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Submission #418841

# Submission time Handle Problem Language Result Execution time Memory
418841 2021-06-06T04:40:47 Z rama_pang Demarcation (BOI14_demarcation) C++17
100 / 100
 269 ms 31884 KB 
#include <bits/stdc++.h>
using namespace std;

int main() {
  ios::sync_with_stdio(0);
  cin.tie(0);

  int N;
  cin >> N;
  vector<array<int, 2>> A(N);
  for (int i = 0; i < N; i++) {
    for (int j = 0; j < 2; j++) {
      cin >> A[i][j];
    }
  }

  // We can make it into a tree-like structure.
  // Then, a split is = pick an edge and delete it.
  // The size of the remaining must be equal, so
  // there are only 1 option for vertical (and 1
  // for horizontal).
  //
  // To check whether they are congruent, we can make
  // a list of (length, degree) and check whether
  // some cyclic shift is equal.
  //
  // Time complexity: O(N log N).

  const auto Solve = [&](vector<array<int, 2>> A) -> pair<bool, array<int, 4>> {
    int N = A.size();
    long long area = 0;
    for (int i = 0; i < N; i++) {
      area += 1ll * A[i][0] * A[(i + 1) % N][1];
      area -= 1ll * A[i][1] * A[(i + 1) % N][0];
    }
    if (area < 0) {
      area *= -1;
      reverse(begin(A), end(A));
    }
    assert(area % 2 == 0);
    area /= 2;
    if (area % 2 == 1) { // we cannot divide by 2
      return {false, {0, 0, 0, 0}};
    }
    area /= 2;

    vector<array<int, 4>> lines;
    vector<array<int, 3>> events;
    for (int i = 0; i < N; i++) {
      auto p = A[i];
      auto q = A[(i + 1) % N];
      if (p[0] == q[0]) {
        continue;
      }
      if (p[0] < q[0]) { // bottom
        lines.push_back({p[1], +1, p[0], q[0]});
      } else { // top
        lines.push_back({p[1], -1, q[0], p[0]});
      }
    }

    vector<int> lastX(lines.size());
    for (int i = 0; i < int(lines.size()); i++) {
      events.push_back({lines[i][2], -1, i});
      events.push_back({lines[i][3], +1, i});
      lastX[i] = lines[i][2];
    }

    vector<array<int, 4>> rectangle;
    sort(begin(events), end(events));
    set<pair<array<int, 4>, int>> active;
    for (auto ev : events) {
      auto [x, type, id] = ev;

      auto top = active.lower_bound({lines[id], -1});
      auto bot = top;
      bool match = true;
      if (top == end(active)) {
        match = false;
      } else {
        if (type < 0) {
          if (bot == begin(active)) {
            match = false;
          } else {
            bot--;
          }
        } else {
          if (lines[id][1] > 0) {
            if (next(top) == end(active)){
              match = false;
            } else {
              top++;
            }
          } else {
            if (bot == begin(active)) {
              match = false;
            } else {
              bot--;
            }
          }
        }
      }

      if (match && bot->first[1] > 0 && top->first[1] < 0) {
        if (lastX[bot->second] <= x - 1 && lastX[top->second] <= x - 1) {
          assert(lastX[bot->second] == lastX[top->second]);
          rectangle.push_back({lastX[bot->second], x - 1, bot->first[0], top->first[0] - 1});
          lastX[bot->second] = lastX[top->second] = x;
        }
      }

      if (type < 0) {
        active.emplace(lines[id], id);
      } else {
        active.erase({lines[id], id});
      }
    }

    map<int, vector<array<int, 3>>> borderL;
    map<int, vector<array<int, 3>>> borderR;

    for (int id = 0; id < int(rectangle.size()); id++) {
      auto rect = rectangle[id];
      borderL[rect[0]].push_back({rect[2], rect[3], id});
      borderR[rect[1]].push_back({rect[2], rect[3], id});
    }

    for (auto &p : borderL) sort(begin(p.second), end(p.second));
    for (auto &p : borderR) sort(begin(p.second), end(p.second));

    vector<vector<int>> treeLft(rectangle.size());
    vector<vector<int>> treeRgt(rectangle.size());
    for (int id = 0; id < int(rectangle.size()); id++) {
      auto rect = rectangle[id];
      if (borderR.count(rect[0] - 1)) {
        auto &v = borderR[rect[0] - 1];
        auto it = lower_bound(begin(v), end(v), array<int, 3>{rect[3] + 1, -int(1e9), -int(1e9)});
        while (it != begin(v)) {
          it--;
          if ((*it)[1] < rect[2]) break;
          treeLft[id].emplace_back((*it)[2]);
        }
      }
      if (borderL.count(rect[1] + 1)) {
        auto &v = borderL[rect[1] + 1];
        auto it = lower_bound(begin(v), end(v), array<int, 3>{rect[3] + 1, -int(1e9), -int(1e9)});
        while (it != begin(v)) {
          it--;
          if ((*it)[1] < rect[2]) break;
          treeRgt[id].emplace_back((*it)[2]);
        }
      }
    }

    vector<array<int, 4>> cut;
    vector<long long> siz(rectangle.size());
    const auto Dfs = [&](const auto &self, int u, int p) -> void {
      for (auto v : treeLft[u]) if (v != p) {
        self(self, v, u);
        siz[u] += siz[v];
      }
      for (auto v : treeRgt[u]) if (v != p) {
        self(self, v, u);
        siz[u] += siz[v];
      }
      long long current = 1ll * (rectangle[u][1] - rectangle[u][0] + 1) * (rectangle[u][3] - rectangle[u][2] + 1);
      siz[u] += current;
    };

    const auto DfsReroot = [&](const auto &self, int u, int p) -> void {
      for (auto v : treeLft[u]) if (v != p) {
        siz[u] -= siz[v];
        siz[v] += siz[u];
        self(self, v, u);
        siz[v] -= siz[u];
        siz[u] += siz[v];
      }
      for (auto v : treeRgt[u]) if (v != p) {
        siz[u] -= siz[v];
        siz[v] += siz[u];
        self(self, v, u);
        siz[v] -= siz[u];
        siz[u] += siz[v];
      }

      long long sumLft = 0;
      long long sumRgt = 0;
      for (auto v : treeLft[u]) {
        sumLft += siz[v];
        if (siz[v] == area) {
          cut.push_back({rectangle[u][0], max(rectangle[u][2], rectangle[v][2]),
                         rectangle[u][0], min(rectangle[u][3], rectangle[v][3]) + 1});
        }
      }
      for (auto v : treeRgt[u]) {
        sumRgt += siz[v];
        if (siz[v] == area) {
          cut.push_back({rectangle[u][1] + 1, max(rectangle[u][2], rectangle[v][2]),
                         rectangle[u][1] + 1, min(rectangle[u][3], rectangle[v][3]) + 1});
        }
      }

      long long current = 1ll * (rectangle[u][1] - rectangle[u][0] + 1) * (rectangle[u][3] - rectangle[u][2] + 1);
      if (sumLft < area && sumLft + current > area) {
        long long need = area - sumLft;
        if (need % (rectangle[u][3] - rectangle[u][2] + 1) == 0) {
          need /= rectangle[u][3] - rectangle[u][2] + 1;
          assert(rectangle[u][0] + need - 1 <= rectangle[u][1]);
          cut.push_back({rectangle[u][0] + int(need), rectangle[u][2],
                         rectangle[u][0] + int(need), rectangle[u][3] + 1});
        }
      }
      if (sumRgt < area && sumRgt + current > area) {
        long long need = area - sumRgt;
        if (need % (rectangle[u][3] - rectangle[u][2] + 1) == 0) {
          need /= rectangle[u][3] - rectangle[u][2] + 1;
          assert(rectangle[u][0] + need - 1 <= rectangle[u][1]);
          cut.push_back({rectangle[u][1] + 1 - int(need), rectangle[u][2],
                         rectangle[u][1] + 1 - int(need), rectangle[u][3] + 1});
        }
      }
    };

    Dfs(Dfs, 0, -1);
    DfsReroot(DfsReroot, 0, -1);

    sort(begin(cut), end(cut));
    cut.resize(unique(begin(cut), end(cut)) - begin(cut));
    assert(cut.size() <= 1);

    if (cut.empty()) {
      return {false, {0, 0, 0, 0}};
    }

    vector<array<int, 2>> polyA;
    vector<array<int, 2>> polyB;
    vector<int> whereIs(2, -1);
    for (int i = 0; i < N; i++) {
      auto p = A[i];
      auto q = A[(i + 1) % N];
      if (p[0] == q[0]) {
        continue;
      }
      if (p[0] < q[0] && p[0] <= cut[0][0] && cut[0][0] <= q[0] && p[1] == cut[0][1]) {
        whereIs[0] = i;
      }
      if (p[0] > q[0] && q[0] <= cut[0][0] && cut[0][0] <= p[0] && p[1] == cut[0][3]) {
        whereIs[1] = i;
      }
    }
    assert(whereIs[0] != -1 && whereIs[1] != -1);
    { // Make polyA
      int cur = (whereIs[0] + 1) % N;
      while (true) {
        polyA.push_back(A[cur]);
        if (cur == whereIs[1]) {
          break;
        }
        cur = (cur + 1) % N;
      }
      polyA.push_back({cut[0][2], cut[0][3]});
      polyA.push_back({cut[0][0], cut[0][1]});
    }
    { // Make polyB
      int cur = (whereIs[1] + 1) % N;
      while (true) {
        polyB.push_back(A[cur]);
        if (cur == whereIs[0]) {
          break;
        }
        cur = (cur + 1) % N;
      }
      polyB.push_back({cut[0][0], cut[0][1]});
      polyB.push_back({cut[0][2], cut[0][3]});
    }

    const auto DeleteUselessPoints = [&](vector<array<int, 2>> poly) {
      vector<int> markBad(poly.size());
      for (int i = 0; i < int(poly.size()); i++) {
        auto p = poly[i];
        auto prv = poly[(i + poly.size() - 1) % poly.size()];
        auto nxt = poly[(i + poly.size() + 1) % poly.size()];
        if (prv[0] == p[0] && p[0] == nxt[0]) {
          markBad[i] = 1;
        }
        if (prv[1] == p[1] && p[1] == nxt[1]) {
          markBad[i] = 1;
        }
      }
      vector<array<int, 2>> newPoly;
      for (int i = 0; i < int(poly.size()); i++) {
        if (!markBad[i]) {
          newPoly.emplace_back(poly[i]);
        }
      }
      return newPoly;
    };

    polyA.resize(unique(begin(polyA), end(polyA)) - begin(polyA));
    polyB.resize(unique(begin(polyB), end(polyB)) - begin(polyB));

    polyA = DeleteUselessPoints(polyA);
    polyB = DeleteUselessPoints(polyB);

    const auto Congruent = [&]() -> bool {
      const auto MakeCanon = [&](vector<array<int, 2>> poly) {
        auto mn = poly[0];
        for (auto p : poly) {
          mn = min(mn, p);
        }
        for (int i = 0; i < int(poly.size()); i++) {
          if (poly[i] == mn) {
            vector<array<int, 2>> newPoly;
            for (int j = i; j < int(poly.size()); j++) {
              newPoly.emplace_back(poly[j]);
            }
            for (int j = 0; j < i; j++) {
              newPoly.emplace_back(poly[j]);
            }
            poly = newPoly;
            break;
          }
        }
        assert(mn == poly[0]);
        for (auto &p : poly) {
          p[0] -= mn[0];
          p[1] -= mn[1];
        }
        return poly;
      };
      polyA = MakeCanon(polyA);
      polyB = MakeCanon(polyB);
      for (int ref1 = 0; ref1 < 2; ref1++) {
        for (int ref2 = 0; ref2 < 2; ref2++) {
          for (int swp = 0; swp < 2; swp++) {
            for (int rot = 0; rot < 4; rot++) {
              if (polyA == MakeCanon(polyB)) {
                return true;
              }

              reverse(begin(polyB), end(polyB));
              if (polyA == MakeCanon(polyB)) {
                return true;
              }
              reverse(begin(polyB), end(polyB));

              for (auto &p : polyB) {
                swap(p[0], p[1]);
                p[1] *= -1;
              }
            }
            for (auto &p : polyB) {
              swap(p[0], p[1]);
            }
          }
          for (auto &p : polyB) {
            p[1] *= -1;
          }
        }
        for (auto &p : polyB) {
          p[0] *= -1;
        }
      }
      return false;
    };

    if (Congruent()) {
      return {true, cut[0]};
    } else {
      return {false, {0, 0, 0, 0}};
    }
  };

  auto ans = Solve(A);
  if (ans.first) {
    for (int i = 0; i < 4; i++) {
      cout << ans.second[i] << " \n"[i == 3];
    }
    return 0;
  }

  for (int i = 0; i < N; i++) {
    swap(A[i][0], A[i][1]);
  }
  ans = Solve(A);
  swap(ans.second[0], ans.second[1]);
  swap(ans.second[2], ans.second[3]);

  if (ans.first) {
    for (int i = 0; i < 4; i++) {
      cout << ans.second[i] << " \n"[i == 3];
    }
    return 0;
  }

  cout << "NO\n";
  return 0;
}

Subtask #1
12.0 / 12.0

# Verdict Execution time Memory Grader output
1 Correct 13 ms 3784 KB Output is correct
2 Correct 1 ms 204 KB Output is correct
3 Correct 1 ms 204 KB Output is correct
4 Correct 17 ms 3396 KB Output is correct
5 Correct 1 ms 316 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 98 ms 19860 KB Output is correct
10 Correct 1 ms 332 KB Output is correct
11 Correct 1 ms 332 KB Output is correct
12 Correct 1 ms 204 KB Output is correct
13 Correct 1 ms 204 KB Output is correct

Subtask #2
15.0 / 15.0

# 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 280 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 308 KB Output is correct
10 Correct 1 ms 204 KB Output is correct
11 Correct 1 ms 204 KB Output is correct
12 Correct 1 ms 204 KB Output is correct
13 Correct 1 ms 204 KB Output is correct
14 Correct 1 ms 312 KB Output is correct
15 Correct 1 ms 204 KB Output is correct
16 Correct 1 ms 204 KB Output is correct
17 Correct 1 ms 332 KB Output is correct
18 Correct 1 ms 204 KB Output is correct
19 Correct 1 ms 204 KB Output is correct
20 Correct 1 ms 332 KB Output is correct
21 Correct 1 ms 332 KB Output is correct
22 Correct 1 ms 332 KB Output is correct
23 Correct 1 ms 204 KB Output is correct
24 Correct 1 ms 204 KB Output is correct
25 Correct 1 ms 204 KB Output is correct
26 Correct 1 ms 204 KB Output is correct
27 Correct 1 ms 204 KB Output is correct
28 Correct 1 ms 204 KB Output is correct
29 Correct 1 ms 204 KB Output is correct
30 Correct 1 ms 204 KB Output is correct

Subtask #3
23.0 / 23.0

# 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 312 KB Output is correct
4 Correct 1 ms 204 KB Output is correct
5 Correct 1 ms 312 KB Output is correct
6 Correct 1 ms 204 KB Output is correct
7 Correct 1 ms 332 KB Output is correct
8 Correct 1 ms 348 KB Output is correct
9 Correct 1 ms 204 KB Output is correct
10 Correct 1 ms 204 KB Output is correct
11 Correct 1 ms 204 KB Output is correct
12 Correct 1 ms 204 KB Output is correct
13 Correct 1 ms 204 KB Output is correct
14 Correct 1 ms 204 KB Output is correct
15 Correct 1 ms 204 KB Output is correct
16 Correct 1 ms 204 KB Output is correct
17 Correct 1 ms 204 KB Output is correct
18 Correct 1 ms 332 KB Output is correct
19 Correct 1 ms 204 KB Output is correct
20 Correct 1 ms 204 KB Output is correct
21 Correct 1 ms 332 KB Output is correct
22 Correct 1 ms 332 KB Output is correct
23 Correct 1 ms 204 KB Output is correct
24 Correct 1 ms 204 KB Output is correct
25 Correct 1 ms 204 KB Output is correct
26 Correct 1 ms 204 KB Output is correct
27 Correct 1 ms 204 KB Output is correct
28 Correct 1 ms 312 KB Output is correct
29 Correct 1 ms 204 KB Output is correct
30 Correct 1 ms 204 KB Output is correct
31 Correct 1 ms 204 KB Output is correct
32 Correct 4 ms 844 KB Output is correct
33 Correct 3 ms 716 KB Output is correct
34 Correct 2 ms 716 KB Output is correct
35 Correct 2 ms 588 KB Output is correct
36 Correct 4 ms 716 KB Output is correct
37 Correct 4 ms 716 KB Output is correct
38 Correct 2 ms 716 KB Output is correct
39 Correct 2 ms 444 KB Output is correct

Subtask #4
50.0 / 50.0

# Verdict Execution time Memory Grader output
1 Correct 13 ms 3856 KB Output is correct
2 Correct 1 ms 204 KB Output is correct
3 Correct 1 ms 204 KB Output is correct
4 Correct 17 ms 3396 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 98 ms 20044 KB Output is correct
10 Correct 1 ms 204 KB Output is correct
11 Correct 1 ms 332 KB Output is correct
12 Correct 1 ms 312 KB Output is correct
13 Correct 1 ms 204 KB Output is correct
14 Correct 1 ms 204 KB Output is correct
15 Correct 1 ms 308 KB Output is correct
16 Correct 1 ms 204 KB Output is correct
17 Correct 1 ms 204 KB Output is correct
18 Correct 1 ms 204 KB Output is correct
19 Correct 1 ms 204 KB Output is correct
20 Correct 1 ms 204 KB Output is correct
21 Correct 1 ms 332 KB Output is correct
22 Correct 1 ms 204 KB Output is correct
23 Correct 1 ms 204 KB Output is correct
24 Correct 1 ms 332 KB Output is correct
25 Correct 1 ms 332 KB Output is correct
26 Correct 1 ms 204 KB Output is correct
27 Correct 1 ms 204 KB Output is correct
28 Correct 1 ms 204 KB Output is correct
29 Correct 1 ms 204 KB Output is correct
30 Correct 1 ms 204 KB Output is correct
31 Correct 1 ms 204 KB Output is correct
32 Correct 1 ms 204 KB Output is correct
33 Correct 1 ms 204 KB Output is correct
34 Correct 1 ms 204 KB Output is correct
35 Correct 4 ms 844 KB Output is correct
36 Correct 3 ms 716 KB Output is correct
37 Correct 2 ms 716 KB Output is correct
38 Correct 2 ms 716 KB Output is correct
39 Correct 4 ms 748 KB Output is correct
40 Correct 3 ms 656 KB Output is correct
41 Correct 3 ms 708 KB Output is correct
42 Correct 2 ms 332 KB Output is correct
43 Correct 3 ms 840 KB Output is correct
44 Correct 95 ms 11756 KB Output is correct
45 Correct 62 ms 7360 KB Output is correct
46 Correct 62 ms 8524 KB Output is correct
47 Correct 36 ms 5024 KB Output is correct
48 Correct 29 ms 6792 KB Output is correct
49 Correct 112 ms 13216 KB Output is correct
50 Correct 58 ms 9308 KB Output is correct
51 Correct 140 ms 25916 KB Output is correct
52 Correct 269 ms 30356 KB Output is correct
53 Correct 23 ms 3024 KB Output is correct
54 Correct 168 ms 14572 KB Output is correct
55 Correct 82 ms 13272 KB Output is correct
56 Correct 131 ms 24124 KB Output is correct
57 Correct 230 ms 23396 KB Output is correct
58 Correct 173 ms 29228 KB Output is correct
59 Correct 181 ms 31884 KB Output is correct
60 Correct 79 ms 13312 KB Output is correct
61 Correct 19 ms 4020 KB Output is correct
62 Correct 31 ms 5944 KB Output is correct
63 Correct 45 ms 8156 KB Output is correct
64 Correct 44 ms 8768 KB Output is correct
65 Correct 9 ms 1228 KB Output is correct
66 Correct 168 ms 24412 KB Output is correct