P3769 [CH弱省胡策R2]TATT [KD-Tree]

Posted 2021-02-20 isaunoya

四维显然不能跑，我们直接排序一下，然后三维数点，插入到 kdt，dp 一下即可。

// by Isaunoya
#include<bits/stdc++.h>
#define int long long
using namespace std;
struct io {
	char buf[1 << 27 | 3], *s;
	int f;
	io() { f = 0, buf[fread(s = buf, 1, 1 << 27, stdin)] = ‘
‘; }
	io& operator >> (int&x) {
		for(x = f = 0; !isdigit(*s); ++s) f |= *s  == ‘-‘;
		while(isdigit(*s)) x = x * 10 + (*s++ ^ 48);
		return x = f ? -x : x, *this;
	}
};
int f = 0, flag = 0;
const int K = 4;
const int maxn = 1e5 + 51;
struct point {
	int d[K], w;
	bool operator < (const point& p) const {
		if(d[f] ^ p.d[f]) { return d[f] < p.d[f]; }
		for(int i = 0 ; i < K - flag ; i ++) {
			if(d[i] ^ p.d[i]) { return d[i] < p.d[i]; }
		}
		return 0;
	}
};

void cmax(int&x, const int&y) {
	if(x < y) x = y;
}
void cmin(int&x, const int&y) {
	if(x > y) x = y;
}

const double alpha = 0.75;
template < short K >
struct KDT {
#define ls son[0]
#define rs son[1]
	struct tree {
		int sz, mxw;
		tree *son[2];
		point range, mn, mx;
		void up() {
			sz = ls -> sz + rs -> sz + 1;
			mxw = range.w;
			cmax(mxw, ls -> mxw);
			cmax(mxw, rs -> mxw);
			mx = mn = range;
			for(int i = 0 ; i < K ; i ++) {
				cmin(mn.d[i], ls -> mn.d[i]);
				cmin(mn.d[i], rs -> mn.d[i]);
				cmax(mx.d[i], ls -> mx.d[i]);
				cmax(mx.d[i], rs -> mx.d[i]);
			}
		}
		bool unb() {
			return ls -> sz > sz * alpha || rs -> sz > sz * alpha;
		}
		bool in(point a, point b) {
			for(int i = 0 ; i < K ; i ++)
				if(a.d[i] > mn.d[i] || b.d[i] < mx.d[i])
					return 0;
			return 1;
		}
		bool out(point a, point b) {
			for(int i = 0 ; i < K ; i ++)
				if(a.d[i] > mx.d[i] || b.d[i] < mn.d[i])
					return 1;
			return 0;
		}
		bool at(point a, point b) {
			for(int i = 0 ; i < K ; i ++)
				if(range.d[i] < a.d[i] || range.d[i] > b.d[i])
					return 0;
			return 1;
		}
	} pool[maxn], * tail, * null, * root, * rec[maxn];
	int top;
	point down;
	
	void init() {
		tail = pool;
		null = tail ++;
		for(int i = 0 ; i < K ; i ++)
			null -> mn.d[i] = 1e18;
		for(int i = 0 ; i < K ; i ++)
			null -> mx.d[i] = -1e18;
		down = null -> mx;
		null -> son[0] = null -> son[1] = null;
		root = null;
	}
	
	tree * newnode(point x) {
		tree *p = top ? rec[top --] : tail ++;
		p -> son[0] = p -> son[1] = null;
		p -> range = p -> mn = p -> mx = x;
		p -> mxw = x.w, p -> sz = 1;
		return p;
	}
	
	point b[maxn];
	int cnt;
	void trv(tree *p) {
		if(p == null) return;
		trv(p -> ls);
		b[++ cnt] = p -> range;
		rec[++ top] = p;
		trv(p -> rs);
	}
	
	tree * build(int l, int r, int d) {
		if(l > r) return null;
		int mid = l + r >> 1;
		f = d;
		nth_element(b + l, b + mid, b + r + 1);
		tree * p = newnode(b[mid]);
		if(l == r) return p;
		p -> ls = build(l, mid - 1, (d + 1) % K);
		p -> rs = build(mid + 1, r, (d + 1) % K);
		p -> up(); return p;
	}
	
	void rebld(tree*&p) {
		cnt = 0, trv(p), p = build(1, cnt, 0);
	}
	
	int ans;
	void qry(tree*p, point a,point b) {
		if(p == null) return;
		if(p -> out(a, b)) return;
		if(p -> in(a, b)) {
			cmax(ans,  p -> mxw);
			return;
		}
		cmax(ans, p -> at(a, b)? p -> range.w : 0);
		if(p -> ls -> mxw > ans) qry(p -> ls, a, b);
		if(p -> rs -> mxw > ans) qry(p -> rs, a, b);
	}
	
	tree ** ins(tree *&p, point x, int d) {
		if(p == null) {
			p = newnode(x);
			return &null;
		}
		tree **unb = ins(p -> son[p -> range.d[d] < x.d[d]], x, (d + 1) % K);
		p -> up();
		if(p -> unb()) unb = &p;
		return unb;
	}
	
	int qry(point up) {
		ans = 0;
		qry(root, down, up);
		return ans;
	}
	
	void ins(point p) {
		tree ** unb = ins(root, p, 0);
		if(*unb == null) return;
		rebld(*unb);
	}
};

KDT <K - 1> kdt;

point a[maxn];
signed main() {
#ifdef LOCAL
	freopen("testdata.in", "r", stdin);
#endif
	kdt.init();
	int n;
//	io in;
#define in cin
	ios :: sync_with_stdio(false);
	cin.tie(nullptr);
	cout.tie(nullptr);
	in >> n;
	for(int i = 1 ; i <= n ; i ++) {
		for(int j = 0 ; j < K ; j ++) {
			in >> a[i].d[j];
		}
	}
	sort(a + 1, a + n + 1);
	flag = 1;
	for(int i = 1 ; i <= n ; i ++) {
		for(int j = 0 ; j < K - 1 ; j ++)
			a[i].d[j] = a[i].d[j + 1];
	}
	int ans = 0;
	for(int i = 1 ; i <= n ; i ++) {
		a[i].w = kdt.qry(a[i]) + 1;
		ans = max(ans, a[i].w);
		kdt.ins(a[i]);
	}
	cout << ans << ‘
‘;
	return 0;
}