Submission #1048594

#	Time	Username	Problem	Language	Result	Execution time	Memory
1048594		Halit	Rectangles (IOI19_rect)	C++17	10 / 100	644 ms	456316 KiB

rect

#include "rect.h"
#include <bits/stdc++.h>

struct disjoint_sets {
  int N;
  std::vector<int> size;
  std::vector<int> rank;
  disjoint_sets(int n) {
    N = n;
    size.resize(N);
    for (int i = 0;i < N; ++i) {
      rank.push_back(i);
      size[i] = 1;
    }
  }
  int get(int x) {
    if (rank[x] == x) return x;
    return rank[x] = get(rank[x]);
  }
  void merge(int x, int y) {
    x = get(x);
    y = get(y);
    if (x == y) {
      return;
    }
    rank[y] = rank[x];
    size[x] += size[y];
    size[y] = 0;
  }
};
long long count_rectangles(std::vector<std::vector<int>> a) {
  int N = a.size();
  int M = a[0].size();
  std::vector<std::array<int, 3>> valid_row, valid_col;
  for (int i = 1;i < N-1; ++i) {
    disjoint_sets left(M), right(M);
    std::set<int> num;
    std::map<int, std::vector<int>> idx;
    for (int j = 0;j < M; ++j) {
      num.insert(a[i][j]);
      idx[a[i][j]].push_back(j);
    }
    std::vector<bool> act(M);
    for (int val : num) {
      for (int j : idx[val]) {
        act[j] = true;
        if (j > 0 && act[j-1]) {
          left.merge(j-1, j);
          right.merge(j, j-1);
        } 
        if (j+1 < M && act[j+1]) {
          right.merge(j+1, j);
          left.merge(j, j+1);
        }
      }
      for (int j : idx[val]) {
        if (left.get(j) > 0 && right.get(j) < M-1) {
          valid_row.push_back({i, left.get(j), right.get(j)});
        }
      }
    }
  }
  for (int j = 1;j < M-1; ++j) {
    disjoint_sets up(N), down(N);
    std::set<int> num;
    std::map<int, std::vector<int>> idx;
    for (int i = 0;i < N; ++i) {
      num.insert(a[i][j]);
      idx[a[i][j]].push_back(i);
    }
    std::vector<bool> act(N);
    for (int val : num) {
      for (int i : idx[val]) {
        act[i] = true;
        if (i > 0 && act[i-1]) {
          up.merge(i-1, i);
          down.merge(i, i-1);
        } 
        if (i+1 < N && act[i+1]) {
          down.merge(i+1, i);
          up.merge(i, i+1);
        }
      }
      for (int i : idx[val]) {
        if (up.get(i) > 0 && down.get(i) < N-1) {
          valid_col.push_back({j, up.get(i), down.get(i)});
        }
      }
    }
  }
  /*
  std::cout << "Valid Rows" << std::endl;
  for (auto [row, left, right] : valid_row) {
    std::cout << row+1 << ' ' << left+1 << ' ' << right+1 << std::endl;
  }
  std::cout << "Valid Columns" << std::endl;
  for (auto [col, up, down] : valid_col) {
    std::cout << col+1 << ' ' << up+1 << ' ' << down+1 << std::endl;
  } 
  */
  std::reverse(valid_row.begin(), valid_row.end());
  std::reverse(valid_col.begin(), valid_col.end());
  std::vector<int> row_value(valid_row.size()), col_value(valid_col.size());
  std::vector start(2, std::vector(std::max(N, M), std::vector<std::vector<int>>(std::max(N, M))));
  {
    std::vector last(M+1, std::vector(M+1, int(-1))), dp(M+1, std::vector(M+1, int(0)));
    for (int i = 0;i < valid_row.size(); ++i) {
      auto [row, left, right] = valid_row[i];
      row_value[i] = dp[left][right] = (last[left][right] != row+1 ? 1 : dp[left][right] + 1);
      start[0][row][left].push_back(i);
      last[left][right] = row;
      // std::cout << row+1 << ' ' << left+1 << ' ' << right+1 << " -> row value " << row_value[i] << std::endl;
    }
  }
  {
    std::vector last(N+1, std::vector(N+1, int(-1))), dp(N+1, std::vector(N+1, int(0)));
    for (int i = 0;i < valid_col.size(); ++i) {
      auto [col, up, down] = valid_col[i];
      col_value[i] = dp[up][down] = (last[up][down] != col+1 ? 1 : dp[up][down] + 1);
      start[1][up][col].push_back(i);
      last[up][down] = col;
      // std::cout << col+1 << ' ' << up+1 << ' ' << down+1 << " -> column value " << col_value[i] << std::endl;
    }
  }
  /*
  for (int x = 1;x < N-1; ++x) {
    for (int y = 1;y < M-1; ++y) {
      int k_row = start[0][x][y].size();
      int k_col = start[1][x][y].size();
      if (k_row == 0 || k_col == 0) {
        continue;
      }
      std::vector<int> idx_row(k_row), idx_col(k_col);
      std::iota(idx_row.begin(), idx_row.end(), 0);
      std::iota(idx_col.begin(), idx_col.end(), 0);
      std::sort(idx_row.begin(), idx_row.end(), [&](int i, int j) { return row_value[start[0][x][y][i]] < row_value[start[0][x][y][j]]; });
      std::sort(idx_col.begin(), idx_col.end(), [&](int i, int j) { return valid_col[start[0][x][y][i]][2] < valid_col[start[0][x][y][j]][2]; });
    }   
  } */
  int ans = 0;
  for (int i = 0;i < valid_row.size(); ++i) {
    auto [row, left, right] = valid_row[i];
    // std::cout << "Current row : " << row + 1 << ' ' << left + 1 << ' ' << right + 1 << std::endl;
    for (int j : start[1][row][left]) {
      // std::cout << "Testing..." << std::endl;
      // std::cout << valid_col[j][0] + 1 << ' ' << valid_col[j][1] + 1 << ' ' << valid_col[j][2] + 1 << std::endl;
      if (valid_col[j][2] - valid_col[j][1] + 1 <= row_value[i] && (right - left + 1 <= col_value[j])) {
        ans += 1;
        // std::cout << "OK!" << std::endl;
      }
    }
    // std::cout << std::endl;
  }
  return ans;
}

Compilation message (stderr)

rect.cpp: In function 'long long int count_rectangles(std::vector<std::vector<int> >)':
rect.cpp:107:22: warning: comparison of integer expressions of different signedness: 'int' and 'std::vector<std::array<int, 3> >::size_type' {aka 'long unsigned int'} [-Wsign-compare]
  107 |     for (int i = 0;i < valid_row.size(); ++i) {
      |                    ~~^~~~~~~~~~~~~~~~~~
rect.cpp:117:22: warning: comparison of integer expressions of different signedness: 'int' and 'std::vector<std::array<int, 3> >::size_type' {aka 'long unsigned int'} [-Wsign-compare]
  117 |     for (int i = 0;i < valid_col.size(); ++i) {
      |                    ~~^~~~~~~~~~~~~~~~~~
rect.cpp:141:20: warning: comparison of integer expressions of different signedness: 'int' and 'std::vector<std::array<int, 3> >::size_type' {aka 'long unsigned int'} [-Wsign-compare]
  141 |   for (int i = 0;i < valid_row.size(); ++i) {
      |                  ~~^~~~~~~~~~~~~~~~~~

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