Submission #622433

#	Time	Username	Problem	Language	Result	Execution time	Memory
622433		Jomnoi	Rectangles (IOI19_rect)	C++17	72 / 100	4387 ms	111488 KiB

rect

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

const int MAX_N = 2505;
const int d[4][2] = {{-1, 0}, {0, -1}, {1, 0}, {0, 1}};

int N, M;
long long ans;
vector <vector <int>> A;
vector <vector <bitset <705>>> validRow, validCol;
vector <vector <vector <bool>>> validRow2, validCol2;
int qs[MAX_N][MAX_N];
short dp[MAX_N];
bool visited[MAX_N][MAX_N];

long long count_rectangles(vector <vector <int>> a) {
	N = a.size(), M = a[0].size();
	A.resize(N + 1, vector <int> (M + 1, 0));
	if(min(N, M) < 3) {
		return 0;
	}

	for(int i = 0; i < N; i++) {
		for(int j = 0; j < M; j++) {
			A[i + 1][j + 1] = a[i][j];
		}
	}
	
	if(N <= 700 and M <= 700) {
		validRow.resize(N + 1, vector <bitset <705>> (M + 1, bitset <705> (M + 1)));
		validCol.resize(M + 1, vector <bitset <705>> (N + 1, bitset <705> (N + 1)));
		for(short r = 2; r <= N - 1; r++) {
			for(short c1 = 2; c1 <= M - 1; c1++) {
				int maxA = 0;
				for(short c2 = c1; c2 <= M - 1; c2++) {
					maxA = max(maxA, A[r][c2]);
					if(min(A[r][c1 - 1], A[r][c2 + 1]) > maxA) {
						validRow[r][c1][c2] = 1;
					}
					else {
						validRow[r][c1][c2] = 0;
					}
				}
			}
		}
		for(short c = 2; c <= M - 1; c++) {
			for(short r1 = 2; r1 <= N - 1; r1++) {
				int maxA = 0;
				for(short r2 = r1; r2 <= N - 1; r2++) {
					maxA = max(maxA, A[r2][c]);
					if(min(A[r1 - 1][c], A[r2 + 1][c]) > maxA) {
						validCol[c][r1][r2] = 1;
					}
					else {
						validCol[c][r1][r2] = 0;
					}
				}
			}
		}

		for(short r1 = 2; r1 <= N - 1; r1++) {
			for(short c1 = 2; c1 <= M - 1; c1++) {
				for(short sz = 1; r1 + sz - 1 <= N - 1; sz++) {
					dp[sz] = 0;
					for(short c2 = c1; c2 <= M - 1; c2++) {
						if(validCol[c2][r1][r1 + sz - 1] == true) {
							dp[sz]++;
						}
						else {
							break;
						}
					}
				}
				for(short sz = 1; c1 + sz - 1 <= M - 1; sz++) {
					for(short r2 = r1; r2 <= N - 1; r2++) {
						if(validRow[r2][c1][c1 + sz - 1] == true) {
							if(dp[r2 - r1 + 1] >= sz) {
								ans++;
							}
						}
						else {
							break;
						}
					}
				}
			}
		}
	}
	else if(N == 3) {
		validRow2.resize(N + 1, vector <vector <bool>> (M + 1, vector <bool> (M + 1, false)));
		validCol2.resize(M + 1, vector <vector <bool>> (N + 1, vector <bool> (N + 1, false)));
		for(int r = 2; r <= N - 1; r++) {
			for(int c1 = 2; c1 <= M - 1; c1++) {
				int maxA = 0;
				for(int c2 = c1; c2 <= M - 1; c2++) {
					maxA = max(maxA, A[r][c2]);
					if(min(A[r][c1 - 1], A[r][c2 + 1]) > maxA) {
						validRow2[r][c1][c2] = true;
					}
				}
			}
		}
		for(int c = 2; c <= M - 1; c++) {
			for(int r1 = 2; r1 <= N - 1; r1++) {
				int maxA = 0;
				for(int r2 = r1; r2 <= N - 1; r2++) {
					maxA = max(maxA, A[r2][c]);
					if(min(A[r1 - 1][c], A[r2 + 1][c]) > maxA) {
						validCol2[c][r1][r2] = true;
					}
				}
			}
		}
 
		for(int r1 = 2; r1 <= N - 1; r1++) {
			for(int c1 = 2; c1 <= M - 1; c1++) {
				for(int sz = 1; sz <= max(N, M); sz++) {
					dp[sz] = 0;
				}
				for(int sz = 1; r1 + sz - 1 <= N - 1; sz++) {
					for(int c2 = c1; c2 <= M - 1; c2++) {
						if(validCol2[c2][r1][r1 + sz - 1] == true) {
							dp[sz]++;
						}
						else {
							break;
						}
					}
				}
				for(int sz = 1; c1 + sz - 1 <= M - 1; sz++) {
					for(int r2 = r1; r2 <= N - 1; r2++) {
						if(validRow2[r2][c1][c1 + sz - 1] == true) {
							if(dp[r2 - r1 + 1] >= sz) {
								ans++;
							}
						}
						else {
							break;
						}
					}
				}
			}
		}
	}
	else {
		for(int i = 1; i <= N; i++) {
			for(int j = 1; j <= M; j++) {
				qs[i][j] = qs[i - 1][j] + qs[i][j - 1] - qs[i - 1][j - 1] + A[i][j];
			}
		}

		for(int i = 1; i <= N; i++) {
			for(int j = 1; j <= M; j++) {
				if(A[i][j] == 0 and visited[i][j] == false) {
					visited[i][j] = true;
					int minR = N, maxR = 1, minC = M, maxC = 1;
					queue <pair <int, int>> q;
					q.emplace(i, j);
					while(!q.empty()) {
						auto [ux, uy] = q.front();
						q.pop();

						minR = min(minR, ux);
						maxR = max(maxR, ux);
						minC = min(minC, uy);
						maxC = max(maxC, uy);
						for(int ii = 0; ii < 4; ii++) {
							int vx = ux + d[ii][0], vy = uy + d[ii][1];
							if(vx < 1 or vx > N or vy < 1 or vy > M) {
								continue;
							}

							if(visited[vx][vy] == false and A[vx][vy] == 0) {
								visited[vx][vy] = true;
								q.emplace(vx, vy);
							}
						}
					}

					if(minR > 1 and minC > 1 and maxR < N and maxC < M and qs[maxR][maxC] - qs[maxR][minC - 1] - qs[minR - 1][maxC] + qs[minR - 1][minC - 1] == 0) {
						ans++;
					}
				}
			}
		}
	}
	return ans;
}

• 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