Submission #895802

#	Time	Username	Problem	Language	Result	Execution time	Memory
895802		MilosMilutinovic	Chessboard (IZhO18_chessboard)	C++14	100 / 100	1238 ms	4432 KiB

chessboard

#include <bits/stdc++.h>

using namespace std;

int main() {
  ios::sync_with_stdio(false);
  cin.tie(0);
  int n, m;
  cin >> n >> m;
  vector<int> x1(m), y1(m), x2(m), y2(m);
  for (int i = 0; i < m; i++) {
    cin >> x1[i] >> y1[i] >> x2[i] >> y2[i];
    --x1[i]; --y1[i]; --x2[i]; --y2[i];
  }
  long long ans = 1e18;
  for (int foo = 0; foo < 2; foo++) {
    for (int k = 1; k < n; k++) {
      if (n % k != 0) {
        continue;
      }
      long long res = 0, area = 0;
      function<long long(int, int, int, int)> Solve = [&](int x1, int y1, int x2, int y2) {
        if (x1 > x2 || y1 > y2) {
          return 0LL;
        }
        if ((x1 / k) == (x2 / k) && (y1 / k) == (y2 / k)) {
          if (foo == (x1 / k + y1 / k) % 2) {
            return 0LL;
          } else {
            return (x2 - x1 + 1) * 1LL * (y2 - y1 + 1);
          }
        }
        if ((x1 / k) == (x2 / k)) {
          long long ret = 0;
          if (y1 % k != 0) {
            ret += Solve(x1, y1, x2, y1 + (k - y1 % k) - 1);
            y1 += (k - y1 % k);
          }
          if (y2 % k != k - 1) {
            ret += Solve(x1, y2 - y2 % k, x2, y2);
            y2 -= (y2 % k) + 1;
          }
          long long blocks = (y2 - y1 + 1) / k;
          if ((x1 / k + y1 / k) % 2 == foo) {
            blocks = blocks / 2;
          } else {
            blocks = (blocks + 1) / 2;
          }
          return ret + blocks * k * (x2 - x1 + 1);
        }
        if ((y1 / k) == (y2 / k)) {
          long long ret = 0;
          if (x1 % k != 0) {
            ret += Solve(x1, y1, x1 + (k - x1 % k) - 1, y2);
            x1 += (k - x1 % k);
          }
          if (x2 % k != k - 1) {
            ret += Solve(x2 - x2 % k, y1, x2, y2);
            x2  -= (x2 % k) + 1;
          }
          long long blocks = (x2 - x1 + 1) / k;
          if ((x1 / k + y1 / k) % 2 == foo) {
            blocks = blocks / 2;
          } else {
            blocks = (blocks + 1) / 2;
          }
          return ret + blocks * k * (y2 - y1 + 1);
        }
        long long ret = 0;
        if (x1 % k != 0) {
          ret += Solve(x1, y1, x1 + (k - x1 % k) - 1, y2);
          x1 += (k - x1 % k);
        }
        if (x2 % k != k - 1) {
          ret += Solve(x2 - x2 % k, y1, x2, y2);
          x2 -= (x2 % k) + 1;
        }
        if (y1 % k != 0) {
          ret += Solve(x1, y1, x2, y1 + (k - y1 % k) - 1);
          y1 += (k - y1 % k);
        }
        if (y2 % k != k - 1) {
          ret += Solve(x1, y2 - (y2 % k), x2, y2);
          y2 -= (y2 % k) + 1;
        }
        long long blocks_x = (x2 - x1 + 1) / k;
        long long blocks_y = (y2 - y1 + 1) / k;
        if ((x1 / k + y1 / k) % 2 == foo) {
          return ret + ((blocks_y + 1) / 2) * (blocks_x / 2) * k * k + (blocks_y / 2) * ((blocks_x + 1) / 2) * k * k;
        } else {
          return ret + ((blocks_y + 1) / 2) * ((blocks_x + 1) / 2) * k * k + (blocks_y / 2) * (blocks_x / 2) * k * k;
        }
      };
      for (int i = 0; i < m; i++) {
        res += Solve(x1[i], y1[i], x2[i], y2[i]);
        area += (x2[i] - x1[i] + 1) * 1LL * (y2[i] - y1[i] + 1);
      }
      long long black = 0;
      long long v = n / k;
      if (foo == 0) {
        black = ((v + 1) / 2) * ((v + 1) / 2) * k * k + (v / 2) * (v / 2) * k * k;
      } else {
        black = ((v + 1) / 2) * (v / 2) * k * k + (v / 2) * ((v + 1) / 2) * k * k;
      }
      ans = min(ans, res + black - (area - res));
    }
  } 
  cout << ans << '\n';
  return 0;
}

• Subtask 1: 8 / 8
• Subtask 2: 8 / 8
• Subtask 3: 15 / 15
• Subtask 4: 16 / 16
• Subtask 5: 23 / 23
• Subtask 6: 30 / 30