oj.uz

답안 #420802

# 제출 시각 아이디 문제 언어 결과 실행 시간 메모리
420802 2021-06-08T14:00:11 Z rama_pang Izvanzemaljci (COI21_izvanzemaljci) C++17
26 / 100
 544 ms 12352 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, vector<int> alive, int config) {
    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 (config == 0) ans.push_back({minX, minY, len});
      if (config == 1) ans.push_back({maxX - len, minY, len});
      if (config == 2) ans.push_back({maxX - len, maxY - len, len});
      if (config == 3) ans.push_back({minX, maxY - len, len});
      return true;
    }
    return false;
  };

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

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

    static vector<lint> prefMinX; prefMinX.resize(alive.size());
    static vector<lint> prefMaxX; prefMaxX.resize(alive.size());
    static vector<lint> prefMinY; prefMinY.resize(alive.size());
    static vector<lint> prefMaxY; prefMaxY.resize(alive.size());

    static vector<lint> suffMinX; suffMinX.resize(alive.size());
    static vector<lint> suffMaxX; suffMaxX.resize(alive.size());
    static vector<lint> suffMinY; suffMinY.resize(alive.size());
    static vector<lint> suffMaxY; suffMaxY.resize(alive.size());

    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));
        assert(SolveK1(L, suff, 0));
        return true;
      }
    }
    return false;
  };

  const auto SolveK3 = [&](int K, lint L) {
    // Configuration: |-

    // Configuration: -|
    // Configuration: -,-
    // Configuration: -`-
    // Configuration: | |
    // Configuration: =

  };

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

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

  assert(Solve(K, lo));
  int it = 0;
  while (ans.size() < K) {
    ans.push_back({lint(3e9 - 2 * it), lint(3e9), 1});
    it++;
  }
  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 function 'int main()':
izvanzemaljci.cpp:194:21: 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]
  194 |   while (ans.size() < K) {
      |          ~~~~~~~~~~~^~~
izvanzemaljci.cpp:151:14: warning: variable 'SolveK3' set but not used [-Wunused-but-set-variable]
  151 |   const auto SolveK3 = [&](int K, lint L) {
      |              ^~~~~~~

Subtask #1
5.0 / 5.0

# 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 0 ms 204 KB Output is correct
6 Correct 1 ms 204 KB Output is correct
7 Correct 84 ms 4288 KB Output is correct
8 Correct 76 ms 4212 KB Output is correct
9 Correct 73 ms 4228 KB Output is correct
10 Correct 78 ms 4224 KB Output is correct
11 Correct 73 ms 4224 KB Output is correct

Subtask #2
21.0 / 21.0

# 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 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 256 KB Output is correct
9 Correct 1 ms 204 KB Output is correct
10 Correct 500 ms 12216 KB Output is correct
11 Correct 473 ms 12216 KB Output is correct
12 Correct 485 ms 12332 KB Output is correct
13 Correct 476 ms 12348 KB Output is correct
14 Correct 459 ms 12352 KB Output is correct
15 Correct 448 ms 12208 KB Output is correct
16 Correct 544 ms 12228 KB Output is correct
17 Correct 402 ms 11288 KB Output is correct
18 Correct 404 ms 10892 KB Output is correct
19 Correct 401 ms 10000 KB Output is correct
20 Correct 482 ms 10652 KB Output is correct
21 Correct 428 ms 12208 KB Output is correct
22 Correct 473 ms 12212 KB Output is correct
23 Correct 524 ms 12200 KB Output is correct

Subtask #3
0 / 12.0

# 결과 실행 시간 메모리 Grader output
1 Runtime error 1 ms 460 KB Execution killed with signal 6
2 Halted 0 ms 0 KB -

Subtask #4
0 / 30.0

# 결과 실행 시간 메모리 Grader output
1 Runtime error 2 ms 460 KB Execution killed with signal 6
2 Halted 0 ms 0 KB -

Subtask #5
0 / 32.0

# 결과 실행 시간 메모리 Grader output
1 Runtime error 2 ms 460 KB Execution killed with signal 6
2 Halted 0 ms 0 KB -