Submission #1207389

#	Time	Username	Problem	Language	Result	Execution time	Memory
1207389		countless	Rectangles (IOI19_rect)	C++20	72 / 100	5094 ms	1023484 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 {
	short coll, colr, rowl, rowr;

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

	// use static for ref
	static stuff merge(const stuff &a, const stuff &b) {
		return stuff{min(a.coll, b.coll), max(a.colr, b.colr), min(a.rowl, b.rowl), max(a.rowr, b.rowr)};
	}
};

const stuff nothing = stuff{INF, -INF, INF, -INF};

struct twotree {
	int n, m;
	vector<vector<stuff>> tree;
	const vector<vector<stuff>> &base; // avoid copies
	
	twotree(const vector<vector<stuff>> &base) : n(base.size()), m(base[0].size()), tree(4*n, vector<stuff>(4*m)), base(base) {
		buildX(1, 0, n-1);
	}

	void buildY(int x, int l, int r, int y, int ll, int rr) {
		if (ll == rr) {
			if (l == r) {
				tree[x][y] = base[l][ll];
			} else {
				tree[x][y] = stuff::merge(tree[x*2][y], tree[x*2+1][y]);
			}
		} else {
			int m = (ll+rr)/2;
			buildY(x, l, r, y*2, ll, m);
			buildY(x, l, r, y*2+1, m+1, rr);
			tree[x][y] = stuff::merge(tree[x][y*2], tree[x][y*2+1]);
		}
	}

	void buildX(int x, int l, int r) {
		if (l != r) {
			int m = (l+r)/2;
			buildX(x*2, l, m);
			buildX(x*2+1, m+1, r);
		}
		buildY(x, l, r, 1, 0, m-1);
	}

	stuff queryY(int x, int y, int ll, int rr, int qll, int qrr) {
		if (qrr < ll or qll > rr) {
			return nothing;
		}

		if (qll <= ll and rr <= qrr) {
			return tree[x][y];
		}

		int m = (ll+rr)/2;
		return stuff::merge(queryY(x, y*2, ll, m, qll, qrr), queryY(x, y*2+1, m+1, rr, qll, qrr));
	}

	stuff queryX(int x, int l, int r, int ql, int qr, int qll, int qrr) {
		if (qr < l or ql > r) {
			return nothing;
		}

		if (ql <= l and r <= qr) {
			return queryY(x, 1, 0, m-1, qll, qrr);
		}

		int m = (l+r)/2;
		return stuff::merge(queryX(x*2, l, m, ql, qr, qll, qrr), queryX(x*2+1, m+1, r, ql, qr, qll, qrr));
	}

	stuff query(int x, int y, int xx, int yy) {
		return queryX(1, 0, n-1, x, xx, y, yy);
	}
};

ll count_rectangles(vector<vector<int>> a) {
	short n = a.size(), m = a[0].size();
	vector<vector<stuff>> base(n, vector<stuff>(m));
	ll ans = 0;

	stack<short> st;

	// O(nm)
	for (short i = 0; i < n; i++) {
		while (!st.empty()) st.pop();

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

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

			st.push(j);
		}

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

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

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

			st.push(j);
		}
	}

	for (short i = 0; i < m ; i++) {
		while (!st.empty()) st.pop();

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

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

			st.push(j);
		}

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

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

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

			st.push(j);
		}
	}

	twotree tree(base);

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

	// O(1)
	unordered_map<rect, bool, rect_hash> vis;
	auto checkRect = [&](short x, short y, short xx, short 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 = tree.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;
		}

		return 1;
	};

	// O(nm)
	for (short i = 1; i < n - 1; i++) {
		for (short j = 1; j < m - 1; j++) {
			stuff q = base[i][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: 22 / 22
• Subtask 5: 10 / 10
• Subtask 6: 13 / 13
• Subtask 7: 0 / 28