Submission #569670

#	Time	Username	Problem	Language	Result	Execution time	Memory
569670		ngpin04	Rectangles (IOI19_rect)	C++17	100 / 100	4200 ms	1037044 KiB

rect

#include "rect.h"
#include <bits/stdc++.h>
#define fi first
#define se second
#define mp make_pair
#define TASK ""
#define bit(x) (1LL << (x))
#define getbit(x, i) (((x) >> (i)) & 1)
#define ALL(x) (x).begin(), (x).end() 
using namespace std;
template <typename T1, typename T2> bool mini(T1 &a, T2 b) {
	if (a > b) {a = b; return true;} return false;
}
template <typename T1, typename T2> bool maxi(T1 &a, T2 b) {
	if (a < b) {a = b; return true;} return false;
}
mt19937_64 rd(chrono::steady_clock::now().time_since_epoch().count());

int rand(int l, int r) {
	return l + rd() % (r - l + 1);
}
const int N = 2505;
const int oo = 1e9;
const long long ooo = 1e18;
const int mod = 1e9 + 7; // 998244353;
const long double pi = acos(-1);

vector <pair <int, int>> sr[N][N], sc[N][N];
vector <tuple <int, int, int>> events[N];
vector <int> col[N][N];
vector <int> row[N];

int pos[N][N];
int limc[N][N];
int lim[N][N];
int a[N][N];
int bit[N];
int v[N];
int l[N];
int r[N];
int n,m;

void update(int pos, int val) {
	for (; pos <= m; pos += pos & -pos)
		bit[pos] += val;
}

int getsum(int pos) {
	int res = 0;
	for (; pos; pos -= pos & -pos)
		res += bit[pos];
	return res;
}

void findmax(int a[], int l[], int n) {
	vector <int> s;
	s.push_back(0);
	a[0] = oo;
	for (int i = 1; i <= n; i++) {
		while (a[i] > a[s.back()]) 
			s.pop_back();
		l[i] = s.back();
		s.push_back(i);
	}
}

void addrow(int i, int u, int v) {
	if (sr[u][v].size() && sr[u][v].back().se == i - 1)
		sr[u][v].back().se = i;
	else
		sr[u][v].push_back(mp(i, i));
}

void addcol(int j, int u, int v) {
	if (sc[u][v].size() && sc[u][v].back().se == j - 1) 
		sc[u][v].back().se = j;
	else
		sc[u][v].push_back(mp(j, j));
	col[u][j].push_back(v);
}

void build() {
	for (int i = 1; i <= n; i++) {
		findmax(a[i], l, m);
		reverse(a[i] + 1, a[i] + m + 1);
		findmax(a[i], r, m);
		reverse(a[i] + 1, a[i] + m + 1);
		reverse(r + 1, r + m + 1);
		for (int j = 1; j <= m; j++)
			r[j] = (m - r[j] + 1);
	
		for (int j = 1; j <= m; j++) {
			if (l[j] > 0 && l[j] != j - 1) {
				auto [u, v] = mp(l[j], j);
				addrow(i, u, v);
			}

			if (r[j] <= m && r[j] != j + 1 && a[i][j] < a[i][r[j]]) {
				auto [u, v] = mp(j, r[j]);
				addrow(i, u, v);
			}
		}	
	}
	for (int j = 1; j <= m; j++) {
		for (int i = 1; i <= n; i++)
			v[i] = a[i][j];

		findmax(v, l, n);
		reverse(v + 1, v + n + 1);
		findmax(v, r, n);
		reverse(r + 1, r + n + 1);

		for (int i = 1; i <= n; i++)
			r[i] = (n - r[i] + 1);
	
		for (int i = 1; i <= n; i++) {
			if (l[i] > 0 && l[i] != i - 1) {
				auto [u, v] = mp(l[i], i);
				addcol(j, u, v);
			}

			if (r[i] <= n && r[i] != i + 1 && a[i][j] < a[r[i]][j]) {
				auto [u, v] = mp(i, r[i]);
				addcol(j, u, v);
			}
		}
	}

	for (int l = 1; l <= m; l++)
	for (int r = l + 1; r <= m; r++) 
	for (auto [u, v] : sr[l][r]) {
		// for (int j = u; j <= v; j++)
		// 	events[j].push_back({l, r});
		
		events[u].push_back({l, r, v});
		events[v + 1].push_back({-l, -r, -v});
	}
}

int solve() {
	build();
	int res = 0;

	vector <pair <int, int>> cand;

	for (int i = 1; i < n; i++) {
		for (auto [l, r, v] : events[i]) {
			if (l > 0) {
				pos[l][r] = cand.size();
				lim[l][r] = v;
				cand.push_back({l, r});
			} else {
				l = -l, r = -r;
				pos[cand.back().fi][cand.back().se] = pos[l][r];
				swap(cand[pos[l][r]], cand.back());
				cand.pop_back();
			}
		}

		if (i == 1)
			continue;

		for (int j = 1; j <= m; j++) 
			row[j].clear();

		for (auto [l, r] : cand)
			row[l].push_back(r);

		for (int l = 1; l <= m; l++) {
			sort(ALL(row[l]), [&](int i, int j) {
				return lim[l][i] < lim[l][j];
			});

			sort(ALL(col[i - 1][l + 1]));

			vector <int> p;
			const vector <int> &f = row[l];
			const vector <int> &g = col[i - 1][l + 1];
			for (int it = 0, jt = 0; it < (int) f.size(); it++) {
				int r = f[it];
				// cerr << "seg " << i << " " << l << " " << r << " " << lim[l][r] << "\n";
				while (jt < (int) g.size()) {
					int k = g[jt];

					if (k <= lim[l][r] + 1) {
						// cerr << "update " << i - 1 << " " << k  << "\n";
						pair <int, int> to_find = {l + 1, oo};
						int tmp = prev(upper_bound(ALL(sc[i - 1][k]), to_find))->se;
						update(tmp, 1);
						p.push_back(tmp);
						jt++;
						continue;
					}
					break;
				}

				res += getsum(m) - getsum(r - 2);
				// cerr << res << "\n";
			}

			for (int lim : p)
				update(lim, -1);
		}
	}

	return res;
}

long long count_rectangles(vector<vector<int>> _a) {
	n = _a.size();
	m = _a[0].size();
	for (int i = 1; i <= n; i++) 
	for (int j = 1; j <= m; j++)
		a[i][j] = _a[i - 1][j - 1];
	return solve();
}

//#include "grader.cpp"

• Subtask 1: 8 / 8
• Subtask 2: 7 / 7
• Subtask 3: 12 / 12
• Subtask 4: 22 / 22
• Subtask 5: 10 / 10
• Subtask 6: 13 / 13
• Subtask 7: 28 / 28