Submission #445388

#	Time	Username	Problem	Language	Result	Execution time	Memory
445388		grt	3D Histogram (COCI20_histogram)	C++17	20 / 110	2568 ms	38800 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];
pair<ll, ll> lines[nax];
ll ans;
vector<pair<ll, ll>>T[(1 << 19)];
int R;

long double intersect(pair<ll,ll>&x, pair<ll,ll>&y) {
	return (long double)(y.ND - x.ND) / (x.ST  - y.ST);
}

void construct(int l, int r) {
	for(int i = l; i <= r; ++i) {
		T[i + R].resize(1);
		T[i + R][0] = lines[i];
	}
	l += R; r += R;
	int memol = l, memor = r;
	while(l/2 > 0) {
		l /= 2; r /= 2;
		for(int i = l; i <= r; ++i) {
			int v = i;
			T[v].clear();
			for(auto x : T[2*v+1]) {
				T[v].PB(x);
			}
			for(auto x : T[2*v]) {
				T[v].PB(x);
			}
		}
	}
	l = memol; r = memor;
	while(l/2 > 0) {
		l /= 2; r /= 2;
		for(int i = l; i <= r; ++i) {
			int v = i;
			vector<pair<ll,ll>>nw = {};
			for(auto x : T[v]) {
				if((int)nw.size() == 0) {
					nw.PB(x);
					continue;
				}
				if(nw.back().ST == x.ST) continue;
				while((int)nw.size() >= 2 && intersect(nw.back(), x) <= intersect(nw.back(), nw[(int)nw.size() - 2])) {
					nw.pop_back();
				}
				nw.PB(x);
			}
			T[v].swap(nw);
		}
	}
}

ll get_mx(vector<pair<ll,ll>>&vec, int x) {
	while((int)vec.size() >= 2 && vec.back().ST * x + vec.back().ND <= vec[(int)vec.size() - 2].ST * x + vec[(int)vec.size() - 2].ND) {
		vec.pop_back();
	}
	return vec.back().ST * x + vec.back().ND;
}

ll ask(int l, int r, int x) {
	l += R; r += R;
	ll w = max(get_mx(T[l], x), get_mx(T[r], x));
	while(l /2 != r/2) {
		if(l % 2 == 0) w = max(w, get_mx(T[l + 1], x));
		if(r % 2 == 1) w = max(w, get_mx(T[r - 1], x));
		l /= 2;
		r /= 2;
	}
	return w;
}

void rec(int l, int r) {
	int mid = (l + r) / 2;
	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};
	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)};
	}
	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};
	}
	construct(mid, r);
	lines[mid] = {g[mid], (ll)g[mid] * (-mid + 1)};
	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;
	for(lp = l; lp <= mid; lp++) {
		while(rp >= mid && (f[lp] > f[rp])) {
			rp--;
			// erase
		}
		while(r2 - 1 >= mid && (g[lp] >= g[r2 - 1])) {
			r2--;
			// add
		}
		if(rp >= mid && g[lp] >= g[r2] && r2 <= rp) {
			// [r2, rp]
			ans = max(ans, ask(r2, rp, -lp + 1) * f[lp]);
		}
	}
	construct(l, mid);
	lp = l;
	l2 = l;
	for(rp = r; rp >= mid; rp--) {
		while(lp <= mid && (f[rp] > f[lp])) {
			lp++;
		}
		while(l2 + 1 <= mid && (g[rp] >= g[l2 + 1])) {
			l2++;
			// add
		}
		if(lp <= mid && g[rp] >= g[l2] && lp <= l2) {
			// [r2, rp]
			ans = max(ans, ask(lp, l2, rp) * 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];
	}
	R = 1;
	while(R < n) R *= 2;
	rec(0, n - 1);
	cout << ans;
}

• Subtask 1: 20 / 20
• Subtask 2: 0 / 90