Submission #420532

#	Time	Username	Problem	Language	Result	Execution time	Memory
420532		rama_pang	Izvanzemaljci (COI21_izvanzemaljci)	C++17	0 / 100	2 ms	460 KiB

izvanzemaljci

#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) {
    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<int> prefMinX(alive.size());
    vector<int> prefMaxX(alive.size());
    vector<int> prefMinY(alive.size());
    vector<int> prefMaxY(alive.size());

    vector<int> suffMinX(alive.size());
    vector<int> suffMaxX(alive.size());
    vector<int> suffMinY(alive.size());
    vector<int> 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) {
      return max(prefMaxX[i] - prefMinX[i], prefMaxY[i] - prefMinY[i]);
    };
    const auto CalcSuff = [&](int i) {
      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 + 1 < int(alive.size()); i++) {
      pref.emplace_back(alive[i]);
      suff.pop_back();
      if (CalcPref(i) <= L && CalcSuff(i + 1) <= L) {
        if (vert == 0) {
          // horizontal
          assert(SolveK1(L, pref, 2));
          assert(SolveK1(L, suff, 0));
          return true;
        } else {
          // vertical
          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 = 1e9;
  while (lo < hi) {
    lint md = (lo + hi) / 2;
    if (Solve(K, md)) {
      hi = md;
    } else {
      lo = md + 1;
    }
  }

  // const auto Solve = [&](const auto &self, lint L, int k, vector<int> dead, vector<pair<int, int>> squares) -> pair<bool, vector<pair<int, int>>> {
  //   if (count(begin(dead), end(dead), 1) == N) {
  //     return {true, vector<pair<int, int>>(k, {0, 0})};
  //   }
  //   if (k == 0) {
  //     return {false, vector<pair<int, int>>()};
  //   }

  //   for (auto x : {minX, maxX - L}) {
  //     for (auto y : {minY, maxY - L}) {
  //       vector<int> newDead = dead;
  //       for (int i = 0; i < N; i++) if (!dead[i]) {
  //         if (x <= X[i] && X[i] <= x + L && y <= Y[i] && Y[i] <= y + L) {
  //           newDead[i] = 1;
  //         }
  //       }
  //       auto res = self(self, L, k - 1, newDead);
  //       if (res.first) {
  //         res.second.emplace_back(x, y);
  //         return res;
  //       }
  //     }
  //   }
  //   return {false, vector<pair<int, int>>()};
  // };

  // lint lo = 1, hi = 2e9;
  // while (lo < hi) {
  //   lint md = (lo + hi) / 2;
  //   if (Solve(Solve, md, K, vector<int>(N, 0)).first) {
  //     hi = md;
  //   } else {
  //     lo = md + 1;
  //   }
  // }

  for (int i = 0; i < K; i++) {
    cout << ans[i][0] << ' ' << ans[i][1] << ' ' << ans[i][2] << '\n';
  }
  return 0;
}

• Subtask 1: 0 / 5
• Subtask 2: 0 / 21
• Subtask 3: 0 / 12
• Subtask 4: 0 / 30
• Subtask 5: 0 / 32