洛谷P3722 [AH2017/HNOI2017]影魔(线段树 set spaly)

题意

题目链接

sol

这题好毒瘤啊。。

首先要观察到几个性质：

1. 将最小值旋转到根相当于把右子树变为祖先的左子树，然后将原来的根变为当前最小值

2. 上述操作对深度的影响相当于右子树不变，其他的位置-1

然后就可以做了，把询问离线之后离散化一下，建一棵权值线段树表示每个值对应的深度

同时用set维护出已经加入的值

每次先找到后继，看一下有没有左孩子，如果有的话说明前驱一定没有右孩子。

注意随时更新信息

复杂度\(o(nlogn)\)

#include<bits/stdc++.h> 
#define pair pair<ll, ll>
#define mp(x, y) make_pair(x, y)
#define fi first
#define se second
#define ll long long 
#define fin(x) {freopen(#x".in","r",stdin);}
#define fout(x) {freopen(#x".out","w",stdout);}
using namespace std;
const int maxn = 1e6 + 10, mod = 1e9 + 7, inf = 1e9 + 10;
inline int read() {
    char c = getchar(); int x = 0, f = 1;
    while(c < '0' || c > '9') {if(c == '-') f = -1; c = getchar();}
    while(c >= '0' && c <= '9') x = x * 10 + c - '0', c = getchar();
    return x * f;
}
int n, m, opt[maxn], val[maxn], date[maxn], cnt;
void des() {
    sort(date + 1, date + cnt + 1);
    cnt = unique(date + 1, date + cnt + 1) - date - 1;
    for(int i = 1; i <= m; i++) if(opt[i] == 1) val[i] = lower_bound(date + 1, date + cnt + 1, val[i]) - date;
}
set<int> s;
#define ls k << 1
#define rs k << 1 | 1
int add[maxn], root, f[maxn], ll[maxn], rr[maxn];
void ps(int k, int v) {
    add[k] += (rr[k] - ll[k] + 1) * v;
    f[k] += v;
}
void pushdown(int k) {
    if(!f[k]) return ;
    ps(ls, f[k]); ps(rs, f[k]);
    f[k] = 0;
}
void update(int k) {
    add[k] = add[ls] + add[rs];
}
void build(int k, int ll, int rr) {
    if(ll == rr) return ;
    int mid = ll + rr >> 1;
    build(ls, ll, mid); build(rs, mid + 1, rr);
}
void intadd(int k, int l, int r, int ql, int qr, int v) {
    if(ql <= l && r <= qr) {ps(k, v); return ;}
    pushdown(k);
    int mid = l + r >> 1;
    if(ql <= mid) intadd(ls, l, mid, ql, qr, v);
    if(qr  > mid) intadd(rs, mid + 1, r, ql, qr, v);
    update(k);
}
void modify(int k, int l, int r, int p, int v) {
    if(l == r) {add[k] = v; return ;}
    int mid = l + r >> 1;
    pushdown(k);
    if(p <= mid) modify(ls, l, mid, p, v);
    else modify(rs, mid + 1, r, p, v);
    update(k);
}
int query(int k, int l, int r, int p) {
    if(l == r) return add[k];
    int mid = l + r >> 1;
    pushdown(k);
    if(p <= mid) return query(ls, l, mid, p);
    else return query(rs, mid + 1, r, p);
}

#undef ls
#undef rs

#define ls(x) ch[x][0]
#define rs(x) ch[x][1]
int ch[maxn][2], fa[maxn];
void connect(int x, int _fa, int tag) {
    if(x == _fa || (_fa == m + 1)) return ;
    ch[_fa][tag] = x;
    fa[x] = _fa;
}
int insert(int v) {
    if(s.empty()) {root = v; modify(1, 1, m, v, 1); s.insert(v); fa[v] = m + 1; return 1;}
    auto nxt = s.upper_bound(v);
    if(nxt != s.end() && !ls(*nxt)) {
        int pos = *nxt;
        modify(1, 1, m, v, query(1, 1, m, pos) + 1);
        connect(v, pos, 0);
    } else {
        nxt--; int pos = *nxt;
        modify(1, 1, m, v, query(1, 1, m, pos) + 1);
        connect(v, pos, 1);
    }
    s.insert(v);
    return query(1, 1, m, v);
}
int rotatemin() {
    int mn = *s.begin(), v = query(1, 1, m, mn);
    intadd(1, 1, m, mn + 1, fa[mn] - 1, -1);
    intadd(1, 1, m, 1, m, 1);
    modify(1, 1, m, mn, 1); 
    connect(rs(mn), fa[mn], 0); 
    connect(root, mn, 1);
    root = mn; fa[root] = m + 1;
    return v;
}
int rotatemax() {
    auto it = s.end(); it--; 
    int mx = *it, v = query(1, 1, m, mx);
    intadd(1, 1, m, (fa[mx] == m + 1) ? 1 : fa[mx] + 1, mx - 1, -1);
    intadd(1, 1, m, 1, m, 1);
    modify(1, 1, m,  mx, 1); 
    connect(ls(mx), fa[mx], 1);
    connect(root, mx, 0);
    root = mx; fa[root] = m + 1;
    return v;
}
int deletmin() {
    int v = rotatemin(); 
    int mn = *s.begin();  fa[rs(mn)] = m + 1;  root = rs(mn);
    intadd(1, 1, m, 1, m, -1);
    modify(1, 1, m, mn, 0);
    fa[mn] = rs(mn) = ls(mn) = 0; 
    s.erase(mn);
    return v;
}
int deletmax() {
    int v = rotatemax();
    auto it = s.end(); it--;
    int mx = *it;  fa[ls(mx)] = m + 1; root = ls(mx);
    intadd(1, 1, m, 1, m, -1);
    modify(1, 1, m, mx, 0); 
    fa[mx] = ls(mx) = rs(mx) = 0;
    s.erase(mx);
    return v;
}
signed main() {
    m = read();
    for(int i = 1; i <= m; i++) {
        opt[i] = read(); 
        if(opt[i] == 1) val[i] = read(), date[++cnt] = val[i];
    }
    build(1, 1, m);
    des();
    for(int i = 1; i <= m; i++) {
        if(opt[i] == 1) printf("%d\n", insert(val[i]));
        else if(opt[i] == 2) printf("%d\n", rotatemin());
        else if(opt[i] == 3) printf("%d\n", rotatemax());
        else if(opt[i] == 4) printf("%d\n", deletmin());
        else printf("%d\n", deletmax());
    }
    return 0;
}
/*
4
1 39877
1 76497
2
1 6377
*/