oj.uz

답안 #420925

# 제출 시각 아이디 문제 언어 결과 실행 시간 메모리
420925 2021-06-08T14:55:47 Z rama_pang Izvanzemaljci (COI21_izvanzemaljci) C++17
56 / 100
 3000 ms 15112 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 conf, 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) {
        if (vert == 1 && conf == 0) {
          assert(SolveK1(L, pref, 2, trace));
          assert(SolveK1(L, suff, 3, trace));          
        }
        if (vert == 1 && conf == 1) {
          assert(SolveK1(L, pref, 1, trace));
          assert(SolveK1(L, suff, 0, trace));          
        }
        if (vert == 0 && conf == 0) {
          assert(SolveK1(L, pref, 2, trace));
          assert(SolveK1(L, suff, 1, trace));          
        }
        if (vert == 0 && conf == 1) {
          assert(SolveK1(L, pref, 3, trace));
          assert(SolveK1(L, suff, 0, trace));
        }
        // 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, 1, 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, 0, 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, 0, trace)) {
        return true;
      }
      ans.clear();
      if (SolveK2(L, alive, 1, 0, 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;
  };

  // if (K == 3) {
  //   vector<int> who(N);
  //   const auto Dfs = [&](const auto &self, int u) -> lint {
  //     if (u == N) {

  //       vector<int> a, b, c;
  //       return 1;
  //     }
  //     pair<lint, vector<array<lint, 3>>> best = {4e9, {}};
  //     who[u] = 0;
  //     best = min(best, self(self, u + 1));
  //     who[u] = 1;
  //     best = min(best, self(self, u + 1));
  //     who[u] = 2;
  //     best = min(best, self(self, u + 1));
  //     return best;
  //   };
  // }

  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:205:22: warning: comparison of integer expressions of different signedness: 'int' and 'std::vector<int>::size_type' {aka 'long unsigned int'} [-Wsign-compare]
  205 |       if (i < 0 || i >= alive.size()) return 0;
      |                    ~~^~~~~~~~~~~~~~~
izvanzemaljci.cpp: In lambda function:
izvanzemaljci.cpp:209:22: warning: comparison of integer expressions of different signedness: 'int' and 'std::vector<int>::size_type' {aka 'long unsigned int'} [-Wsign-compare]
  209 |       if (i < 0 || i >= alive.size()) return 0;
      |                    ~~^~~~~~~~~~~~~~~
izvanzemaljci.cpp: In lambda function:
izvanzemaljci.cpp:216:19: warning: comparison of integer expressions of different signedness: 'int' and 'std::vector<int>::size_type' {aka 'long unsigned int'} [-Wsign-compare]
  216 |       if (!(i + 1 == alive.size() ||
      |             ~~~~~~^~~~~~~~~~~~~~~
izvanzemaljci.cpp:291:21: warning: comparison of integer expressions of different signedness: 'int' and 'std::vector<int>::size_type' {aka 'long unsigned int'} [-Wsign-compare]
  291 |         if (!(j + 1 == alive.size() ||
      |               ~~~~~~^~~~~~~~~~~~~~~
izvanzemaljci.cpp: In function 'int main()':
izvanzemaljci.cpp:393:21: 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]
  393 |   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 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 1 ms 204 KB Output is correct
6 Correct 1 ms 204 KB Output is correct
7 Correct 68 ms 3820 KB Output is correct
8 Correct 71 ms 3836 KB Output is correct
9 Correct 80 ms 3812 KB Output is correct
10 Correct 73 ms 3812 KB Output is correct
11 Correct 69 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 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 0 ms 204 KB Output is correct
10 Correct 445 ms 12216 KB Output is correct
11 Correct 453 ms 12308 KB Output is correct
12 Correct 463 ms 12220 KB Output is correct
13 Correct 456 ms 12216 KB Output is correct
14 Correct 483 ms 12208 KB Output is correct
15 Correct 463 ms 12348 KB Output is correct
16 Correct 522 ms 12204 KB Output is correct
17 Correct 369 ms 11260 KB Output is correct
18 Correct 370 ms 10976 KB Output is correct
19 Correct 371 ms 10092 KB Output is correct
20 Correct 409 ms 10644 KB Output is correct
21 Correct 364 ms 12216 KB Output is correct
22 Correct 433 ms 12332 KB Output is correct
23 Correct 525 ms 12252 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 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 0 ms 204 KB Output is correct
9 Incorrect 1 ms 204 KB Output isn't correct
10 Halted 0 ms 0 KB -

Subtask #4
30.0 / 30.0

# 결과 실행 시간 메모리 Grader output
1 Correct 113 ms 460 KB Output is correct
2 Correct 83 ms 492 KB Output is correct
3 Correct 88 ms 460 KB Output is correct
4 Correct 66 ms 460 KB Output is correct
5 Correct 65 ms 460 KB Output is correct
6 Correct 92 ms 460 KB Output is correct
7 Correct 87 ms 492 KB Output is correct
8 Correct 60 ms 460 KB Output is correct
9 Correct 47 ms 460 KB Output is correct
10 Correct 81 ms 460 KB Output is correct
11 Correct 70 ms 460 KB Output is correct
12 Correct 93 ms 484 KB Output is correct
13 Correct 47 ms 464 KB Output is correct
14 Correct 78 ms 476 KB Output is correct
15 Correct 47 ms 480 KB Output is correct
16 Correct 39 ms 460 KB Output is correct
17 Correct 46 ms 460 KB Output is correct
18 Correct 46 ms 460 KB Output is correct
19 Correct 47 ms 460 KB Output is correct
20 Correct 60 ms 460 KB Output is correct
21 Correct 52 ms 580 KB Output is correct
22 Correct 55 ms 460 KB Output is correct
23 Correct 46 ms 460 KB Output is correct
24 Correct 46 ms 460 KB Output is correct

Subtask #5
0 / 32.0

# 결과 실행 시간 메모리 Grader output
1 Correct 91 ms 480 KB Output is correct
2 Correct 79 ms 460 KB Output is correct
3 Correct 72 ms 460 KB Output is correct
4 Correct 83 ms 492 KB Output is correct
5 Correct 89 ms 460 KB Output is correct
6 Correct 90 ms 476 KB Output is correct
7 Correct 53 ms 480 KB Output is correct
8 Correct 52 ms 480 KB Output is correct
9 Correct 64 ms 460 KB Output is correct
10 Correct 89 ms 492 KB Output is correct
11 Correct 91 ms 460 KB Output is correct
12 Correct 87 ms 476 KB Output is correct
13 Correct 98 ms 484 KB Output is correct
14 Execution timed out 3017 ms 15112 KB Time limit exceeded
15 Halted 0 ms 0 KB -