Submission #1282364

#TimeUsernameProblemLanguageResultExecution timeMemory
1282364c4lTeam Contest (JOI22_team)C++17
64 / 100
2122 ms708816 KiB
#include <bits/stdc++.h>
// #define int long long
using namespace std;
using ll = long long;
const ll MOD = 1000000007LL;
const int BUF_SZ = 1 << 15;

inline namespace Input {
char buf[BUF_SZ];
int pos = 0;
int len = 0;
char next_char() {
	if (pos == len) {
		pos = 0;
		len = (int)fread(buf, 1, BUF_SZ, stdin);
		if (!len) { return EOF; }
	}
	return buf[pos++];
}

// đọc 64-bit signed
ll read_ll() {
	ll x = 0;
	char ch;
	int sgn = 1;
	// skip đến digit hoặc dấu '-'
	while (!isdigit(ch = next_char())) {
		if (ch == '-') { sgn = -1; break; }
	}
	// nếu vừa gặp '-', lấy char tiếp theo (nếu là EOF thì behavior như cũ của bạn)
	if (ch == '-') ch = next_char();
	x = ch - '0';
	while (isdigit(ch = next_char())) {
		x = x * 10 + (ch - '0');
	}
	return x * sgn;
}
} // namespace Input

inline namespace Output {
char buf[BUF_SZ];
int pos = 0;

void flush_out() {
	fwrite(buf, 1, pos, stdout);
	pos = 0;
}

void write_char(char c) {
	if (pos == BUF_SZ) flush_out();
	buf[pos++] = c;
}

void write_ll(ll x) {
	static char num_buf[100];
	if (x < 0) write_char('-');
	// chuyển sang unsigned để xử lý LLONG_MIN đúng
	unsigned long long ux = x < 0 ? (unsigned long long)(-(x + 1)) + 1ULL : (unsigned long long)x;
	int len = 0;
	while (ux >= 10ULL) {
		num_buf[len++] = char('0' + (ux % 10ULL));
		ux /= 10ULL;
	}
	write_char(char('0' + ux));
	while (len) write_char(num_buf[--len]);
	write_char('\n');
}

void init_output() { assert(atexit(flush_out) == 0); }
} // namespace Output
struct mem{
	int x, y, z;
};
mem a[150001];
vector<int> luu[600005];
vector<pair<int, int>> tr[600005];
int inf = -1e9;
struct pst{
	struct Node{
		int val;
		int l, r;
		Node(int v){
			val = v;
			l = -1, r= -1;
		}
	};
	vector<Node> luu;
	void clear(){
		luu.clear();
	}
	int build(int start, int end){
		if(start==end){
			Node tmp(inf);
			luu.push_back(tmp);
			return luu.size()-1;
		}else{
			int mid = (start+end)/2;
			Node tmp(inf);
			int t = build(start, mid);
			int p = build(mid+1, end);
			tmp.l = t, tmp.r = p;
			luu.push_back(tmp);
			return luu.size()-1;
		}
	}
	
	int update(int start, int end, int p, int x, int id){
		if(start==end){
			Node tmp(0);
			tmp.val = luu[id].val;
			tmp.val = max(tmp.val, x);
			luu.push_back(tmp);
			return luu.size()-1;
		}else{
			int mid = (start+end)/2;
			Node tmp(0);
			tmp.val = luu[id].val;
			tmp.l = luu[id].l, tmp.r = luu[id].r;
			if(p<=mid){
				int tr = update(start, mid, p, x, luu[id].l);
				tmp.l = tr;
			}else{
				int tr = update(mid+1, end, p, x, luu[id].r);
				tmp.r = tr;
			}
			tmp.val = max(luu[tmp.l].val, luu[tmp.r].val);
			luu.push_back(tmp);
			return luu.size()-1;
		}
	}
	
	int query(int start, int end, int l, int r, int id){
		if(start > r or end<l)return inf;
		if(l<=start and end<=r){
			return luu[id].val;
		}
		int mid = (start+end)/2;
		return max(query(start, mid, l, r, luu[id].l), query(mid+1,end, l, r, luu[id].r));
	}
};

pst cay[600005];
vector<int> seg[600005];
vector<int> pf[600005], lz[600005]; //X
void merge(vector<pair<int, int>> &a, vector<pair<int, int>> &b, vector<pair<int, int>> &c, int node){
	int i = 1, j = 1;
	while(i<a.size() and j<b.size()){
		if(a[i] < b[j]){
			c.push_back(a[i]);
			pf[node].push_back(pf[2*node][i]);
			i++;
		}else{
			c.push_back(b[j]);
			pf[node].push_back(pf[2*node+1][j]);
			j++;
		}
	}
	while(i<a.size()){
		c.push_back(a[i]);
		pf[node].push_back(pf[2*node][i]);
		i++;
	}
	while(j<b.size()){
		c.push_back(b[j]);
		pf[node].push_back(pf[2*node+1][j]);
		j++;
	}
	
}

void merge2(vector<int> &a, vector<int> &b, vector<int> &c){
	int i = 1, j = 1;
	while(i<a.size() and j<b.size()){
		if(a[i] < b[j]){
			c.push_back(a[i]);
			i++;
		}else{
			c.push_back(b[j]);
			j++;
		}
	}
	while(i<a.size()){
		c.push_back(a[i]);
		i++;
	}
	while(j<b.size()){
		c.push_back(b[j]);
		j++;
	}
	
}

void reset(int node, int start, int end){
	tr[node].clear();
	luu[node].clear();
	pf[node].clear();
	lz[node].clear();
	seg[node].clear();
	cay[node].clear();
	if(start!=end){
		int mid = (start+end)/2;
		reset(2*node, start, mid);
		reset(2*node+1, mid+1, end);
	}
}

void build(int node, int start, int end){
	tr[node].push_back({-1, -1});
	luu[node].push_back(-1);
	pf[node].push_back(-1);
	lz[node].push_back(-1);
	if(start==end){
		pf[node].push_back(a[start].x);
		tr[node].push_back({a[start].y, a[start].z});
		luu[node].push_back(a[start].z);
		lz[node].push_back(a[start].z);
		int m=tr[node].size()-1;
		int root = cay[node].build(1, m);
		seg[node].push_back(root);
		for (int i = 1;i<=m;++i){
			int p = lower_bound(luu[node].begin(), luu[node].end(), tr[node][i].second)-luu[node].begin();
			int nr = cay[node].update(1, m, p, pf[node][i], seg[node].back());
			seg[node].push_back(nr);
		}
	}else{
		int mid = (start+end)/2;
		build(2*node, start, mid);
		build(2*node+1, mid+1, end);
		merge(tr[2*node], tr[2*node+1], tr[node], node);
		merge2(luu[2*node], luu[2*node+1], luu[node]);
		int m=tr[node].size()-1;
		int root = cay[node].build(1, m);
		seg[node].push_back(root);
		for (int i = 1;i<=m;++i){
			int p = lower_bound(luu[node].begin(), luu[node].end(), tr[node][i].second)-luu[node].begin();
			int nr = cay[node].update(1, m, p, pf[node][i], seg[node].back());
			seg[node].push_back(nr);
		}
		for (int i = 1;i<=m;++i){
			lz[node].push_back(tr[node][i].second);
			lz[node][i] = max(lz[node][i], lz[node][i-1]);
		}
	}
}

int q1(int node, int start, int end, int l, int r, int y){
	if(start > r or end < l){
		return -1;
	}else if (l<=start and end<=r){
		int p = lower_bound(tr[node].begin(), tr[node].end(), make_pair(y, (int)-1))-tr[node].begin()-1;
		return lz[node][p];
	}else{
		int mid= (start+end)/2;
		return max(q1(2*node, start, mid, l, r, y), q1(2*node+1, mid+1, end, l, r, y));
	}
}

int q2(int node, int start, int end, int l, int r, int y, int z){
	if(start > r or end < l){
		return inf;
	}
	if(l<=start and end<=r){
		int p = lower_bound(tr[node].begin(), tr[node].end(), make_pair(y, (int)-1))-tr[node].begin()-1;
		int m = tr[node].size()-1;
		int q = lower_bound(luu[node].begin(), luu[node].end(), z)-luu[node].begin()-1;
		int sol = cay[node].query(1, m, 1, q, seg[node][p]);
		return sol;
	}
	int mid = (start+end)/2;
	return max(q2(2*node, start, mid, l, r, y, z), q2(2*node+1, mid+1, end, l, r, y, z));
}

signed main(){
	// ios_base::sync_with_stdio(0);
	// cin.tie(0);
	// freopen("team_contest.inp","r",stdin);
	// freopen("team_contest.out","w",stdout);
	init_output();
	int n;
	// cin >> n;
	n = read_ll();
	for (int i = 1;i<=n;++i){
		// cin >> a[i].x >> a[i].y >> a[i].z;
		a[i].x = read_ll();
		a[i].y = read_ll();
		a[i].z = read_ll();
	}
	sort(a+1, a+n+1, [](mem p, mem q){
		return p.x < q.x;
	});
	int tro = 1;
	build(1, 1, n);
	int res = -1;
	for (int i = 2;i<=n;++i){
		while(tro<=n and a[tro].x<=a[i].x){
			tro++;
		}
		int mz = q1(1, 1, n, 1, i-1, a[i].y);
		if(mz >a[i].z){
			int sol = q2(1, 1, n, tro, n, a[i].y, mz);
			if(sol!=inf){
				res = max(res, a[i].y + mz + sol);
			}
		}
	}
	reset(1, 1, n);
	for (int i = 1;i<=n;++i){
		swap(a[i].y, a[i].z);
	}
	tro = 1;
	build(1, 1, n);
	// int res = 0;
	for (int i = 2;i<=n;++i){
		while(tro<=n and a[tro].x<=a[i].x){
			tro++;
		}
		int mz = q1(1, 1, n, 1, i-1, a[i].y);
		if(mz > a[i].z){
			int sol = q2(1, 1, n, tro, n, a[i].y, mz);
			if(sol!=inf){
				res = max(res, a[i].y + mz + sol);
			}
		}
	}
	write_ll(res);
}
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