Submission #445466

#	Time	Username	Problem	Language	Result	Execution time	Memory
445466		grt	3D Histogram (COCI20_histogram)	C++17	110 / 110	158 ms	15248 KiB

histogram

#include <bits/stdc++.h>
#define ST first
#define ND second
#define PB push_back
 
using namespace std;
using ll = long long;
using pi = pair<int,int>;
using vi = vector<int>;
 
const int nax = 200 * 1000 + 10;
int n;
int a[nax], b[nax], f[nax], g[nax];

struct Point {
	ll x, y;
	int id;
};

Point lines[nax];
ll ans;
vector<Point>S1, S2;
int ptr, last;
 
ll intersect(Point&x, Point&y, Point&z) {
	return (z.x - x.x) * (y.y - x.y) - (y.x - x.x)*(z.y - x.y);
}
 
ll get_mx(vector<Point>&vec, int x) {
	if((int)vec.size() == 0) return -1;
	while((int)vec.size() >= 2 && (ll)vec.back().x * x + vec.back().y <= (ll)vec[(int)vec.size() - 2].x * x + vec[(int)vec.size() - 2].y) {
		vec.pop_back();
	}
	return (ll)vec.back().x * x + vec.back().y;
}
 
ll get_mx2(int x) {
	if((int)S2.size() == 0) return -1;
	while(ptr + 1 < (int)S2.size() && S2[ptr+1].x * x + S2[ptr+1].y >= S2[ptr].x * x + S2[ptr].y) {
		ptr++;
	}
	return S2[ptr].x * x + S2[ptr].y;
}

vi rem[nax];
 
void rec(int l, int r) {
	int mid = ((l + r) >> 1);
	if(l <= mid - 1) rec(l, mid - 1);
	if(mid + 1 <= r) rec(mid + 1, r);
	f[mid] = a[mid];
	g[mid] = b[mid];
	lines[mid] = {g[mid], (ll)g[mid] * mid, mid};
	for(int i = mid - 1; i >= l; --i) {
		f[i] = min(f[i + 1], a[i]);
		g[i] = min(g[i + 1], b[i]);
		lines[i] = {g[i], (ll)g[i] * (-i + 1), i};
	}
	for(int i = mid + 1; i <= r; ++i) {
		f[i] = min(f[i - 1], a[i]);
		g[i] = min(g[i - 1], b[i]);
		lines[i] = {g[i], (ll)g[i] * i, i};
	}
	int lp, rp, l2, r2;
	rp = r;
	for(lp = l; lp <= mid; ++lp) {
		while(rp >= mid && (f[lp] > f[rp] || g[lp] > g[rp])) {
			rp--;
		}
		if(rp >= mid) {
			ans = max(ans, (ll)f[lp] * g[lp] * (rp - lp + 1));
		}
	}
	lp = l;
	for(rp = r; rp >= mid; rp--) {
		while(lp <= mid && (f[rp] > f[lp] || g[rp] > g[lp])) {
			lp++;
		}
		if(lp <= mid) {
			ans = max(ans, (ll)f[rp] * g[rp] * (rp - lp + 1));
		}
	}
	// --------------------------
	rp = r;
	r2 = r;
	S1.clear(); S2.clear();
	last = r + 1;
	ptr = 0;
	S1.PB(lines[r]);
	for(int i = mid; i <= r; ++i) rem[i].clear();
	for(lp = l; lp <= mid; lp++) {
		while(r2 - 1 >= mid && (g[lp] >= g[r2 - 1])) {
			r2--;
			if((int)S1.size() >= 1 && S1.back().x == lines[r2].x) continue;
			while((int)S1.size() >= 2 && intersect(S1.back(), lines[r2], S1[(int)S1.size() - 2]) <= 0) {
				S1.pop_back();
			}
			S1.PB(lines[r2]);
			// add
		}
		while(rp >= mid && (f[lp] > f[rp])) {
			rp--;
			// erase
		}
		if(rp >= mid && g[lp] >= g[r2] && r2 <= rp) {
			// [r2, rp]
			while(S2.size() > 0 && S2.back().id >= rp + 1) {
				if(ptr > 0) ptr--;
				reverse(rem[S2.back().id].begin(), rem[S2.back().id].end());
				int id = S2.back().id;
				S2.pop_back();
				for(int x : rem[id]) {
					S2.PB(lines[x]);
				}
				// must add points
			}
			if((int)S1.size() > 0 && S1[0].id >= rp + 1) {
				int nxt = S1.back().id;
				while((int)S1.size() > 0) {
					S1.pop_back();
				}
				for(int i = nxt; i < last; ++i) {
					if((int)S2.size() >= 1 && S2.back().x == lines[i].x) continue;
					while((int)S2.size() >= 2 && intersect(S2.back(), lines[i], S2[(int)S2.size() - 2]) >= 0) {
						rem[i].PB(S2.back().id);
						S2.pop_back();
					}
					S2.PB(lines[i]);
				}
				last = nxt;
				ptr = 0;
			}
			while(S2.size() > 0 && S2.back().id >= rp + 1) {
				if(ptr > 0) ptr--;
				reverse(rem[S2.back().id].begin(), rem[S2.back().id].end());
				int id = S2.back().id;
				S2.pop_back();
				for(int x : rem[id]) {
					S2.PB(lines[x]);
				}
				// must add points
				
			}
			ll w1 = get_mx(S1, -lp + 1);
			ll w2 = get_mx2(-lp + 1);
			//cerr << lp << " " << r2 << " " << rp << " " << max(w1, w2) * f[lp] << "\n";
			ans = max(ans, max(w1,w2) * f[lp]);
		}
	}
	// ---------------------------
	lp = l;
	l2 = l;
	lines[mid] = {(ll)g[mid], (ll)g[mid] * (-mid + 1), mid};
	S1.clear(); S2.clear();
	S1.PB(lines[l]);
	ptr = 0;
	last = l - 1;
	for(int i = l; i <= mid; ++i) rem[i].clear();
	for(rp = r; rp >= mid; rp--) {
		while(l2 + 1 <= mid && (g[rp] >= g[l2 + 1])) {
			l2++;
			if((int)S1.size() >= 1 && S1.back().x == lines[l2].x) continue;
			while((int)S1.size() >= 2 && intersect(S1.back(), lines[l2], S1[(int)S1.size() - 2]) <= 0) {
				S1.pop_back();
			}
			S1.PB(lines[l2]);
			// add
		}
		while(lp <= mid && (f[rp] > f[lp])) {
			lp++;
		}
		if(lp <= mid && g[rp] >= g[l2] && lp <= l2) {
			// [r2, rp]
			// ans = max(ans, ask(lp, l2, rp) * f[rp]);
			while(S2.size() > 0 && S2.back().id <= lp - 1) {
				if(ptr > 0) ptr--;
				reverse(rem[S2.back().id].begin(), rem[S2.back().id].end());
				int id = S2.back().id;
				S2.pop_back();
				for(int x : rem[id]) {
					S2.PB(lines[x]);
				}
				// must add points
			}
			if((int)S1.size() > 0 && S1[0].id <= lp - 1) {
				int nxt = S1.back().id;
				while((int)S1.size() > 0) {
					S1.pop_back();
				}
				for(int i = nxt; i > last; --i) {
					if((int)S2.size() >= 1 && S2.back().x == lines[i].x) continue;
					while((int)S2.size() >= 2 && intersect(S2.back(), lines[i], S2[(int)S2.size() - 2]) >= 0) {
						rem[i].PB(S2.back().id);
						S2.pop_back();
					}
					S2.PB(lines[i]);
				}
				last = nxt;
				ptr = 0;
			}
			while(S2.size() > 0 && S2.back().id <= lp - 1) {
				if(ptr > 0) ptr--;
				reverse(rem[S2.back().id].begin(), rem[S2.back().id].end());
				int id = S2.back().id;
				S2.pop_back();
				for(int x : rem[id]) {
					S2.PB(lines[x]);
				}
				// must add points
			}
			ll w1 = get_mx(S1, rp);
			ll w2 = get_mx2(rp);
			//if(mid == 1) {
				//cerr << rp << ":\n";
				//for(auto x : S1) {
					//cerr << x.x << " " << x.y << " " << x.id << "\n";
				//}
				//cerr << "---\n";
				//for(auto x : S2) {
					//cerr << x.x << " " << x.y << " " << x.id << "\n";
				//}
				//cerr << "---\n";
			//}
			ans = max(ans, max(w1,w2) * f[rp]);
		}
	}
	
	
}
 
int main() {
	ios_base::sync_with_stdio(0);
	cin.tie(0);
	cin >> n;
	for(int i = 0; i < n; ++i) {
		cin >> a[i] >> b[i];
	}
	rec(0, n - 1);
	cout << ans;
}

• Subtask 1: 20 / 20
• Subtask 2: 90 / 90