模板 - Treap

来自这个神仙的https://www.luogu.org/space/show?uid=56230

终于明白了Treap，不知道是因为有了足够的积累了吗？

#include<bits/stdc++.h>
typedef long long ll;
using namespace std;

const int MAXN = 1000000;

int na;
int ch[MAXN + 5][2];
int val[MAXN + 5], dat[MAXN + 5];
int siz[MAXN + 5], cnt[MAXN + 5];
int tot, root;

inline void Init() {
    tot = 0;
    root = 0;
}

inline int NewNode(int v) {
    val[++tot] = v, dat[tot] = rand();
    ch[tot][0] = ch[tot][1] = 0;
    siz[tot] = 1, cnt[tot] = 1;
    return tot;
}

inline void PushUp(int id) {
    siz[id] = siz[ch[id][0]] + siz[ch[id][1]] + cnt[id];
}

inline void Rotate(int &id, int d) {
    int temp = ch[id][d ^ 1];
    ch[id][d ^ 1] = ch[temp][d];
    ch[temp][d] = id;
    id = temp;
    PushUp(ch[id][d]), PushUp(id);
}

inline void Insert(int &id, int v) {
    if(!id)
        id = NewNode(v);
    else {
        if(v == val[id])
            ++cnt[id];
        else {
            int d = v < val[id] ? 0 : 1;
            Insert(ch[id][d], v);
            if(dat[id] < dat[ch[id][d]])
                Rotate(id, d ^ 1);
        }
        PushUp(id);
    }
}

void Remove(int &id, int v) {
    if(!id)
        return;
    else {
        if(v == val[id]) {
            if(cnt[id] > 1) {
                cnt[id]--;
                PushUp(id);
            } else if(ch[id][0] || ch[id][1]) {
                if(!ch[id][1] || dat[ch[id][0]] > dat[ch[id][1]])
                    Rotate(id, 1), Remove(ch[id][1], v);
                else
                    Rotate(id, 0), Remove(ch[id][0], v);
                PushUp(id);
            } else
                id = 0;
        } else {
            v < val[id] ? Remove(ch[id][0], v) : Remove(ch[id][1], v);
            PushUp(id);
        }
    }
}

int GetRank(int id, int v) {
    if(!id)
        return 0;
    else {
        if(v == val[id])
            return siz[ch[id][0]] + 1;
        else if(v < val[id])
            return GetRank(ch[id][0], v);
        else
            return siz[ch[id][0]] + cnt[id] + GetRank(ch[id][1], v);
    }
}

int GetValue(int id, int rk) {
    if(!id)
        return -1;
    else {
        if(rk <= siz[ch[id][0]])
            return GetValue(ch[id][0], rk);
        else if(rk <= siz[ch[id][0]] + cnt[id])
            return val[id];
        else
            return GetValue(ch[id][1], rk - siz[ch[id][0]] - cnt[id]);
    }
}

int GetPrev(int v) {
    int id = root, prev = -1;
    while(id) {
        if(val[id] < v)
            prev = val[id], id = ch[id][1];
        else
            id = ch[id][0];
    }
    return prev;
}

int GetNext(int v) {
    int id = root, next = -1;
    while(id) {
        if(val[id] > v)
            next = val[id], id = ch[id][0];
        else
            id = ch[id][1];
    }
    return next;
}

int main() {
#ifdef Yinku
    freopen("Yinku.in", "r", stdin);
#endif // Yinku
    init();
    int ops;
    scanf("%d", &ops);
    for(int i = 1; i <= ops; i++) {
        int op, x;
        scanf("%d%d", &op, &x);
        if(op == 1)
            Insert(root, x);
        else if(op == 2)
            Remove(root, x);
        else if(op == 3)
            printf("%d\n", GetRank(root, x));
        else if(op == 4)
            printf("%d\n", GetValue(root, x));
        else if(op == 5)
            printf("%d\n", GetPrev(x));
        else if(op == 6)
            printf("%d\n", GetNext(x));
    }
    return 0;
}

那么就再也不需要什么对顶堆了，平衡树最多也就浪费一点空间。
https://www.luogu.org/problem/P3871
https://www.luogu.org/problem/P1801

所以说类似找排名的思想，可以找出树中的前k大的和，前k小的和，或者奇奇怪怪的其他值。也可以像之前那样加入限定，找小于v的至多k个和，每找一个还减掉一个v，总之非常灵活。
下面是找前k小的和的办法。

const int MAXN = 200005;

int ch[MAXN][2];
int val[MAXN], dat[MAXN];
ll siz[MAXN], cnt[MAXN];
ll sum[MAXN];
int tot, root;

inline void Init() {
    tot = 0;
    root = 0;
}

inline int NewNode(int v, ll num) {
    ch[++tot][0] = ch[tot][1] = 0;
    val[tot] = v, dat[tot] = rand();
    siz[tot] = cnt[tot] = num;
    sum[tot] = 1ll * val[tot] * cnt[tot];
    return tot;
}

inline void PushUp(int id) {
    siz[id] = siz[ch[id][0]] + siz[ch[id][1]] + cnt[id];
    sum[id] = sum[ch[id][0]] + sum[ch[id][1]] + 1ll * val[id] * cnt[id];
}

inline void Rotate(int &id, int d) {
    int temp = ch[id][d ^ 1];
    ch[id][d ^ 1] = ch[temp][d];
    ch[temp][d] = id;
    id = temp;
    PushUp(ch[id][d]), PushUp(id);
}

inline void Insert(int &id, int v, ll num) {
    if(!id)
        id = NewNode(v, num);
    else {
        if(v == val[id])
            cnt[id] += num;
        else {
            int d = v < val[id] ? 0 : 1;
            Insert(ch[id][d], v, num);
            if(dat[id] < dat[ch[id][d]])
                Rotate(id, d ^ 1);
        }
        PushUp(id);
    }
}

ll GetSum(int id, ll k) {
    if(!id||k<=0)
        return 0;
    else {
        if(k >= siz[ch[id][0]] + cnt[id])
            return GetSum(ch[id][1], k - siz[ch[id][0]] - cnt[id]) + sum[ch[id][0]] + 1ll * val[id] * cnt[id];
        else if(k >= siz[ch[id][0]])
            return sum[ch[id][0]] + 1ll * val[id] * (k - siz[ch[id][0]]);
        else
            return GetSum(ch[id][0], k);
    }
}