oj.uz

답안 #420901

# 제출 시각 아이디 문제 언어 결과 실행 시간 메모리
420901 2021-06-08T14:44:57 Z rama_pang Izvanzemaljci (COI21_izvanzemaljci) C++17
26 / 100
 514 ms 12344 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];
  }

  // There is a vertical or horizontal line which divides K = 3 -> {1, 2}.
  // Binary search the answer L. If cuts are shaped like (|-), then we
  // can greedily take big left part. If cuts are shaped like (| |), we
  // brute force middle (as we can greedily take middle), precompute left part
  // and right part.
  //
  // This takes O(N log MAX).

  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 = [&](lint L, const vector<int> &alive, int config, int trace) {
    if (alive.empty()) return true;
    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]);
    }
    if (maxX - minX <= L && maxY - minY <= L) {
      lint len = max({1ll, maxX - minX, maxY - minY});
      if (trace == 1 && config == 0) ans.push_back({minX, minY, len});
      if (trace == 1 && config == 1) ans.push_back({maxX - len, minY, len});
      if (trace == 1 && config == 2) ans.push_back({maxX - len, maxY - len, len});
      if (trace == 1 && config == 3) ans.push_back({minX, maxY - len, len});
      return true;
    }
    return false;
  };

  const auto SolveK2 = [&](int L, vector<int> alive, int vert, int trace) {
    if (alive.empty()) return true;

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

    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 == alive.size() ||
           (vert == 0 && Y[alive[i + 1]] != Y[alive[i]]) ||
           (vert == 1 && X[alive[i + 1]] != X[alive[i]]))) {
        continue;
      }

      if (CalcPref(i) <= L && CalcSuff(i + 1) <= L) {
        assert(SolveK1(L, pref, 2, trace));
        assert(SolveK1(L, suff, 0, trace));
        return true;
      }
    }
    return false;
  };

  const auto SolveK3 = [&](lint L, vector<int> alive, int vert, int trace) {
    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 >= alive.size()) return 0;
      return max(prefMaxX[i] - prefMinX[i], prefMaxY[i] - prefMinY[i]);
    };
    const auto CalcSuff = [&](int i) -> lint {
      if (i < 0 || i >= alive.size()) return 0;
      return max(suffMaxX[i] - suffMinX[i], suffMaxY[i] - suffMinY[i]);
    };

    // Configuration: |-
    int last = -1;
    for (int i = 0; i < int(alive.size()); i++) {
      if (!(i + 1 == alive.size() ||
           (vert == 0 && Y[alive[i + 1]] != Y[alive[i]]) ||
           (vert == 1 && X[alive[i + 1]] != X[alive[i]]))) {
        continue;
      }
      if (CalcPref(i) <= L) {
        last = i;
      }
    }
    if (last != -1) {
      vector<int> other;
      for (int i = last + 1; i < int(alive.size()); i++) {
        other.emplace_back(alive[i]);
      }
      if (SolveK2(L, other, 1 - vert, trace)) {
        if (trace) {
          other.clear();
          for (int i = 0; i <= last; i++) {
            other.emplace_back(alive[i]);
          }
          SolveK1(L, other, 2, trace);
        }
        return true;
      }
    }

    // Configuration: -|
    last = -1;
    for (int i = int(alive.size()) - 1; i >= 0; i--) {
      if (!(i == 0 ||
           (vert == 0 && Y[alive[i - 1]] != Y[alive[i]]) ||
           (vert == 1 && X[alive[i - 1]] != X[alive[i]]))) {
        continue;
      }
      if (CalcSuff(i) <= L) {
        last = i;
      }
    }
    if (last != -1) {
      vector<int> other;
      for (int i = 0; i < last; i++) {
        other.emplace_back(alive[i]);
      }
      if (SolveK2(L, other, 1 - vert, trace)) {
        if (trace) {
          other.clear();
          for (int i = last; i < int(alive.size()); i++) {
            other.emplace_back(alive[i]);
          }
          SolveK1(L, other, 0, trace);
        }
        return true;
      }
    }

    // Configuration: | |

    for (int i = 0; i < int(alive.size()); i++) {
      lint minX = X[alive[i]];
      lint maxX = X[alive[i]];
      lint minY = Y[alive[i]];
      lint maxY = Y[alive[i]];

      if (!(i == 0 ||
           (vert == 0 && Y[alive[i - 1]] != Y[alive[i]]) ||
           (vert == 1 && X[alive[i - 1]] != X[alive[i]]))) {
        continue;
      }

      for (int j = i; j < int(alive.size()); j++) {
        minX = min(minX, X[alive[j]]);
        maxX = max(maxX, X[alive[j]]);
        minY = min(minY, Y[alive[j]]);
        maxY = max(maxY, Y[alive[j]]);

        if (!(j + 1 == alive.size() ||
            (vert == 0 && Y[alive[j + 1]] != Y[alive[j]]) ||
            (vert == 1 && X[alive[j + 1]] != X[alive[j]]))) {
          continue;
        }

        if ((vert == 0 && maxX - minX <= maxY - minY && maxY - minY <= L) ||
            (vert == 1 && maxY - minY <= maxX - minX && maxX - minX <= L)) {
          if (CalcPref(i - 1) <= L && CalcSuff(j + 1) <= L) {
            if (trace) {
              vector<int> a, b, c;
              for (int x = 0; x < int(alive.size()); x++) {
                if (x < i) a.emplace_back(alive[x]);
                else if (x > j) c.emplace_back(alive[x]);
                else b.emplace_back(alive[x]);
              }
              assert(SolveK1(L, a, 2, trace));
              assert(SolveK1(L, b, 0, trace));
              assert(SolveK1(L, c, 0, trace));
            }
            return true;
          }
        }
      }
    }
    return false;

    // deque<pair<lint, int>> minQue;
    // deque<pair<lint, int>> maxQue;

    // const auto CanInsert = [&](int id) {
    //   if (minQue.empty() || maxQue.empty()) return true;
    //   lint val;
    //   if (vert == 0) {
    //     // horizontal, keep minX and maxX
    //     val = X[id];
    //   } else {
    //     // vertical, keep minY and maxY
    //     val = Y[id];
    //   }
    //   if (max(maxQue.front().first, val) - min(minQue.front().first, val) <= L) {
    //     return true;
    //   }
    // };

    // for (int i = 0, j = -1; i < int(alive.size()); i++) {
    //   while (j + 1 < int(alive.size()) &&
    //          (vert == 0 ? (Y[alive[j + 1]] - Y[alive[i]]) : (X[alive[j + 1]] - X[alive[i]])) <= L &&
    //          CanInsert(alive[j + 1])) {
    //     Insert(alive[j++]);
    //   }
    //   if (CalcPref(i - 1) <= L && CalcSuff(j + 1) <= L) {

    //   }
    //   Erase(alive[i]);
    // }



  };

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

  lint lo = 1;
  lint hi = 2e9;
  while (lo < hi) {
    lint md = (lo + hi) / 2;
    if (Solve(K, md, 0)) {
      hi = md;
    } else {
      lo = md + 1;
    }
  }

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

  const auto NotIntersect = [&](vector<array<lint, 3>> sq) {
    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;
            }
          }
        }
      }
    }
    return true;
  };

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

Compilation message

izvanzemaljci.cpp: In lambda function:
izvanzemaljci.cpp:121:22: warning: comparison of integer expressions of different signedness: 'int' and 'std::vector<int>::size_type' {aka 'long unsigned int'} [-Wsign-compare]
  121 |       if (i < 0 || i >= alive.size()) return 0;
      |                    ~~^~~~~~~~~~~~~~~
izvanzemaljci.cpp: In lambda function:
izvanzemaljci.cpp:125:22: warning: comparison of integer expressions of different signedness: 'int' and 'std::vector<int>::size_type' {aka 'long unsigned int'} [-Wsign-compare]
  125 |       if (i < 0 || i >= alive.size()) return 0;
      |                    ~~^~~~~~~~~~~~~~~
izvanzemaljci.cpp: In lambda function:
izvanzemaljci.cpp:136:19: warning: comparison of integer expressions of different signedness: 'int' and 'std::vector<int>::size_type' {aka 'long unsigned int'} [-Wsign-compare]
  136 |       if (!(i + 1 == alive.size() ||
      |             ~~~~~~^~~~~~~~~~~~~~~
izvanzemaljci.cpp: In lambda function:
izvanzemaljci.cpp:189:22: warning: comparison of integer expressions of different signedness: 'int' and 'std::vector<int>::size_type' {aka 'long unsigned int'} [-Wsign-compare]
  189 |       if (i < 0 || i >= alive.size()) return 0;
      |                    ~~^~~~~~~~~~~~~~~
izvanzemaljci.cpp: In lambda function:
izvanzemaljci.cpp:193:22: warning: comparison of integer expressions of different signedness: 'int' and 'std::vector<int>::size_type' {aka 'long unsigned int'} [-Wsign-compare]
  193 |       if (i < 0 || i >= alive.size()) return 0;
      |                    ~~^~~~~~~~~~~~~~~
izvanzemaljci.cpp: In lambda function:
izvanzemaljci.cpp:200:19: warning: comparison of integer expressions of different signedness: 'int' and 'std::vector<int>::size_type' {aka 'long unsigned int'} [-Wsign-compare]
  200 |       if (!(i + 1 == alive.size() ||
      |             ~~~~~~^~~~~~~~~~~~~~~
izvanzemaljci.cpp:275:21: warning: comparison of integer expressions of different signedness: 'int' and 'std::vector<int>::size_type' {aka 'long unsigned int'} [-Wsign-compare]
  275 |         if (!(j + 1 == alive.size() ||
      |               ~~~~~~^~~~~~~~~~~~~~~
izvanzemaljci.cpp: In function 'int main()':
izvanzemaljci.cpp:377:21: warning: comparison of integer expressions of different signedness: 'std::vector<std::array<long long int, 3> >::size_type' {aka 'long unsigned int'} and 'int' [-Wsign-compare]
  377 |   while (ans.size() < K) {
      |          ~~~~~~~~~~~^~~

Subtask #1
5.0 / 5.0

# 결과 실행 시간 메모리 Grader output
1 Correct 0 ms 204 KB Output is correct
2 Correct 1 ms 204 KB Output is correct
3 Correct 1 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 87 ms 3792 KB Output is correct
8 Correct 84 ms 3780 KB Output is correct
9 Correct 70 ms 3840 KB Output is correct
10 Correct 71 ms 3780 KB Output is correct
11 Correct 75 ms 3900 KB Output is correct

Subtask #2
21.0 / 21.0

# 결과 실행 시간 메모리 Grader output
1 Correct 1 ms 204 KB Output is correct
2 Correct 1 ms 204 KB Output is correct
3 Correct 1 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 1 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 463 ms 12204 KB Output is correct
11 Correct 486 ms 12216 KB Output is correct
12 Correct 473 ms 12344 KB Output is correct
13 Correct 501 ms 12236 KB Output is correct
14 Correct 467 ms 12228 KB Output is correct
15 Correct 460 ms 12272 KB Output is correct
16 Correct 514 ms 12240 KB Output is correct
17 Correct 357 ms 11244 KB Output is correct
18 Correct 357 ms 10884 KB Output is correct
19 Correct 399 ms 9980 KB Output is correct
20 Correct 412 ms 10680 KB Output is correct
21 Correct 380 ms 12316 KB Output is correct
22 Correct 431 ms 12216 KB Output is correct
23 Correct 511 ms 12212 KB Output is correct

Subtask #3
0 / 12.0

# 결과 실행 시간 메모리 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 0 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 0 ms 204 KB Output is correct
9 Runtime error 1 ms 460 KB Execution killed with signal 6
10 Halted 0 ms 0 KB -

Subtask #4
0 / 30.0

# 결과 실행 시간 메모리 Grader output
1 Runtime error 94 ms 836 KB Execution killed with signal 6
2 Halted 0 ms 0 KB -

Subtask #5
0 / 32.0

# 결과 실행 시간 메모리 Grader output
1 Correct 88 ms 480 KB Output is correct
2 Runtime error 81 ms 872 KB Execution killed with signal 6
3 Halted 0 ms 0 KB -