oj.uz

답안 #420732

# 제출 시각 아이디 문제 언어 결과 실행 시간 메모리
420732 2021-06-08T13:36:30 Z rama_pang Izvanzemaljci (COI21_izvanzemaljci) C++17
26 / 100
 1375 ms 12484 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 N log MAX).

  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;

    sort(begin(alive), end(alive), [&](int i, int j) {
      if (!vert) {
        return pair(Y[i], X[i]) < pair(Y[j], X[j]);
      } else {
        return pair(X[i], Y[i]) < pair(X[j], Y[j]);
      }
    });

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

    vector<lint> suffMinX(alive.size());
    vector<lint> suffMaxX(alive.size());
    vector<lint> suffMinY(alive.size());
    vector<lint> suffMaxY(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 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:92:22: warning: comparison of integer expressions of different signedness: 'int' and 'std::vector<int>::size_type' {aka 'long unsigned int'} [-Wsign-compare]
   92 |       if (i < 0 || i >= alive.size()) return 0;
      |                    ~~^~~~~~~~~~~~~~~
izvanzemaljci.cpp: In lambda function:
izvanzemaljci.cpp:96:22: warning: comparison of integer expressions of different signedness: 'int' and 'std::vector<int>::size_type' {aka 'long unsigned int'} [-Wsign-compare]
   96 |       if (i < 0 || i >= alive.size()) return 0;
      |                    ~~^~~~~~~~~~~~~~~
izvanzemaljci.cpp: In lambda function:
izvanzemaljci.cpp:107:19: warning: comparison of integer expressions of different signedness: 'int' and 'std::vector<int>::size_type' {aka 'long unsigned int'} [-Wsign-compare]
  107 |       if (!(i + 1 == alive.size() ||
      |             ~~~~~~^~~~~~~~~~~~~~~
izvanzemaljci.cpp: In function 'int main()':
izvanzemaljci.cpp:154:21: 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]
  154 |   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 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 40 ms 2656 KB Output is correct
8 Correct 46 ms 2648 KB Output is correct
9 Correct 48 ms 2656 KB Output is correct
10 Correct 43 ms 2716 KB Output is correct
11 Correct 44 ms 2712 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 1300 ms 12340 KB Output is correct
11 Correct 1177 ms 12384 KB Output is correct
12 Correct 1304 ms 12472 KB Output is correct
13 Correct 1233 ms 12484 KB Output is correct
14 Correct 1294 ms 12484 KB Output is correct
15 Correct 1217 ms 12348 KB Output is correct
16 Correct 1375 ms 12272 KB Output is correct
17 Correct 902 ms 11208 KB Output is correct
18 Correct 833 ms 10852 KB Output is correct
19 Correct 930 ms 9984 KB Output is correct
20 Correct 1032 ms 10656 KB Output is correct
21 Correct 942 ms 12244 KB Output is correct
22 Correct 1221 ms 12200 KB Output is correct
23 Correct 1247 ms 12208 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 1 ms 460 KB Execution killed with signal 6
2 Halted 0 ms 0 KB -