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IDProblemSubmitterResultTimeMemoryLanguageFile sizeSubmit timeJudge time
#113916#6570. Who Watches the Watchmen?maspyWA 1ms3568kbC++2318.9kb2023-06-20 02:09:092023-06-20 02:09:11

Judging History

你现在查看的是最新测评结果

  • [2023-08-10 23:21:45]
  • System Update: QOJ starts to keep a history of the judgings of all the submissions.
  • [2023-06-20 02:09:11]
  • 评测
  • 测评结果:WA
  • 用时:1ms
  • 内存:3568kb
  • [2023-06-20 02:09:09]
  • 提交

answer

#line 1 "library/my_template.hpp"
#if defined(LOCAL)
#include <my_template_compiled.hpp>
#else
#pragma GCC optimize("Ofast")
#pragma GCC optimize("unroll-loops")

#include <bits/stdc++.h>

using namespace std;

using ll = long long;
using u32 = unsigned int;
using u64 = unsigned long long;
using i128 = __int128;

template <class T>
constexpr T infty = 0;
template <>
constexpr int infty<int> = 1'000'000'000;
template <>
constexpr ll infty<ll> = ll(infty<int>) * infty<int> * 2;
template <>
constexpr u32 infty<u32> = infty<int>;
template <>
constexpr u64 infty<u64> = infty<ll>;
template <>
constexpr i128 infty<i128> = i128(infty<ll>) * infty<ll>;
template <>
constexpr double infty<double> = infty<ll>;
template <>
constexpr long double infty<long double> = infty<ll>;

using pi = pair<ll, ll>;
using vi = vector<ll>;
template <class T>
using vc = vector<T>;
template <class T>
using vvc = vector<vc<T>>;
template <class T>
using vvvc = vector<vvc<T>>;
template <class T>
using vvvvc = vector<vvvc<T>>;
template <class T>
using vvvvvc = vector<vvvvc<T>>;
template <class T>
using pq = priority_queue<T>;
template <class T>
using pqg = priority_queue<T, vector<T>, greater<T>>;

#define vv(type, name, h, ...) \
  vector<vector<type>> name(h, vector<type>(__VA_ARGS__))
#define vvv(type, name, h, w, ...)   \
  vector<vector<vector<type>>> name( \
      h, vector<vector<type>>(w, vector<type>(__VA_ARGS__)))
#define vvvv(type, name, a, b, c, ...)       \
  vector<vector<vector<vector<type>>>> name( \
      a, vector<vector<vector<type>>>(       \
             b, vector<vector<type>>(c, vector<type>(__VA_ARGS__))))

// https://trap.jp/post/1224/
#define FOR1(a) for (ll _ = 0; _ < ll(a); ++_)
#define FOR2(i, a) for (ll i = 0; i < ll(a); ++i)
#define FOR3(i, a, b) for (ll i = a; i < ll(b); ++i)
#define FOR4(i, a, b, c) for (ll i = a; i < ll(b); i += (c))
#define FOR1_R(a) for (ll i = (a)-1; i >= ll(0); --i)
#define FOR2_R(i, a) for (ll i = (a)-1; i >= ll(0); --i)
#define FOR3_R(i, a, b) for (ll i = (b)-1; i >= ll(a); --i)
#define overload4(a, b, c, d, e, ...) e
#define overload3(a, b, c, d, ...) d
#define FOR(...) overload4(__VA_ARGS__, FOR4, FOR3, FOR2, FOR1)(__VA_ARGS__)
#define FOR_R(...) overload3(__VA_ARGS__, FOR3_R, FOR2_R, FOR1_R)(__VA_ARGS__)

#define FOR_subset(t, s) \
  for (ll t = (s); t >= 0; t = (t == 0 ? -1 : (t - 1) & (s)))
#define all(x) x.begin(), x.end()
#define len(x) ll(x.size())
#define elif else if

#define eb emplace_back
#define mp make_pair
#define mt make_tuple
#define fi first
#define se second

#define stoi stoll

int popcnt(int x) { return __builtin_popcount(x); }
int popcnt(u32 x) { return __builtin_popcount(x); }
int popcnt(ll x) { return __builtin_popcountll(x); }
int popcnt(u64 x) { return __builtin_popcountll(x); }
// (0, 1, 2, 3, 4) -> (-1, 0, 1, 1, 2)
int topbit(int x) { return (x == 0 ? -1 : 31 - __builtin_clz(x)); }
int topbit(u32 x) { return (x == 0 ? -1 : 31 - __builtin_clz(x)); }
int topbit(ll x) { return (x == 0 ? -1 : 63 - __builtin_clzll(x)); }
int topbit(u64 x) { return (x == 0 ? -1 : 63 - __builtin_clzll(x)); }
// (0, 1, 2, 3, 4) -> (-1, 0, 1, 0, 2)
int lowbit(int x) { return (x == 0 ? -1 : __builtin_ctz(x)); }
int lowbit(u32 x) { return (x == 0 ? -1 : __builtin_ctz(x)); }
int lowbit(ll x) { return (x == 0 ? -1 : __builtin_ctzll(x)); }
int lowbit(u64 x) { return (x == 0 ? -1 : __builtin_ctzll(x)); }

template <typename T, typename U>
T ceil(T x, U y) {
  return (x > 0 ? (x + y - 1) / y : x / y);
}
template <typename T, typename U>
T floor(T x, U y) {
  return (x > 0 ? x / y : (x - y + 1) / y);
}
template <typename T, typename U>
pair<T, T> divmod(T x, U y) {
  T q = floor(x, y);
  return {q, x - q * y};
}

template <typename T, typename U>
T SUM(const vector<U> &A) {
  T sum = 0;
  for (auto &&a: A) sum += a;
  return sum;
}

#define MIN(v) *min_element(all(v))
#define MAX(v) *max_element(all(v))
#define LB(c, x) distance((c).begin(), lower_bound(all(c), (x)))
#define UB(c, x) distance((c).begin(), upper_bound(all(c), (x)))
#define UNIQUE(x) \
  sort(all(x)), x.erase(unique(all(x)), x.end()), x.shrink_to_fit()

template <typename T>
T POP(deque<T> &que) {
  T a = que.front();
  que.pop_front();
  return a;
}
template <typename T>
T POP(pq<T> &que) {
  T a = que.top();
  que.pop();
  return a;
}
template <typename T>
T POP(pqg<T> &que) {
  assert(!que.empty());
  T a = que.top();
  que.pop();
  return a;
}
template <typename T>
T POP(vc<T> &que) {
  assert(!que.empty());
  T a = que.back();
  que.pop_back();
  return a;
}

template <typename F>
ll binary_search(F check, ll ok, ll ng, bool check_ok = true) {
  if (check_ok) assert(check(ok));
  while (abs(ok - ng) > 1) {
    auto x = (ng + ok) / 2;
    tie(ok, ng) = (check(x) ? mp(x, ng) : mp(ok, x));
  }
  return ok;
}
template <typename F>
double binary_search_real(F check, double ok, double ng, int iter = 100) {
  FOR(iter) {
    double x = (ok + ng) / 2;
    tie(ok, ng) = (check(x) ? mp(x, ng) : mp(ok, x));
  }
  return (ok + ng) / 2;
}

template <class T, class S>
inline bool chmax(T &a, const S &b) {
  return (a < b ? a = b, 1 : 0);
}
template <class T, class S>
inline bool chmin(T &a, const S &b) {
  return (a > b ? a = b, 1 : 0);
}

// ? は -1
vc<int> s_to_vi(const string &S, char first_char) {
  vc<int> A(S.size());
  FOR(i, S.size()) { A[i] = (S[i] != '?' ? S[i] - first_char : -1); }
  return A;
}

template <typename T, typename U>
vector<T> cumsum(vector<U> &A, int off = 1) {
  int N = A.size();
  vector<T> B(N + 1);
  FOR(i, N) { B[i + 1] = B[i] + A[i]; }
  if (off == 0) B.erase(B.begin());
  return B;
}

// stable sort
template <typename T>
vector<int> argsort(const vector<T> &A) {
  vector<int> ids(len(A));
  iota(all(ids), 0);
  sort(all(ids),
       [&](int i, int j) { return (A[i] == A[j] ? i < j : A[i] < A[j]); });
  return ids;
}

// A[I[0]], A[I[1]], ...
template <typename T>
vc<T> rearrange(const vc<T> &A, const vc<int> &I) {
  vc<T> B(len(I));
  FOR(i, len(I)) B[i] = A[I[i]];
  return B;
}
#endif
#line 1 "library/other/io.hpp"
// based on yosupo's fastio
#include <unistd.h>

namespace fastio {
#define FASTIO
// クラスが read(), print() を持っているかを判定するメタ関数
struct has_write_impl {
  template <class T>
  static auto check(T &&x) -> decltype(x.write(), std::true_type{});

  template <class T>
  static auto check(...) -> std::false_type;
};

template <class T>
class has_write : public decltype(has_write_impl::check<T>(std::declval<T>())) {
};

struct has_read_impl {
  template <class T>
  static auto check(T &&x) -> decltype(x.read(), std::true_type{});

  template <class T>
  static auto check(...) -> std::false_type;
};

template <class T>
class has_read : public decltype(has_read_impl::check<T>(std::declval<T>())) {};

struct Scanner {
  FILE *fp;
  char line[(1 << 15) + 1];
  size_t st = 0, ed = 0;
  void reread() {
    memmove(line, line + st, ed - st);
    ed -= st;
    st = 0;
    ed += fread(line + ed, 1, (1 << 15) - ed, fp);
    line[ed] = '\0';
  }
  bool succ() {
    while (true) {
      if (st == ed) {
        reread();
        if (st == ed) return false;
      }
      while (st != ed && isspace(line[st])) st++;
      if (st != ed) break;
    }
    if (ed - st <= 50) {
      bool sep = false;
      for (size_t i = st; i < ed; i++) {
        if (isspace(line[i])) {
          sep = true;
          break;
        }
      }
      if (!sep) reread();
    }
    return true;
  }
  template <class T, enable_if_t<is_same<T, string>::value, int> = 0>
  bool read_single(T &ref) {
    if (!succ()) return false;
    while (true) {
      size_t sz = 0;
      while (st + sz < ed && !isspace(line[st + sz])) sz++;
      ref.append(line + st, sz);
      st += sz;
      if (!sz || st != ed) break;
      reread();
    }
    return true;
  }
  template <class T, enable_if_t<is_integral<T>::value, int> = 0>
  bool read_single(T &ref) {
    if (!succ()) return false;
    bool neg = false;
    if (line[st] == '-') {
      neg = true;
      st++;
    }
    ref = T(0);
    while (isdigit(line[st])) { ref = 10 * ref + (line[st++] & 0xf); }
    if (neg) ref = -ref;
    return true;
  }
  template <typename T,
            typename enable_if<has_read<T>::value>::type * = nullptr>
  inline bool read_single(T &x) {
    x.read();
    return true;
  }
  bool read_single(double &ref) {
    string s;
    if (!read_single(s)) return false;
    ref = std::stod(s);
    return true;
  }
  bool read_single(char &ref) {
    string s;
    if (!read_single(s) || s.size() != 1) return false;
    ref = s[0];
    return true;
  }
  template <class T>
  bool read_single(vector<T> &ref) {
    for (auto &d: ref) {
      if (!read_single(d)) return false;
    }
    return true;
  }
  template <class T, class U>
  bool read_single(pair<T, U> &p) {
    return (read_single(p.first) && read_single(p.second));
  }
  template <size_t N = 0, typename T>
  void read_single_tuple(T &t) {
    if constexpr (N < std::tuple_size<T>::value) {
      auto &x = std::get<N>(t);
      read_single(x);
      read_single_tuple<N + 1>(t);
    }
  }
  template <class... T>
  bool read_single(tuple<T...> &tpl) {
    read_single_tuple(tpl);
    return true;
  }
  void read() {}
  template <class H, class... T>
  void read(H &h, T &... t) {
    bool f = read_single(h);
    assert(f);
    read(t...);
  }
  Scanner(FILE *fp) : fp(fp) {}
};

struct Printer {
  Printer(FILE *_fp) : fp(_fp) {}
  ~Printer() { flush(); }

  static constexpr size_t SIZE = 1 << 15;
  FILE *fp;
  char line[SIZE], small[50];
  size_t pos = 0;
  void flush() {
    fwrite(line, 1, pos, fp);
    pos = 0;
  }
  void write(const char val) {
    if (pos == SIZE) flush();
    line[pos++] = val;
  }
  template <class T, enable_if_t<is_integral<T>::value, int> = 0>
  void write(T val) {
    if (pos > (1 << 15) - 50) flush();
    if (val == 0) {
      write('0');
      return;
    }
    if (val < 0) {
      write('-');
      val = -val; // todo min
    }
    size_t len = 0;
    while (val) {
      small[len++] = char(0x30 | (val % 10));
      val /= 10;
    }
    for (size_t i = 0; i < len; i++) { line[pos + i] = small[len - 1 - i]; }
    pos += len;
  }
  void write(const string s) {
    for (char c: s) write(c);
  }
  void write(const char *s) {
    size_t len = strlen(s);
    for (size_t i = 0; i < len; i++) write(s[i]);
  }
  void write(const double x) {
    ostringstream oss;
    oss << fixed << setprecision(15) << x;
    string s = oss.str();
    write(s);
  }
  void write(const long double x) {
    ostringstream oss;
    oss << fixed << setprecision(15) << x;
    string s = oss.str();
    write(s);
  }
  template <typename T,
            typename enable_if<has_write<T>::value>::type * = nullptr>
  inline void write(T x) {
    x.write();
  }
  template <class T>
  void write(const vector<T> val) {
    auto n = val.size();
    for (size_t i = 0; i < n; i++) {
      if (i) write(' ');
      write(val[i]);
    }
  }
  template <class T, class U>
  void write(const pair<T, U> val) {
    write(val.first);
    write(' ');
    write(val.second);
  }
  template <size_t N = 0, typename T>
  void write_tuple(const T t) {
    if constexpr (N < std::tuple_size<T>::value) {
      if constexpr (N > 0) { write(' '); }
      const auto x = std::get<N>(t);
      write(x);
      write_tuple<N + 1>(t);
    }
  }
  template <class... T>
  bool write(tuple<T...> tpl) {
    write_tuple(tpl);
    return true;
  }
  template <class T, size_t S>
  void write(const array<T, S> val) {
    auto n = val.size();
    for (size_t i = 0; i < n; i++) {
      if (i) write(' ');
      write(val[i]);
    }
  }
  void write(i128 val) {
    string s;
    bool negative = 0;
    if (val < 0) {
      negative = 1;
      val = -val;
    }
    while (val) {
      s += '0' + int(val % 10);
      val /= 10;
    }
    if (negative) s += "-";
    reverse(all(s));
    if (len(s) == 0) s = "0";
    write(s);
  }
};
Scanner scanner = Scanner(stdin);
Printer printer = Printer(stdout);
void flush() { printer.flush(); }
void print() { printer.write('\n'); }
template <class Head, class... Tail>
void print(Head &&head, Tail &&... tail) {
  printer.write(head);
  if (sizeof...(Tail)) printer.write(' ');
  print(forward<Tail>(tail)...);
}

void read() {}
template <class Head, class... Tail>
void read(Head &head, Tail &... tail) {
  scanner.read(head);
  read(tail...);
}
} // namespace fastio
using fastio::print;
using fastio::flush;
using fastio::read;

#define INT(...)   \
  int __VA_ARGS__; \
  read(__VA_ARGS__)
#define LL(...)   \
  ll __VA_ARGS__; \
  read(__VA_ARGS__)
#define STR(...)      \
  string __VA_ARGS__; \
  read(__VA_ARGS__)
#define CHAR(...)   \
  char __VA_ARGS__; \
  read(__VA_ARGS__)
#define DBL(...)      \
  double __VA_ARGS__; \
  read(__VA_ARGS__)

#define VEC(type, name, size) \
  vector<type> name(size);    \
  read(name)
#define VV(type, name, h, w)                     \
  vector<vector<type>> name(h, vector<type>(w)); \
  read(name)

void YES(bool t = 1) { print(t ? "YES" : "NO"); }
void NO(bool t = 1) { YES(!t); }
void Yes(bool t = 1) { print(t ? "Yes" : "No"); }
void No(bool t = 1) { Yes(!t); }
void yes(bool t = 1) { print(t ? "yes" : "no"); }
void no(bool t = 1) { yes(!t); }
#line 3 "main.cpp"

#line 1 "library/flow/hungarian.hpp"
// 最小重み最大マッチング。O(N^2M) time。
// ポテンシャルは次の双対問題の解である:
//   maximize \sum x_i + \sum y_j, subj to x_i + y_j\leq C_{ij}
// returns:
//   (ans, match, X, Y)
template <typename T>
tuple<T, vc<int>, vc<T>, vc<T>> hungarian(vvc<T>& C) {
  int N = len(C);
  int M = len(C[0]);
  assert(N <= M);
  vv(T, A, N + 1, M + 1);
  FOR(i, N) FOR(j, M) A[1 + i][1 + j] = C[i][j];
  ++N, ++M;

  vector<int> P(M), way(M);
  vector<T> X(N), Y(M);
  vc<T> minV;
  vc<bool> used;

  for (int i = 1; i < N; i++) {
    P[0] = i;
    minV.assign(M, infty<T>);
    used.assign(M, false);
    int j0 = 0;
    while (P[j0] != 0) {
      int i0 = P[j0], j1 = 0;
      used[j0] = true;
      T delta = infty<T>;
      for (int j = 1; j < M; j++) {
        if (used[j]) continue;
        T curr = A[i0][j] - X[i0] - Y[j];
        if (curr < minV[j]) minV[j] = curr, way[j] = j0;
        if (minV[j] < delta) delta = minV[j], j1 = j;
      }
      for (int j = 0; j < M; j++) {
        if (used[j])
          X[P[j]] += delta, Y[j] -= delta;
        else
          minV[j] -= delta;
      }
      j0 = j1;
    }
    do {
      P[j0] = P[way[j0]];
      j0 = way[j0];
    } while (j0 != 0);
  }
  T res = -Y[0];
  X.erase(X.begin());
  Y.erase(Y.begin());
  vc<int> match(N);
  FOR(i, N) match[P[i]] = i;
  match.erase(match.begin());
  for (auto&& i: match) --i;
  return {res, match, X, Y};
}
#line 5 "main.cpp"

template <typename T>
struct Point {
  T x, y, z;

  Point() = default;

  template <typename A, typename B, typename C>
  Point(A x, B y, C z) : x(x), y(y), z(z) {}

  Point operator+(Point p) const { return {x + p.x, y + p.y, z + p.z}; }
  Point operator-(Point p) const { return {x - p.x, y - p.y, z - p.z}; }
  bool operator==(Point p) const { return x == p.x && y == p.y && z == p.z; }
  bool operator!=(Point p) const { return x != p.x || y != p.y || z == p.z; }
  Point operator-() const { return {-x, -y, -z}; }

  bool is_parallel(Point p) const {
    return x * p.y == y * p.x && y * p.z == z * p.y && z * p.x == x * p.z;
  }

  T dot(Point other) { return x * other.x + y * other.y + z * other.z; }
  Point cross(Point other) {
    return Point(y * other.z - z * other.y, z * other.x - x * other.z,
                 x * other.y - y * other.x);
  }
};

using P = Point<i128>;

void solve() {
  LL(N);
  if (N == 1) return print(-1);

  vc<P> A(N), TO(N);
  FOR(i, N) {
    INT(a, b, c, d, e, f);
    A[i] = P{a, b, c};
    TO[i] = P{d, e, f};
  }

  // 方向の変更だけで見えるようにするためのコスト
  vv(ll, mat, N, N, infty<int>);
  FOR(i, N) FOR(j, N) {
    if (i == j) continue;
    bool ok = 1;
    FOR(k, N) {
      if (k == i || k == j) continue;
      P a = A[j] - A[i], b = A[k] - A[i];
      if (!a.is_parallel(b)) continue;
      ll d = b.dot(a);
      if (0 < d && d < a.dot(a)) ok = 0;
    }
    if (!ok) continue;
    ok = 1;
    P a = A[j] - A[i];
    P d = TO[i];
    if (!a.is_parallel(d)) ok = 0;
    if (a.dot(d) < 0) ok = 0;
    mat[i][j] = (ok ? 0 : 1);
  }

  auto cost = get<0>(hungarian<ll>(mat));
  if (cost <= N) { return print(cost); }

  // 同一直線上のはず
  P v = A[1] - A[0];
  vc<ll> val(N);
  FOR(i, N) val[i] = v.dot(A[i]);
  auto I = argsort(val);
  A = rearrange(A, I);
  TO = rearrange(TO, I);

  assert(N % 2 == 1);
  FOR(i, N - 1) assert(v.is_parallel(A[i + 1] - A[i]));

  // 動かすものはひとつ、これを固定するごとに解く
  auto solve = [&](vc<P> A, vc<P> TO, P to) -> ll {
    P v = A[1] - A[0];
    // どこかに奇サイクルができる
    // matching + cycle + matching
    ll N = len(A);
    assert(N % 2 == 0);
    // cost_1:i -> i + 1
    // cost_2:i + 1 -> i
    vi cost_1(N - 1, 1), cost_2(N - 1, 1);
    FOR(i, N - 1) {
      if (v.is_parallel(TO[i]) && v.dot(TO[i]) > 0) { cost_1[i] = 0; }
      if (v.is_parallel(TO[i + 1]) && v.dot(TO[i + 1]) < 0) { cost_2[i] = 0; }
    }
    auto C1 = cumsum<ll>(cost_1);
    auto C2 = cumsum<ll>(cost_2);

    // matching cost
    vi match(N / 2);
    FOR(i, N / 2) { match[i] = cost_1[2 * i] + cost_2[2 * i]; }
    auto match_c = cumsum<ll>(match);

    auto can = [&](P S, P T, P v1, P v2) -> bool {
      // S -(v1)-> . -(v2)-> T
      if (v1.is_parallel(v2)) { return 0; }
      // S + xv1 + yv2 = T
      P norm = v1.cross(v2);
      P xx = (T - S).cross(v2);
      P yy = (S - T).cross(v1);
      // x norm = xx
      // y norm = yy
      if (!norm.is_parallel(xx)) return 0;
      if (!norm.is_parallel(yy)) return 0;
      if (norm.dot(xx) <= 0) return 0;
      if (norm.dot(yy) <= 0) return 0;
      return 1;
    };

    ll ANS = infty<ll>;
    FOR(L, N) FOR(R, L + 1, N) {
      if (L % 2 != 0) continue;
      if (R % 2 == 0) continue;
      ll ans1 = 0, ans2 = 0;
      ans1 += match_c[L / 2];
      ans1 += match_c[N / 2] - match_c[(R + 1) / 2];
      ans2 = ans1;
      ans1 += C1[R] - C1[L];
      ans2 += C2[R] - C2[L];
      if (!can(A[R], A[L], TO[R], to)) ans1 += 1;
      if (!can(A[L], A[R], TO[L], to)) ans2 += 1;
      chmin(ANS, ans1);
      chmin(ANS, ans2);
    }
    return ANS;
  };

  ll ANS = infty<ll>;
  FOR(i, N) {
    vc<P> A1, TO1;
    FOR(j, N) if (j != i) A1.eb(A[j]);
    FOR(j, N) if (j != i) TO1.eb(TO[j]);
    chmin(ANS, solve(A1, TO1, TO[i]) + 1000);
  }
  print(ANS);
}

signed main() {
  solve();
  return 0;
}

Details

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Test #1:

score: 0
Wrong Answer
time: 1ms
memory: 3568kb

input:

7
0 0 0 1 0 0
1 0 0 -1 0 0
2 0 0 1 0 0
3 0 0 1 0 0
4 0 0 1 0 0
5 0 0 1 0 0
6 0 0 -1 0 0

output:

1001

result:

wrong answer 1st lines differ - expected: '1002', found: '1001'