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Submission #421160

# Submission time Handle Problem Language Result Execution time Memory
421160 2021-06-08T19:35:03 Z rama_pang Izvanzemaljci (COI21_izvanzemaljci) C++17
100 / 100
 2141 ms 16696 KB 
#include <bits/stdc++.h>
using namespace std;

using lint = long long;

int main() {
  ios::sync_with_stdio(0);
  cin.tie(0);

  int N, K;
  cin >> N >> K;

  vector<lint> X(N), Y(N);
  for (int i = 0; i < N; i++) {
    cin >> X[i] >> Y[i];
  }

  long long answerScore = 1e18;
  vector<array<lint, 4>> answer;

  for (int rot = 0; rot < 4; rot++) {
    vector<int> sortByX(N);
    vector<int> sortByY(N);
    iota(begin(sortByX), end(sortByX), 0);
    iota(begin(sortByY), end(sortByY), 0);
    sort(begin(sortByX), end(sortByX), [&](int i, int j) {
      return pair(X[i], Y[i]) < pair(X[j], Y[j]);
    });
    sort(begin(sortByY), end(sortByY), [&](int i, int j) {
      return pair(Y[i], X[i]) < pair(Y[j], X[j]);
    });
    vector<int> posInSortByX(N);
    vector<int> posInSortByY(N);
    for (int i = 0; i < N; i++) {
      posInSortByX[sortByX[i]] = i;
      posInSortByY[sortByY[i]] = i;
    }

    const auto CountingSort = [&](vector<int> &a, const vector<int> &sorted, const vector<int> &pos) {
      static vector<int> res(N);
      fill(begin(res), end(res), 0);
      for (auto i : a) {
        res[pos[i]] = 1;
      }
      a.clear();
      for (int i = 0; i < N; i++) {
        if (res[i]) {
          a.emplace_back(sorted[i]);
        }
      }
    };

    vector<array<lint, 3>> ans;
    const auto SolveK1 = [&](vector<int> alive, lint boundLftX, lint boundRgtX, lint boundLftY, lint boundRgtY, int trace) -> lint {
      if (alive.empty()) return 0;
      lint minX = +2e9;
      lint maxX = -2e9;
      lint minY = +2e9;
      lint maxY = -2e9;
      for (auto i : alive) {
        minX = min(minX, X[i]);
        maxX = max(maxX, X[i]);
        minY = min(minY, Y[i]);
        maxY = max(maxY, Y[i]);
      }

      lint len = max({1ll, maxX - minX, maxY - minY});
      if (boundRgtX - boundLftX < len) return 1e18;
      if (boundRgtY - boundLftY < len) return 1e18;

      if (!trace) {
        return len;
      }

      for (auto x : {boundLftX, minX, maxX - len, boundRgtX - len}) if (-3e9 <= x && x <= 3e9) {
        if (boundLftX <= x && x + len <= boundRgtX) {
          for (auto y : {boundLftY, minY, maxY - len, boundRgtY - len}) if (-3e9 <= y && y <= 3e9) {
            if (boundLftY <= y && y + len <= boundRgtY) {
              bool bad = false;
              for (auto i : alive) {
                if (x <= X[i] && X[i] <= x + len && y <= Y[i] && Y[i] <= y + len) {

                } else {
                  bad = true;
                  break;
                }
              }
              if (!bad) {
                ans.push_back({x, y, len});
                return len;
              }
            }
          }
        }
      }
      cout << rot << '\n';
      cout << boundLftX << ' ' << boundRgtX << ' ' << boundLftY << ' ' << boundRgtY << '\n';
      for (auto i : alive) cout << X[i] << ' ' << Y[i] << endl;
      assert(false);
      return 1e18;
    };

    const auto SolveK2 = [&](vector<int> alive, int vert, lint boundLftX, int trace) -> lint {
      if (alive.empty()) return 0;

      lint res = SolveK1(alive, boundLftX, 1e18, -1e18, 1e18, 0);

      if (!vert) {
        CountingSort(alive, sortByY, posInSortByY);
      } else {
        CountingSort(alive, sortByX, posInSortByX);
      }

      static vector<lint> prefMinX(N);
      static vector<lint> prefMaxX(N);
      static vector<lint> prefMinY(N);
      static vector<lint> prefMaxY(N);

      static vector<lint> suffMinX(N);
      static vector<lint> suffMaxX(N);
      static vector<lint> suffMinY(N);
      static vector<lint> suffMaxY(N);

      for (int i = 0; i < int(alive.size()); i++) {
        int id = alive[i];
        prefMinX[i] = prefMaxX[i] = X[id];
        prefMinY[i] = prefMaxY[i] = Y[id];
        suffMinX[i] = suffMaxX[i] = X[id];
        suffMinY[i] = suffMaxY[i] = Y[id];
      }
      for (int i = 1; i < int(alive.size()); i++) {
        prefMinX[i] = min(prefMinX[i], prefMinX[i - 1]);
        prefMaxX[i] = max(prefMaxX[i], prefMaxX[i - 1]);
        prefMinY[i] = min(prefMinY[i], prefMinY[i - 1]);
        prefMaxY[i] = max(prefMaxY[i], prefMaxY[i - 1]);
      }
      for (int i = int(alive.size()) - 2; i >= 0; i--) {
        suffMinX[i] = min(suffMinX[i], suffMinX[i + 1]);
        suffMaxX[i] = max(suffMaxX[i], suffMaxX[i + 1]);
        suffMinY[i] = min(suffMinY[i], suffMinY[i + 1]);
        suffMaxY[i] = max(suffMaxY[i], suffMaxY[i + 1]);
      }

      const auto CalcPref = [&](int i) -> lint {
        if (i < 0 || i >= int(alive.size())) return 0;
        return max(prefMaxX[i] - prefMinX[i], prefMaxY[i] - prefMinY[i]);
      };

      const auto CalcSuff = [&](int i) -> lint {
        if (i < 0 || i >= int(alive.size())) return 0;
        return max(suffMaxX[i] - suffMinX[i], suffMaxY[i] - suffMinY[i]);
      };

      if (vert == 0) {
        for (int i = 0; i < int(alive.size()); i++) {
          if (!(i + 1 == int(alive.size()) || Y[alive[i + 1]] != Y[alive[i]])) {
            continue;
          }
          res = min(res, max(CalcPref(i), CalcSuff(i + 1)));
        }

        if (res == 1e18) {
          return res;
        }

        vector<int> pref;
        vector<int> suff = alive;
        reverse(begin(suff), end(suff));
        for (int i = 0; i < int(alive.size()); i++) {
          pref.emplace_back(alive[i]);
          suff.pop_back();
          if (!(i + 1 == int(alive.size()) || Y[alive[i + 1]] != Y[alive[i]])) {
            continue;
          }
          if (res == max(CalcPref(i), CalcSuff(i + 1))) {
            SolveK1(pref, boundLftX, 1e18, -1e18, Y[alive[i]], trace);
            SolveK1(suff, boundLftX, 1e18, Y[alive[i]] + 1, 1e18, trace);
            return res;
          }
        }
      } else {
        for (int i = 0; i < int(alive.size()); i++) {
          if (!(i + 1 == int(alive.size()) || X[alive[i + 1]] != X[alive[i]])) {
            continue;
          }
          lint len = CalcPref(i);
          lint upTo = (i + 1 == int(alive.size())) ? 1e18 : (X[alive[i + 1]] - 1);
          if (upTo - max(boundLftX, prefMinX[i]) < len) continue;
          res = min(res, max(CalcPref(i), CalcSuff(i + 1)));
        }

        if (res == 1e18) {
          return res;
        }

        vector<int> pref;
        vector<int> suff = alive;
        reverse(begin(suff), end(suff));
        for (int i = 0; i < int(alive.size()); i++) {
          pref.emplace_back(alive[i]);
          suff.pop_back();
          if (!(i + 1 == int(alive.size()) || X[alive[i + 1]] != X[alive[i]])) {
            continue;
          }
          lint len = CalcPref(i);
          lint upTo = (i + 1 == int(alive.size())) ? 1e18 : (X[alive[i + 1]] - 1);
          if (upTo - max(boundLftX, prefMinX[i]) < len) continue;
          if (res == max(CalcPref(i), CalcSuff(i + 1))) {
            SolveK1(pref, boundLftX, upTo, -1e18, 1e18, trace);
            SolveK1(suff, upTo + 1, 1e18, -1e18, 1e18, trace);
            return res;
          }
        }
      }

      if (res == SolveK1(alive, boundLftX, 1e18, -1e18, 1e18, 0)) {
        return SolveK1(alive, boundLftX, 1e18, -1e18, 1e18, trace);
      }

      return 1e18;
    };

    const auto SolveK3 = [&](vector<int> alive, int trace) -> lint {
      lint res = 1e18;
      res = min(res, SolveK2(alive, 0, -1e18, 0));
      res = min(res, SolveK2(alive, 1, +1e18, 0));

      CountingSort(alive, sortByX, posInSortByX);

      static vector<lint> prefMinX(N);
      static vector<lint> prefMaxX(N);
      static vector<lint> prefMinY(N);
      static vector<lint> prefMaxY(N);

      for (int i = 0; i < int(alive.size()); i++) {
        int id = alive[i];
        prefMinX[i] = prefMaxX[i] = X[id];
        prefMinY[i] = prefMaxY[i] = Y[id];
      }
      for (int i = 1; i < int(alive.size()); i++) {
        prefMinX[i] = min(prefMinX[i], prefMinX[i - 1]);
        prefMaxX[i] = max(prefMaxX[i], prefMaxX[i - 1]);
        prefMinY[i] = min(prefMinY[i], prefMinY[i - 1]);
        prefMaxY[i] = max(prefMaxY[i], prefMaxY[i - 1]);
      }

      const auto CalcPref = [&](int i) -> lint {
        if (i < 0 || i >= int(alive.size())) return 0;
        return max(prefMaxX[i] - prefMinX[i], prefMaxY[i] - prefMinY[i]);
      };

      vector<lint> coordX = X;
      sort(begin(coordX), end(coordX));
      coordX.resize(unique(begin(coordX), end(coordX)) - begin(coordX));

      const auto Check = [&](lint maxD) -> pair<int, bool> {
        int ok = -1;
        for (int i = 0; i < int(alive.size()); i++) {
          if (!(i + 1 == int(alive.size()) || X[alive[i + 1]] != X[alive[i]])) {
            continue;
          }
          if (CalcPref(i) <= maxD) {
            ok = i;
          }
        }

        vector<int> other;
        for (int i = ok + 1; i < int(alive.size()); i++) {
          other.emplace_back(alive[i]);
        }

        return {ok, min(SolveK2(other, 0, ok == -1 ? -1e18 : (X[alive[ok]] + 1), 0),
                        SolveK2(other, 1, ok == -1 ? -1e18 : (X[alive[ok]] + 1), 0)) <= maxD};
      };

      lint lo = 1, hi = 2e9;
      while (lo < hi) {
        lint md = (lo + hi) / 2;
        if (Check(md).second) {
          hi = md;
        } else {
          lo = md + 1;
        }
      }

      int cand = Check(lo).first;
      vector<int> suff = alive;
      reverse(begin(suff), end(suff));
      for (int i = 0; i < int(alive.size()); i++) {
        suff.pop_back();
        if (!(i + 1 == int(alive.size()) || X[alive[i + 1]] != X[alive[i]])) {
          continue;
        }
        if (i != cand) continue;
        res = min(res, max(CalcPref(i), SolveK2(suff, 0, X[alive[i]] + 1, 0)));
        res = min(res, max(CalcPref(i), SolveK2(suff, 1, X[alive[i]] + 1, 0)));
      }

      if (res == 1e18) {
        return res;
      }

      suff = alive;
      vector<int> pref;
      reverse(begin(suff), end(suff));
      for (int i = 0; i < int(alive.size()); i++) {
        pref.emplace_back(alive[i]);
        suff.pop_back();
        if (!(i + 1 == int(alive.size()) || X[alive[i + 1]] != X[alive[i]])) {
          continue;
        }
        if (i != cand) continue;
        if (res == max(CalcPref(i), SolveK2(suff, 0, X[alive[i]] + 1, 0))) {
          SolveK1(pref, -1e18, X[alive[i]], -1e18, 1e18, trace);
          SolveK2(suff, 0, X[alive[i]] + 1, trace);
          return res;
        }
        if (res == max(CalcPref(i), SolveK2(suff, 1, X[alive[i]] + 1, 0))) {
          SolveK1(pref, -1e18, X[alive[i]], -1e18, 1e18, trace);
          SolveK2(suff, 1, X[alive[i]] + 1, trace);
          return res;
        }
      }

      if (res == SolveK2(alive, 0, -1e18, 0)) {
        return SolveK2(alive, 0, -1e18, trace);
      }

      if (res == SolveK2(alive, 1, -1e18, 0)) {
        return SolveK2(alive, 1, -1e18, trace);
      }

      return 1e18;
    };

    const auto Solve = [&](int K, int trace) -> lint {
      vector<int> alive(N);
      iota(begin(alive), end(alive), 0);
      if (K == 1) {
        ans.clear();
        return SolveK1(alive, -1e18, 1e18, -1e18, 1e18, trace);
      } else if (K == 2) {
        ans.clear();
        lint res1 = SolveK2(alive, 0, -1e18, trace);
        auto ans1 = ans;
        ans.clear();
        lint res2 = SolveK2(alive, 1, -1e18, trace);
        auto ans2 = ans;
        if (res1 < res2) {
          ans = ans1;
          return res1;
        } else {
          ans = ans2;
          return res2;
        }
      } else if (K == 3) {
        ans.clear();
        return SolveK3(alive, trace);
      } else {
        assert(false);
        return -1;
      }
    };

    lint res = Solve(K, 1);
    if (res < answerScore) {
      answerScore = res;
      answer.clear();
      for (auto &a : ans) {
        answer.push_back({a[0], a[1], a[0] + a[2], a[1] + a[2]});
      }
    }

    for (int i = 0; i < N; i++) {
      swap(X[i], Y[i]); Y[i] *= -1;
    }
    for (int i = 0; i < int(answer.size()); i++) {
      swap(answer[i][0], answer[i][1]); answer[i][1] *= -1;
      swap(answer[i][2], answer[i][3]); answer[i][3] *= -1;
    }
  }

  vector<array<lint, 3>> ans;
  for (auto a : answer) {
    if (a[0] > a[2]) swap(a[0], a[2]);
    if (a[1] > a[3]) swap(a[1], a[3]);
    assert(a[2] - a[0] == a[3] - a[1]);
    ans.push_back({a[0], a[1], a[2] - a[0]});
  }

  int it = 0;
  while (int(ans.size()) < K) {
    ans.push_back({lint(-3e9 + 2 * it), lint(3e9), 1});
    it++;
  }

  const auto ValidAnswer = [&](vector<array<lint, 3>> sq) {
    assert(int(sq.size()) <= K);
    for (int i = 0; i < int(sq.size()); i++) {
      for (int j = 0; j < int(sq.size()); j++) if (i != j) {
        for (auto x : {sq[j][0], sq[j][0] + sq[j][2]}) {
          for (auto y : {sq[j][1], sq[j][1] + sq[j][2]}) {
            lint minX = sq[i][0];
            lint maxX = sq[i][0] + sq[i][2];
            lint minY = sq[i][1];
            lint maxY = sq[i][1] + sq[i][2];
            if (minX <= x && x <= maxX && minY <= y && y <= maxY) {
              return false;
            }
          }
        }
      }
    }
    for (int i = 0; i < N; i++) {
      bool found = false;
      for (auto [x, y, l] : sq) {
        if (x <= X[i] && X[i] <= x + l && y <= Y[i] && Y[i] <= y + l) {
          found = true;
          break;
        }
      }
      if (!found) {
        return false;
      }
    }
    return true;
  };

  assert(ValidAnswer(ans));
  for (int i = 0; i < K; i++) {
    cout << ans[i][0] << ' ' << ans[i][1] << ' ' << ans[i][2] << '\n';
  }
  return 0;
}

Subtask #1
5.0 / 5.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 204 KB Output is correct
2 Correct 0 ms 204 KB Output is correct
3 Correct 0 ms 204 KB Output is correct
4 Correct 0 ms 204 KB Output is correct
5 Correct 0 ms 204 KB Output is correct
6 Correct 0 ms 204 KB Output is correct
7 Correct 155 ms 4204 KB Output is correct
8 Correct 153 ms 4216 KB Output is correct
9 Correct 152 ms 4276 KB Output is correct
10 Correct 154 ms 4196 KB Output is correct
11 Correct 157 ms 4212 KB Output is correct

Subtask #2
21.0 / 21.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 204 KB Output is correct
2 Correct 1 ms 204 KB Output is correct
3 Correct 0 ms 204 KB Output is correct
4 Correct 0 ms 204 KB Output is correct
5 Correct 1 ms 204 KB Output is correct
6 Correct 0 ms 204 KB Output is correct
7 Correct 0 ms 204 KB Output is correct
8 Correct 1 ms 204 KB Output is correct
9 Correct 1 ms 204 KB Output is correct
10 Correct 221 ms 12048 KB Output is correct
11 Correct 220 ms 12044 KB Output is correct
12 Correct 252 ms 12072 KB Output is correct
13 Correct 222 ms 12608 KB Output is correct
14 Correct 228 ms 12668 KB Output is correct
15 Correct 222 ms 12160 KB Output is correct
16 Correct 220 ms 12592 KB Output is correct
17 Correct 201 ms 11312 KB Output is correct
18 Correct 195 ms 10828 KB Output is correct
19 Correct 176 ms 9920 KB Output is correct
20 Correct 190 ms 10536 KB Output is correct
21 Correct 222 ms 12412 KB Output is correct
22 Correct 219 ms 12012 KB Output is correct
23 Correct 221 ms 12240 KB Output is correct

Subtask #3
12.0 / 12.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 204 KB Output is correct
2 Correct 1 ms 204 KB Output is correct
3 Correct 0 ms 204 KB Output is correct
4 Correct 1 ms 204 KB Output is correct
5 Correct 1 ms 204 KB Output is correct
6 Correct 1 ms 204 KB Output is correct
7 Correct 0 ms 204 KB Output is correct
8 Correct 1 ms 204 KB Output is correct
9 Correct 0 ms 204 KB Output is correct
10 Correct 1 ms 204 KB Output is correct
11 Correct 1 ms 204 KB Output is correct
12 Correct 1 ms 204 KB Output is correct
13 Correct 1 ms 204 KB Output is correct
14 Correct 1 ms 204 KB Output is correct
15 Correct 1 ms 204 KB Output is correct
16 Correct 1 ms 204 KB Output is correct
17 Correct 1 ms 204 KB Output is correct
18 Correct 1 ms 204 KB Output is correct
19 Correct 1 ms 204 KB Output is correct
20 Correct 1 ms 204 KB Output is correct
21 Correct 1 ms 204 KB Output is correct
22 Correct 1 ms 204 KB Output is correct
23 Correct 1 ms 204 KB Output is correct
24 Correct 1 ms 204 KB Output is correct
25 Correct 1 ms 204 KB Output is correct
26 Correct 1 ms 316 KB Output is correct

Subtask #4
30.0 / 30.0

# Verdict Execution time Memory Grader output
1 Correct 13 ms 460 KB Output is correct
2 Correct 12 ms 492 KB Output is correct
3 Correct 12 ms 496 KB Output is correct
4 Correct 12 ms 460 KB Output is correct
5 Correct 12 ms 496 KB Output is correct
6 Correct 13 ms 484 KB Output is correct
7 Correct 12 ms 496 KB Output is correct
8 Correct 12 ms 460 KB Output is correct
9 Correct 12 ms 460 KB Output is correct
10 Correct 12 ms 460 KB Output is correct
11 Correct 12 ms 488 KB Output is correct
12 Correct 12 ms 496 KB Output is correct
13 Correct 10 ms 464 KB Output is correct
14 Correct 10 ms 460 KB Output is correct
15 Correct 10 ms 484 KB Output is correct
16 Correct 10 ms 460 KB Output is correct
17 Correct 9 ms 468 KB Output is correct
18 Correct 9 ms 460 KB Output is correct
19 Correct 9 ms 460 KB Output is correct
20 Correct 9 ms 460 KB Output is correct
21 Correct 11 ms 472 KB Output is correct
22 Correct 9 ms 460 KB Output is correct
23 Correct 8 ms 460 KB Output is correct
24 Correct 8 ms 460 KB Output is correct

Subtask #5
32.0 / 32.0

# Verdict Execution time Memory Grader output
1 Correct 12 ms 460 KB Output is correct
2 Correct 12 ms 460 KB Output is correct
3 Correct 12 ms 500 KB Output is correct
4 Correct 12 ms 460 KB Output is correct
5 Correct 13 ms 496 KB Output is correct
6 Correct 12 ms 492 KB Output is correct
7 Correct 15 ms 488 KB Output is correct
8 Correct 14 ms 460 KB Output is correct
9 Correct 12 ms 460 KB Output is correct
10 Correct 16 ms 496 KB Output is correct
11 Correct 12 ms 460 KB Output is correct
12 Correct 12 ms 492 KB Output is correct
13 Correct 13 ms 496 KB Output is correct
14 Correct 1770 ms 13856 KB Output is correct
15 Correct 1787 ms 15248 KB Output is correct
16 Correct 1791 ms 16004 KB Output is correct
17 Correct 2141 ms 15528 KB Output is correct
18 Correct 1796 ms 15392 KB Output is correct
19 Correct 1830 ms 15432 KB Output is correct
20 Correct 1871 ms 16696 KB Output is correct
21 Correct 1476 ms 13480 KB Output is correct
22 Correct 1718 ms 14748 KB Output is correct
23 Correct 1731 ms 15304 KB Output is correct
24 Correct 1991 ms 15448 KB Output is correct
25 Correct 1987 ms 15204 KB Output is correct
26 Correct 1850 ms 15384 KB Output is correct