oj.uz

Submission #420810

# Submission time Handle Problem Language Result Execution time Memory
420810 2021-06-08T14:02:08 Z rama_pang Izvanzemaljci (COI21_izvanzemaljci) C++17
26 / 100
 536 ms 12324 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, 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 config, int trace) {
    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) {
        if (trace == 1) {
          assert(SolveK1(L, pref, 2, trace));
          assert(SolveK1(L, suff, 0, trace));
        }
        return true;
      }
    }
    return false;
  };

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

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

  };

  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;
      }
    }
    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++;
  }
  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:196:21: 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]
  196 |   while (ans.size() < K) {
      |          ~~~~~~~~~~~^~~
izvanzemaljci.cpp:153:14: warning: variable 'SolveK3' set but not used [-Wunused-but-set-variable]
  153 |   const auto SolveK3 = [&](int K, lint L, int trace) {
      |              ^~~~~~~

Subtask #1
5.0 / 5.0

# Verdict Execution time Memory 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 91 ms 4224 KB Output is correct
8 Correct 84 ms 4240 KB Output is correct
9 Correct 78 ms 4228 KB Output is correct
10 Correct 77 ms 4220 KB Output is correct
11 Correct 78 ms 4272 KB Output is correct

Subtask #2
21.0 / 21.0

# Verdict Execution time Memory Grader output
1 Correct 0 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 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 476 ms 12220 KB Output is correct
11 Correct 449 ms 12248 KB Output is correct
12 Correct 460 ms 12208 KB Output is correct
13 Correct 466 ms 12216 KB Output is correct
14 Correct 491 ms 12292 KB Output is correct
15 Correct 445 ms 12292 KB Output is correct
16 Correct 536 ms 12224 KB Output is correct
17 Correct 403 ms 11320 KB Output is correct
18 Correct 386 ms 10876 KB Output is correct
19 Correct 402 ms 9988 KB Output is correct
20 Correct 431 ms 10636 KB Output is correct
21 Correct 391 ms 12208 KB Output is correct
22 Correct 467 ms 12324 KB Output is correct
23 Correct 497 ms 12204 KB Output is correct

Subtask #3
0 / 12.0

# Verdict Execution time Memory 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

# Verdict Execution time Memory Grader output
1 Runtime error 1 ms 460 KB Execution killed with signal 6
2 Halted 0 ms 0 KB -

Subtask #5
0 / 32.0

# Verdict Execution time Memory Grader output
1 Runtime error 1 ms 460 KB Execution killed with signal 6
2 Halted 0 ms 0 KB -