio ios::sync_with_stdio(false);cin.tie(0);cout.tie(0);
//head

const int N = 2e5 + 10;
int ch[N][2], val[N], cnt[N], fa[N], sz[N], ncnt = 0, rt = 0;
inline int ck(int x) {
    return ch[fa[x]][1] == x;
}
inline void push_up(int x) {
    sz[x] = sz[ch[x][0]] + sz[ch[x][1]] + cnt[x];
}
void Rotate(int x) {
    int y = fa[x], z = fa[y], k = ck(x), w = ch[x][k^1];
    ch[y][k] = w, fa[w] = y;
    ch[z][ck(y)] = x, fa[x] = z;
    ch[x][k^1] = y, fa[y] = x;
    push_up(y), push_up(x);
}
void Splay(int x, int goal = 0) {
    while(fa[x] != goal) {
        int y = fa[x], z = fa[y];
        if(z != goal) {
            if(ck(x) == ck(y)) Rotate(y);
            else Rotate(x);
        }
        Rotate(x);
    }
    if(!goal) rt = x;
}
void Find(int x) {
    if(!rt) return ;
    int cur = rt;
    while(ch[cur][x>val[cur]] && x != val[cur]) cur = ch[cur][x>val[cur]];
    Splay(cur);
}
void Insert(int x) {
    int cur = rt, p = 0;
    while(cur && val[cur] != x) {
        p = cur;
        cur = ch[cur][x>val[cur]];
    }
    if(cur) cnt[cur]++;
    else {
        cur = ++ncnt;
        if(p) ch[p][x>val[p]] = cur;
        fa[cur] = p;
        ch[cur][0] = ch[cur][1] = 0;
        val[cur] = x;
        cnt[cur] = sz[cur] = 1;
    }
    Splay(cur);
}
int Kth(int k) {
    int cur = rt;
    while(true) {
        if(ch[cur][0] && k <= sz[ch[cur][0]]) cur = ch[cur][0];
        else if(k > sz[ch[cur][0]] + cnt[cur]) k -=sz[ch[cur][0]] + cnt[cur], cur = ch[cur][1];
        else return cur;
    }
}
int Pre(int x) {
    Find(x);
    if(val[rt] < x) return rt;
    int cur = ch[rt][0];
    while(ch[cur][1]) cur = ch[cur][1];
    return cur;
}
int Succ(int x) {
    Find(x);
    if(val[rt] > x) return rt;
    int cur = ch[rt][1];
    while(ch[cur][0]) cur = ch[cur][0];
    return cur;
}
void Remove(int x) {
    int last = Pre(x), next = Succ(x);
    Splay(last), Splay(next, last);
    int del = ch[next][0];
    if(cnt[del] > 1) cnt[del]--, Splay(del);
    else ch[next][0] = 0/*, push_up(next), push_up(last)*/;
}
int n, opt, x;
int main() {
    Insert(INT_MIN);
    Insert(INT_MAX);
    scanf("%d", &n);
    for (int i = 1; i <= n; ++i) {
        scanf("%d %d", &opt, &x);
        if(opt == 1) Insert(x);
        else if(opt == 2) Remove(x);
        else if(opt == 3) Find(x), printf("%d\n", sz[ch[rt][0]]);
        else if(opt == 4) printf("%d\n", val[Kth(x+1)]);
        else if(opt == 5) printf("%d\n", val[Pre(x)]);
        else printf("%d\n", val[Succ(x)]);
    }
    return 0;
}
View Code

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