Submission #769717

#	Time	Username	Problem	Language	Result	Execution time	Memory
769717		SanguineChameleon	Rectangles (IOI19_rect)	C++17	72 / 100	1320 ms	1048576 KiB

rect

#include "rect.h"
#include <bits/stdc++.h>
using namespace std;

const int maxn = 2.5e3 + 20;
int a[maxn][maxn];
int pref[maxn][maxn];
int mx[maxn];
int streak[maxn];
vector<pair<int, int>> cand_left[maxn][maxn];
vector<pair<int, int>> cand_up[maxn][maxn];
vector<pair<int, int>> row_queries[maxn][maxn];
vector<pair<int, int>> col_queries[maxn][maxn];
int n, m;
bool sub6;

void add_left(int row, int lt, int rt) {
	if (lt > rt) {
		return;
	}
	if (sub6 && (a[row][lt - 1] == 0 || a[row][rt + 1] == 0)) {
		return;
	}
	row_queries[lt][rt].emplace_back(row, cand_left[row][lt].size());
	cand_left[row][lt].emplace_back(rt - lt + 1, -1);
}

void find_left(int row) {
	vector<int> q;
	for (int i = 1; i <= m; i++) {
		while (!q.empty() && a[row][i] > a[row][q.back()]) {
			q.pop_back();
		}
		if (!q.empty() && a[row][i] < a[row][q.back()]) {
			add_left(row, q.back() + 1, i - 1);
		}
		q.push_back(i);
	}
	q.clear();
	for (int i = m; i >= 1; i--) {
		while (!q.empty() && a[row][i] > a[row][q.back()]) {
			q.pop_back();
		}
		if (!q.empty()) {
			add_left(row, i + 1, q.back() - 1);
		}
		q.push_back(i);
	}
}

void add_up(int col, int lt, int rt) {
	if (lt > rt) {
		return;
	}
	if (sub6 && (a[lt - 1][col] == 0 || a[rt + 1][col] == 0)) {
		return;
	}
	col_queries[lt][rt].emplace_back(col, cand_up[lt][col].size());
	cand_up[lt][col].emplace_back(rt - lt + 1, -1);
}

void find_up(int col) {
	vector<int> q;
	for (int i = 1; i <= n; i++) {
		while (!q.empty() && a[i][col] > a[q.back()][col]) {
			q.pop_back();
		}
		if (!q.empty() && a[i][col] < a[q.back()][col]) {
			add_up(col, q.back() + 1, i - 1);
		}
		q.push_back(i);
	}
	q.clear();
	for (int i = n; i >= 1; i--) {
		while (!q.empty() && a[i][col] > a[q.back()][col]) {
			q.pop_back();
		}
		if (!q.empty()) {
			add_up(col, i + 1, q.back() - 1);
		}
		q.push_back(i);
	}
}

void solve_row() {
	for (int lt = 1; lt <= m; lt++) {
		for (int i = 1; i <= n; i++) {
			mx[i] = 0;
		}
		for (int rt = lt; rt <= m; rt++) {
			streak[n + 1] = 0;
			for (int i = n; i >= 1; i--) {
				mx[i] = max(mx[i], a[i][rt]);
				if (mx[i] < a[i][lt - 1] && mx[i] < a[i][rt + 1]) {
					streak[i] = streak[i + 1] + 1;
				}
				else {
					streak[i] = 0;
				}
			}
			for (auto q: row_queries[lt][rt]) {
				int row = q.first;
				int id = q.second;
				cand_left[row][lt][id].second = streak[row];
			}
		}
	}
}

void solve_col() {
	for (int lt = 1; lt <= n; lt++) {
		for (int i = 1; i <= m; i++) {
			mx[i] = 0;
		}
		for (int rt = lt; rt <= n; rt++) {
			streak[m + 1] = 0;
			for (int i = m; i >= 1; i--) {
				mx[i] = max(mx[i], a[rt][i]);
				if (mx[i] < a[lt - 1][i] && mx[i] < a[rt + 1][i]) {
					streak[i] = streak[i + 1] + 1;
				}
				else {
					streak[i] = 0;
				}
			}
			for (auto q: col_queries[lt][rt]) {
				int col = q.first;
				int id = q.second;
				cand_up[lt][col][id].second = streak[col];
			}
		}
	}
}

int get(int lx, int ly, int rx, int ry) {
	return pref[rx][ry] - pref[rx][ly - 1] - pref[lx - 1][ry] + pref[lx - 1][ly - 1];
}

bool check(int lx, int ly, int rx, int ry) {
	return get(lx, ly, rx, ry) == 0 && get(lx - 1, ly, lx - 1, ry) == ry - ly + 1 && get(rx + 1, ly, rx + 1, ry) == ry - ly + 1 && get(lx, ly - 1, rx, ly - 1) == rx - lx + 1 && get(lx, ry + 1, rx, ry + 1) == rx - lx + 1;
}

long long count_rectangles(vector<vector<int>> _a) {
	n = _a.size();
	m = _a[0].size();
	if (n < 3 || m < 3) {
		return 0;
	}
	sub6 = true;
	for (int i = 1; i <= n; i++) {
		for (int j = 1; j <= m; j++) {
			a[i][j] = _a[i - 1][j - 1];
			sub6 &= (a[i][j] <= 1);
		}
	}
	for (int i = 1; i <= n; i++) {
		find_left(i);
	}
	for (int i = 1; i <= m; i++) {
		find_up(i);
	}
	if (sub6) {
		for (int i = 1; i <= n; i++) {
			for (int j = 1; j <= m; j++) {
				pref[i][j] = pref[i][j - 1] + a[i][j];
			}
		}
		for (int i = 1; i <= n; i++) {
			for (int j = 1; j <= m; j++) {
				pref[i][j] += pref[i - 1][j];
			}
		}
		int res = 0;
		for (int i = 1; i <= n; i++) {
			for (int j = 1; j <= m; j++) {
				for (auto p1: cand_left[i][j]) {
					for (auto p2: cand_up[i][j]) {
						if (check(i, j, i + p2.first - 1, j + p1.first - 1)) {
							res++;
						}
					}
				}
			}
		}
		return res;
	}
	else {
		solve_row();
		solve_col();
		int res = 0;
		for (int i = 1; i <= n; i++) {
			for (int j = 1; j <= m; j++) {
				for (auto p1: cand_left[i][j]) {
					for (auto p2: cand_up[i][j]) {
						if (p1.second >= p2.first && p2.second >= p1.first) {
							res++;
						}
					}
				}
			}
		}
		return res;
	}
}

• 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: 0 / 28