oj.uz

Submission #370005

# Submission time Handle Problem Language Result Execution time Memory
370005 2021-02-22T21:43:50 Z penguinhacker 3D Histogram (COCI20_histogram) C++14
110 / 110
 271 ms 5628 KB 
#include <bits/stdc++.h>
using namespace std;

#define ll long long
#define ar array

#define debug(x) cerr << "[" << #x << "] = [" << x << "]\n"

template<class T> ostream& operator<< (ostream& out, vector<T>& v) {
	out << '[';
	for (int i = 0; i < v.size(); ++i) {
		if (i > 0) {
			out << ", ";
		}
		out << v[i];
	}
	return out << ']';
}

struct Line {
	ll m, b;
	ll eval(ll x) {
		return m * x + b;
	}
};

double isect(Line a, Line b) {
	return (double)(a.b - b.b) / (b.m - a.m);
}

int n, a[200000], b[200000];
ll ans = 0;

void cmp(vector<int>& la, vector<int>& lb, vector<int>& ra, vector<int>& rb) {
	for (int i = 0, j = 0; i < la.size(); ++i) {
		while(j < ra.size() && ra[j] >= la[i] && rb[j] >= lb[i]) ++j;
		ans = max(ans, (ll)(i + j + 1) * la[i] * lb[i]);
	}
	/*debug(la);
	debug(lb);
	debug(ra);
	debug(rb);*/
	deque<Line> dq;
	for (int i = 0, j = 0; i < la.size(); ++i) {
		while(j < ra.size() && ra[j] >= la[i]) {
			Line cur = {rb[j], (ll)rb[j] * (j + 2)};
			while(dq.size() > 1) {
				if (cur.m == dq[0].m) {
					if (cur.b <= dq[0].b) break;
					dq.pop_front();
				}
				else {
					if (isect(cur, dq[1]) >= isect(dq[0], dq[1])) dq.pop_front();
					else break;
				}
			}
			dq.push_front(cur);
			while(!dq.empty() && dq.back().m > lb[i])
				dq.pop_back();
			++j;
		}
		while(!dq.empty() && dq.back().m > lb[i])
			dq.pop_back();
		if (dq.empty()) continue;
		int l = 0, r = dq.size() - 1;
		while(l < r) {
			int mid = (l + r + 1) / 2;
			double x = mid == 0 ? -1e9 : isect(dq[mid - 1], dq[mid]);
			if (x <= i) l = mid;
			else r = mid - 1;
		}
		//cerr << la[i] << " " << dq[l].eval(i) << "\n";
		ans = max(ans, la[i] * dq[l].eval(i));
	}
}

void solve(int l, int r) {
	if (l == r) {
		ans = max(ans, (ll)a[l] * b[l]);
		return;
	}
	int mid = (l + r) / 2;
	vector<int> la(1, a[mid]), lb(1, b[mid]), ra(1, a[mid + 1]), rb(1, b[mid + 1]);
	for (int i = mid - 1; i >= l; --i) {
		la.push_back(min(la.back(), a[i]));
		lb.push_back(min(lb.back(), b[i]));
	}
	for (int i = mid + 2; i <= r; ++i) {
		ra.push_back(min(ra.back(), a[i]));
		rb.push_back(min(rb.back(), b[i]));
	}
	//cerr << "RANGE OF [" << l << ", " << r << "]\n";
	cmp(la, lb, ra, rb);
	//cerr << "--SWAPPED--\n";
	cmp(ra, rb, la, lb);
	solve(l, mid);
	solve(mid + 1, r);
}

int main() {
	ios::sync_with_stdio(0);
	cin.tie(0);
	cin >> n;
	for (int i = 0; i < n; ++i) cin >> a[i] >> b[i];
	solve(0, n - 1);
	cout << ans;
	return 0;
}

Compilation message

histogram.cpp: In function 'void cmp(std::vector<int>&, std::vector<int>&, std::vector<int>&, std::vector<int>&)':
histogram.cpp:35:27: warning: comparison of integer expressions of different signedness: 'int' and 'std::vector<int>::size_type' {aka 'long unsigned int'} [-Wsign-compare]
   35 |  for (int i = 0, j = 0; i < la.size(); ++i) {
      |                         ~~^~~~~~~~~~~
histogram.cpp:36:11: warning: comparison of integer expressions of different signedness: 'int' and 'std::vector<int>::size_type' {aka 'long unsigned int'} [-Wsign-compare]
   36 |   while(j < ra.size() && ra[j] >= la[i] && rb[j] >= lb[i]) ++j;
      |         ~~^~~~~~~~~~~
histogram.cpp:44:27: warning: comparison of integer expressions of different signedness: 'int' and 'std::vector<int>::size_type' {aka 'long unsigned int'} [-Wsign-compare]
   44 |  for (int i = 0, j = 0; i < la.size(); ++i) {
      |                         ~~^~~~~~~~~~~
histogram.cpp:45:11: warning: comparison of integer expressions of different signedness: 'int' and 'std::vector<int>::size_type' {aka 'long unsigned int'} [-Wsign-compare]
   45 |   while(j < ra.size() && ra[j] >= la[i]) {
      |         ~~^~~~~~~~~~~

Subtask #1
20.0 / 20.0

# Verdict Execution time Memory Grader output
1 Correct 2 ms 332 KB Output is correct
2 Correct 2 ms 332 KB Output is correct
3 Correct 2 ms 332 KB Output is correct
4 Correct 2 ms 332 KB Output is correct
5 Correct 2 ms 332 KB Output is correct
6 Correct 2 ms 332 KB Output is correct
7 Correct 2 ms 332 KB Output is correct
8 Correct 2 ms 332 KB Output is correct
9 Correct 2 ms 376 KB Output is correct
10 Correct 3 ms 332 KB Output is correct
11 Correct 0 ms 204 KB Output is correct
12 Correct 2 ms 332 KB Output is correct

Subtask #2
90.0 / 90.0

# Verdict Execution time Memory Grader output
1 Correct 2 ms 332 KB Output is correct
2 Correct 2 ms 332 KB Output is correct
3 Correct 2 ms 332 KB Output is correct
4 Correct 2 ms 332 KB Output is correct
5 Correct 2 ms 332 KB Output is correct
6 Correct 2 ms 332 KB Output is correct
7 Correct 2 ms 332 KB Output is correct
8 Correct 2 ms 332 KB Output is correct
9 Correct 2 ms 376 KB Output is correct
10 Correct 3 ms 332 KB Output is correct
11 Correct 0 ms 204 KB Output is correct
12 Correct 2 ms 332 KB Output is correct
13 Correct 189 ms 5184 KB Output is correct
14 Correct 161 ms 5212 KB Output is correct
15 Correct 198 ms 5256 KB Output is correct
16 Correct 231 ms 5472 KB Output is correct
17 Correct 260 ms 5436 KB Output is correct
18 Correct 271 ms 5308 KB Output is correct
19 Correct 269 ms 5628 KB Output is correct
20 Correct 245 ms 5320 KB Output is correct
21 Correct 206 ms 5428 KB Output is correct
22 Correct 244 ms 5548 KB Output is correct
23 Correct 20 ms 844 KB Output is correct
24 Correct 204 ms 5216 KB Output is correct