Submission #1206636

#	Time	Username	Problem	Language	Result	Execution time	Memory
1206636		countless	Rectangles (IOI19_rect)	C++20	37 / 100	5118 ms	1114112 KiB

rect

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

typedef long long ll;
typedef long double ld;

const ll MOD = 998244353;
// const ll INF = 1e18;
const int INF = 5e3;
const ld EPS = 1e-12;

#define endl "\n"
#define sp <<" "<<
#define REP(i, a, b) for(ll i = a; i < b; i++)
#define dbg(x) cout << #x << " = " << x << endl
#define mp make_pair
#define pb push_back
#define fi first
#define se second
#define fast_io() ios_base::sync_with_stdio(false); cin.tie(NULL)
#define all(x) (x).begin(), (x).end()
#define rall(x) (x).rbegin(), (x).rend()
#define sz(x) ((ll)(x).size())

struct custom_hash {
	static uint64_t splitmix64(uint64_t x) {
		// http://xorshift.di.unimi.it/splitmix64.c
		x += 0x9e3779b97f4a7c15;
		x = (x ^ (x >> 30)) * 0xbf58476d1ce4e5b9;
		x = (x ^ (x >> 27)) * 0x94d049bb133111eb;
		return x ^ (x >> 31);
	}

	size_t operator()(uint64_t x) const {
		static const uint64_t FIXED_RANDOM = chrono::steady_clock::now().time_since_epoch().count();
		return splitmix64(x + FIXED_RANDOM);
	}
};

struct pair_hash {
	size_t operator()(const pair<int, int> &p) const {
		size_t h1 = custom_hash{}(p.first);
		size_t h2 = custom_hash{}(p.second);
		return h1 ^ (h2 << 1);
	}
};

struct rect_hash {
	size_t operator()(const pair<pair<int, int>, pair<int, int>> &p) const {
		size_t h1 = pair_hash{}(p.first);
		size_t h2 = pair_hash{}(p.second);
		return h1 ^ (h2 << 1);
	}
};

using rect = pair<pair<int, int>, pair<int, int>>;

template <typename Key, typename Value>
using hash_map = unordered_map<Key, Value, custom_hash>;

mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());
// uniform_int_distribution<int>(a, b)(rng);
// shuffle(all(a), rng);

struct stuff {
	int coll, colr, rowl, rowr;

	stuff(int coll = -INF, int colr = INF, int rowl = -INF, int rowr = INF) : coll(coll), colr(colr), rowl(rowl), rowr(rowr) {;;}
};

ll count_rectangles(vector<vector<int>> a) {
	ll n = a.size(), m = a[0].size();
	ll logn = log2(n) + 1, logm = log2(m) + 1;
	ll ans = 0;

	vector<vector<vector<vector<stuff>>>> searchr(logn,
		vector<vector<vector<stuff>>>(n,
			vector<vector<stuff>>(logm,
				vector<stuff>(m)
			)
		)
	);

	stack<int> st;

	// O(nm)
	REP(i, 0, n) {
		while (!st.empty()) st.pop();

		REP(j, 0, m) {
			while (!st.empty() and a[i][st.top()] <= a[i][j]) {
				st.pop();
			}

			if (!st.empty()) {
				searchr[0][i][0][j].rowl = st.top();
			}

			st.push(j);
		}

		while (!st.empty()) st.pop();

		for (int j = m-1; j >= 0; j--) {
			while (!st.empty() and a[i][st.top()] <= a[i][j]) {
				st.pop();
			}

			if (!st.empty()) {
				searchr[0][i][0][j].rowr = st.top();
			}

			st.push(j);
		}
	}

	REP(i, 0, m) {
		while (!st.empty()) st.pop();

		REP(j, 0, n) {
			while (!st.empty() and a[st.top()][i] <= a[j][i]) {
				st.pop();
			}

			if (!st.empty()) {
				searchr[0][j][0][i].coll = st.top();
			}

			st.push(j);
		}

		while (!st.empty()) st.pop();

		for (int j = n-1; j >= 0; j--) {
			while (!st.empty() and a[st.top()][i] <= a[j][i]) {
				st.pop();
			}

			if (!st.empty()) {
				searchr[0][j][0][i].colr = st.top();
			}

			st.push(j);
		}
	}

	auto merge = [&](const stuff &a, const stuff &b) -> stuff {
		stuff res;
		res.coll = min(a.coll, b.coll);
		res.colr = max(a.colr, b.colr);
		res.rowl = min(a.rowl, b.rowl);
		res.rowr = max(a.rowr, b.rowr);
		return res;	
	};

	// O(nm lg n lg m)
	REP(i, 0, n) {
		REP(j, 1, logm) {
			for (int k = 0; k + (1 << j) - 1 < m; k++) {
				searchr[0][i][j][k] = merge(searchr[0][i][j-1][k], searchr[0][i][j-1][k+(1<<(j-1))]);
			}
		}
	}

	REP(i, 1, logn) {
		for (int j = 0; j + (1 << i) - 1 < n; j++) {
			REP(k, 0, logm) {
				REP(l, 0, m) {
					searchr[i][j][k][l] = merge(searchr[i-1][j][k][l], searchr[i-1][j+(1<<(i-1))][k][l]);
				}
			}
		}
	}

	auto in = [&](int x, int y) -> bool {
		return (0 < x and x < n-1 and 0 < y and y < m-1);
	};

	auto query = [&](int x, int y, int xx, int yy) -> stuff {
		int szx = xx - x + 1, szy = yy - y + 1;
		int lgx = log2(szx), lgy = log2(szy);

		stuff r1 = merge(searchr[lgx][x][lgy][y], searchr[lgx][x][lgy][yy-(1<<lgy)+1]);
		stuff r2 = merge(searchr[lgx][xx-(1<<lgx)+1][lgy][y], searchr[lgx][xx-(1<<lgx)+1][lgy][yy-(1<<lgy)+1]);
		return merge(r1, r2);
	};

	// O(n + m)
	unordered_map<rect, bool, rect_hash> vis;
	auto checkRect = [&](int x, int y, int xx, int yy) -> int {
		if (!in(x,y) or !in(xx, yy)) return 0;

		if (x > xx) swap(x, xx);
		if (y > yy) swap(y, yy);

		if (vis[{{x, y}, {xx, yy}}]) return 0;

		vis[{{x, y}, {xx, yy}}] = true;

		stuff q = query(x, y, xx, yy);

		if (q.coll < x-1 or q.colr > xx+1 or q.rowl < y-1 or q.rowr > yy+1) {
			return 0;
		}
		cerr << x sp y sp xx sp yy << endl;
		cerr << q.coll sp q.colr sp q.rowl sp q.rowr << endl;

		return 1;
	};

	// O(nm (n+m))
	REP(i, 1, n-1) {
		REP(j, 1, m-1) {
			stuff q = searchr[0][i][0][j];
			if (q.coll == -INF or q.colr == INF or q.rowl == -INF or q.rowr == INF) {
				continue;
			}
			ans += checkRect(q.coll+1, q.rowl+1, q.colr-1, q.rowr-1);
		}
	}

	return ans;
}

// int main() {
// 	int n, m; cin >> n >> m;
// 	vector<vector<int>> a(n, vector<int>(m));
// 	REP(i, 0, n) {
// 		REP(j, 0, m) {
// 			cin >> a[i][j];
// 		}
// 	}

// 	cout << count_rectangles(a) << endl;
// }

• Subtask 1: 8 / 8
• Subtask 2: 7 / 7
• Subtask 3: 12 / 12
• Subtask 4: 0 / 22
• Subtask 5: 10 / 10
• Subtask 6: 0 / 13
• Subtask 7: 0 / 28