洛谷P3721 [AH2017/HNOI2017]单旋(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
*/