Submission #1049416

#	Time	Username	Problem	Language	Result	Execution time	Memory
1049416		Halit	Rectangles (IOI19_rect)	C++17	25 / 100	991 ms	480928 KiB

rect

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

#define int short 

struct FenwickTree {
  std::vector<int32_t> bit;
  int N;
  FenwickTree(int n) {
    N = n+1;
    bit.resize(N+1);
  }
  int32_t sum(int idx) {
    int32_t res = 0;
    for (++idx; idx > 0; idx -= idx & -idx) {
      res += bit[idx];
    }
    return res;
  }
  int32_t get(int l, int r) {
    return sum(r) - sum(l-1);
  }
  void add(int idx, int delta) {
    for (++idx;idx < N; idx += idx & -idx) {
      bit[idx] += delta;
    }
  }
};

struct SegmentTree {
  int N;
  std::vector<int> tree;
  std::vector<int> lazy;
  SegmentTree(int n) {
    N = n;
    tree.resize(4*N);
    lazy.resize(4*N);
  }
  void push(int node, int left, int right) {
    if (lazy[node]) {
      tree[node] = 0;
    }
    if (left != right) {
      lazy[node*2] |= lazy[node];
      lazy[node*2+1] |= lazy[node];
    }
    lazy[node] = 0;
  }
  int get(int node, int left, int right, int tl, int tr) {
    push(node, left, right);
    if (left > tr || right < tl) {
      return 0;
    }
    if (left >= tl && right <= tr) {
      return tree[node];
    }
    return get(node*2, left, (left+right)/2, tl, tr) + get(node*2+1, (left+right)/2+1, right, tl, tr);
  }
  void add(int node, int left, int right, int idx) {
    push(node, left, right);
    if (left > idx || right < idx) {
      return;
    }
    if (left == idx && right == idx) {
      tree[node] += 1;
      return;
    }
    add(node*2, left, (left+right)/2, idx);
    add(node*2+1, (left+right)/2+1, right, idx);
    tree[node] = tree[node*2] + tree[node*2+1];
  }
  void clear() {
    lazy[1] = 1;
  }
  int get(int left, int right) {
    return get(1, 0, N-1, left, right);
  }
  void add(int idx) {
    add(1, 0, N-1, idx);
  }
};
 
struct disjoint_sets {
  int N;
  std::vector<int> rank;
  disjoint_sets(int n) {
    N = n;
    for (int i = 0;i < N; ++i) {
      rank.push_back(i);
    }
  }
  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];
  }
  void clear() {
    for (int i = 0;i < N; ++i) {
      rank[i] = i;
    }
  }
};
long long count_rectangles(std::vector<std::vector<int32_t>> a) {
  int N = a.size();
  int M = a[0].size();
  std::set<std::array<int, 3>> temp_valid_row, temp_valid_col;
  {
    std::vector<int> idx(M);
    std::iota(idx.begin(), idx.end(), 0);
    disjoint_sets left(M), right(M);
    for (int i = 1;i < N-1; ++i) {
      left.clear(); right.clear();
      std::sort(idx.begin(), idx.end(), [&](int j, int k) { return a[i][j] < a[i][k]; });
      int first = 0;
      std::vector<bool> act(M);
      for (int jj = 0;jj < M; ++jj) {
        int j = idx[jj];
        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);
        }
        if (jj+1 < M && a[i][idx[jj+1]] == a[i][j]) {
          continue;
        } else {
          for (int k = first;k <= jj; ++k) {
            if (left.get(idx[k]) > 0 && right.get(idx[k]) < M-1) {
              temp_valid_row.insert({i, left.get(idx[k]), right.get(idx[k])});
            }
          }
          first = jj+1;
        }
      }
    }
  }
    /*
    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) {
          temp_valid_row.insert({i, left.get(j), right.get(j)});
        }
      }
    }
    */
  {
    std::vector<int> idx(N);
    std::iota(idx.begin(), idx.end(), 0);
    disjoint_sets left(N), right(N);
    for (int j = 1;j < M-1; ++j) {
      left.clear(); right.clear();
      std::sort(idx.begin(), idx.end(), [&](int i, int k) { return a[i][j] < a[k][j]; });
      int first = 0;
      std::vector<bool> act(N);
      for (int imi = 0;imi < N; ++imi) {
        int i = idx[imi];
        act[i] = true;
        if (i > 0 && act[i-1]) {
          left.merge(i-1, i);
          right.merge(i, i-1);
        }
        if (i+1 < N && act[i+1]) {
          right.merge(i+1, i);
          left.merge(i, i+1);
        }
        if (imi+1 < N && a[idx[imi+1]][j] == a[i][j]) {
          continue;
        } else {
          for (int k = first;k <= imi; ++k) {
            if (left.get(idx[k]) > 0 && right.get(idx[k]) < N-1) {
              // std::cout << i+1 << ' ' << j+1 << ' ' << left.get(idx[k]) << ' ' << right.get(idx[k]) << std::endl;
              temp_valid_col.insert({j, left.get(idx[k]), right.get(idx[k])});
            }
          }
          first = imi+1;
        }
      }
    }
  }
    /*
  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) {
          temp_valid_col.insert({j, up.get(i), down.get(i)});
        }
      }
    }
  }
  */
  std::vector<std::array<int, 3>> valid_row(temp_valid_row.begin(), temp_valid_row.end());
  std::vector<std::array<int, 3>> valid_col(temp_valid_col.begin(), temp_valid_col.end());
  /*
  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<std::vector<std::vector<std::vector<int>>>> start(2, std::vector<std::vector<std::vector<int>>>(std::max(N, M), std::vector<std::vector<int>>(std::max(N, M))));
  {
    std::vector<std::vector<int>> last(M+1, std::vector<int>(M+1, int(-1))), dp(M+1, std::vector<int>(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<std::vector<int>> last(N+1, std::vector<int>(N+1, int(-1))), dp(N+1, std::vector<int>(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;
    }
  }
  int64_t ans = 0;
  constexpr int MAX = 2500;
  // SegmentTree st(MAX+1);
  FenwickTree fenw(MAX);
  for (int x = 1;x < N-1; ++x) {
    for (int y = 1;y < M-1; ++y) {
      // std::cout << "Current : " << x+1 << ' ' << y+1 << std::endl;
      auto &row = start[0][x][y];
      auto &col = start[1][x][y];
      if (row.size() == 0 || col.size() == 0) {
        continue;
      }
      std::vector<int> idx_row(row.size()), idx_col(col.size());
      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[row[i]] < row_value[row[j]]; });
      std::sort(idx_col.begin(), idx_col.end(), [&](int i, int j) { return valid_col[col[i]][2] < valid_col[col[j]][2]; });
      int j = -1;
      int64_t cnt = 0;
      std::vector<int> rollback;
      // std::cout << "#Rows : " << k_row << '\t' << "#Columns : " << k_col << std::endl;
      for (int i : idx_row) {
        // std::cout << "Current row : " << valid_row[start[0][x][y][i]][0]+1 << ' ' << valid_row[start[0][x][y][i]][1]+1 << ' ' << valid_row[start[0][x][y][i]][2]+1 << std::endl;
        while (j+1 < col.size() && valid_col[col[idx_col[j+1]]][2] - valid_col[col[idx_col[j+1]]][1] + 1 <= row_value[row[i]]) {
          j += 1;
          // st.add(col_value[col[idx_col[j]]]);
          fenw.add(col_value[col[idx_col[j]]], +1);
          rollback.push_back(col_value[col[idx_col[j]]]);
          // std::cout << j << "-th column to Segment Tree (value : " << col_value[j] << " )" << std::endl;
        }
        // cnt += st.get(valid_row[row[i]][2] - valid_row[row[i]][1] + 1, MAX);
        cnt += fenw.get(valid_row[row[i]][2] - valid_row[row[i]][1] + 1, MAX);
      }
      ans += cnt;
      for (int op : rollback) {
        fenw.add(op, -1);
      }
      // st.clear();
    }   
  } 
  /*
  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:248:22: warning: comparison of integer expressions of different signedness: 'short int' and 'std::vector<std::array<short int, 3> >::size_type' {aka 'long unsigned int'} [-Wsign-compare]
  248 |     for (int i = 0;i < valid_row.size(); ++i) {
      |                    ~~^~~~~~~~~~~~~~~~~~
rect.cpp:258:22: warning: comparison of integer expressions of different signedness: 'short int' and 'std::vector<std::array<short int, 3> >::size_type' {aka 'long unsigned int'} [-Wsign-compare]
  258 |     for (int i = 0;i < valid_col.size(); ++i) {
      |                    ~~^~~~~~~~~~~~~~~~~~
rect.cpp:289:20: warning: comparison of integer expressions of different signedness: 'int' and 'std::vector<short int>::size_type' {aka 'long unsigned int'} [-Wsign-compare]
  289 |         while (j+1 < col.size() && valid_col[col[idx_col[j+1]]][2] - valid_col[col[idx_col[j+1]]][1] + 1 <= row_value[row[i]]) {
      |                ~~~~^~~~~~~~~~~~

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