oj.uz

답안 #420897

# 제출 시각 아이디 문제 언어 결과 실행 시간 메모리
420897 2021-06-08T14:43:27 Z rama_pang Izvanzemaljci (COI21_izvanzemaljci) C++17
26 / 100
 569 ms 12504 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 1 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 1 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 67 ms 3836 KB Output is correct
8 Correct 69 ms 3780 KB Output is correct
9 Correct 84 ms 3808 KB Output is correct
10 Correct 81 ms 3808 KB Output is correct
11 Correct 72 ms 3816 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 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 0 ms 204 KB Output is correct
9 Correct 1 ms 204 KB Output is correct
10 Correct 490 ms 12364 KB Output is correct
11 Correct 504 ms 12260 KB Output is correct
12 Correct 493 ms 12320 KB Output is correct
13 Correct 511 ms 12308 KB Output is correct
14 Correct 487 ms 12200 KB Output is correct
15 Correct 466 ms 12220 KB Output is correct
16 Correct 569 ms 12200 KB Output is correct
17 Correct 371 ms 11220 KB Output is correct
18 Correct 386 ms 10976 KB Output is correct
19 Correct 379 ms 10000 KB Output is correct
20 Correct 453 ms 10776 KB Output is correct
21 Correct 398 ms 12200 KB Output is correct
22 Correct 433 ms 12256 KB Output is correct
23 Correct 505 ms 12504 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 0 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 0 ms 204 KB Output is correct
6 Correct 1 ms 204 KB Output is correct
7 Correct 1 ms 272 KB Output is correct
8 Correct 1 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 101 ms 748 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 114 ms 484 KB Output is correct
2 Runtime error 120 ms 740 KB Execution killed with signal 6
3 Halted 0 ms 0 KB -