結果

問題 No.2180 Comprehensive Line Segments
ユーザー NyaanNyaan
提出日時 2023-01-06 22:39:32
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
WA  
実行時間 -
コード長 11,411 bytes
コンパイル時間 2,518 ms
コンパイル使用メモリ 266,036 KB
最終ジャッジ日時 2025-02-10 00:12:54
ジャッジサーバーID
（参考情報） 		judge5 / judge5
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ファイルパターン 結果
sample AC * 4
other AC * 20 WA * 5
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ソースコード

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プレゼンテーションモードにする

/**
 *  date : 2023-01-06 22:39:27
 */
#define NDEBUG
using namespace std;
// intrinstic
#include <immintrin.h>
#include <algorithm>
#include <array>
#include <bitset>
#include <cassert>
#include <cctype>
#include <cfenv>
#include <cfloat>
#include <chrono>
#include <cinttypes>
#include <climits>
#include <cmath>
#include <complex>
#include <cstdarg>
#include <cstddef>
#include <cstdint>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <deque>
#include <fstream>
#include <functional>
#include <initializer_list>
#include <iomanip>
#include <ios>
#include <iostream>
#include <istream>
#include <iterator>
#include <limits>
#include <list>
#include <map>
#include <memory>
#include <new>
#include <numeric>
#include <ostream>
#include <queue>
#include <random>
#include <set>
#include <sstream>
#include <stack>
#include <streambuf>
#include <string>
#include <tuple>
#include <type_traits>
#include <typeinfo>
#include <unordered_map>
#include <unordered_set>
#include <utility>
#include <vector>
// utility
namespace Nyaan {
using ll = long long;
using i64 = long long;
using u64 = unsigned long long;
using i128 = __int128_t;
using u128 = __uint128_t;
template <typename T>
using V = vector<T>;
template <typename T>
using VV = vector<vector<T>>;
using vi = vector<int>;
using vl = vector<long long>;
using vd = V<double>;
using vs = V<string>;
using vvi = vector<vector<int>>;
using vvl = vector<vector<long long>>;
template <typename T, typename U>
struct P : pair<T, U> {
  template <typename... Args>
  P(Args... args) : pair<T, U>(args...) {}
  using pair<T, U>::first;
  using pair<T, U>::second;
  P &operator+=(const P &r) {
    first += r.first;
    second += r.second;
    return *this;
  }
  P &operator-=(const P &r) {
    first -= r.first;
    second -= r.second;
    return *this;
  }
  P &operator*=(const P &r) {
    first *= r.first;
    second *= r.second;
    return *this;
  }
  template <typename S>
  P &operator*=(const S &r) {
    first *= r, second *= r;
    return *this;
  }
  P operator+(const P &r) const { return P(*this) += r; }
  P operator-(const P &r) const { return P(*this) -= r; }
  P operator*(const P &r) const { return P(*this) *= r; }
  template <typename S>
  P operator*(const S &r) const {
    return P(*this) *= r;
  }
  P operator-() const { return P{-first, -second}; }
};
using pl = P<ll, ll>;
using pi = P<int, int>;
using vp = V<pl>;
constexpr int inf = 1001001001;
constexpr long long infLL = 4004004004004004004LL;
template <typename T>
int sz(const T &t) {
  return t.size();
}
template <typename T, typename U>
inline bool amin(T &x, U y) {
  return (y < x) ? (x = y, true) : false;
}
template <typename T, typename U>
inline bool amax(T &x, U y) {
  return (x < y) ? (x = y, true) : false;
}
template <typename T>
inline T Max(const vector<T> &v) {
  return *max_element(begin(v), end(v));
}
template <typename T>
inline T Min(const vector<T> &v) {
  return *min_element(begin(v), end(v));
}
template <typename T>
inline long long Sum(const vector<T> &v) {
  return accumulate(begin(v), end(v), 0LL);
}
template <typename T>
int lb(const vector<T> &v, const T &a) {
  return lower_bound(begin(v), end(v), a) - begin(v);
}
template <typename T>
int ub(const vector<T> &v, const T &a) {
  return upper_bound(begin(v), end(v), a) - begin(v);
}
constexpr long long TEN(int n) {
  long long ret = 1, x = 10;
  for (; n; x *= x, n >>= 1) ret *= (n & 1 ? x : 1);
  return ret;
}
template <typename T, typename U>
pair<T, U> mkp(const T &t, const U &u) {
  return make_pair(t, u);
}
template <typename T>
vector<T> mkrui(const vector<T> &v, bool rev = false) {
  vector<T> ret(v.size() + 1);
  if (rev) {
    for (int i = int(v.size()) - 1; i >= 0; i--) ret[i] = v[i] + ret[i + 1];
  } else {
    for (int i = 0; i < int(v.size()); i++) ret[i + 1] = ret[i] + v[i];
  }
  return ret;
};
template <typename T>
vector<T> mkuni(const vector<T> &v) {
  vector<T> ret(v);
  sort(ret.begin(), ret.end());
  ret.erase(unique(ret.begin(), ret.end()), ret.end());
  return ret;
}
template <typename F>
vector<int> mkord(int N,F f) {
  vector<int> ord(N);
  iota(begin(ord), end(ord), 0);
  sort(begin(ord), end(ord), f);
  return ord;
}
template <typename T>
vector<int> mkinv(vector<T> &v) {
  int max_val = *max_element(begin(v), end(v));
  vector<int> inv(max_val + 1, -1);
  for (int i = 0; i < (int)v.size(); i++) inv[v[i]] = i;
  return inv;
}
vector<int> mkiota(int n) {
  vector<int> ret(n);
  iota(begin(ret), end(ret), 0);
  return ret;
}
template <typename T>
T mkrev(const T &v) {
  T w{v};
  reverse(begin(w), end(w));
  return w;
}
template <typename T>
bool nxp(vector<T> &v) {
  return next_permutation(begin(v), end(v));
}
template <typename T>
using minpq = priority_queue<T, vector<T>, greater<T>>;
}  // namespace Nyaan
// bit operation
namespace Nyaan {
__attribute__((target("popcnt"))) inline int popcnt(const u64 &a) {
  return _mm_popcnt_u64(a);
}
inline int lsb(const u64 &a) { return a ? __builtin_ctzll(a) : 64; }
inline int ctz(const u64 &a) { return a ? __builtin_ctzll(a) : 64; }
inline int msb(const u64 &a) { return a ? 63 - __builtin_clzll(a) : -1; }
template <typename T>
inline int gbit(const T &a, int i) {
  return (a >> i) & 1;
}
template <typename T>
inline void sbit(T &a, int i, bool b) {
  if (gbit(a, i) != b) a ^= T(1) << i;
}
constexpr long long PW(int n) { return 1LL << n; }
constexpr long long MSK(int n) { return (1LL << n) - 1; }
}  // namespace Nyaan
// inout
namespace Nyaan {
template <typename T, typename U>
ostream &operator<<(ostream &os, const pair<T, U> &p) {
  os << p.first << " " << p.second;
  return os;
}
template <typename T, typename U>
istream &operator>>(istream &is, pair<T, U> &p) {
  is >> p.first >> p.second;
  return is;
}
template <typename T>
ostream &operator<<(ostream &os, const vector<T> &v) {
  int s = (int)v.size();
  for (int i = 0; i < s; i++) os << (i ? " " : "") << v[i];
  return os;
}
template <typename T>
istream &operator>>(istream &is, vector<T> &v) {
  for (auto &x : v) is >> x;
  return is;
}
istream &operator>>(istream &is, __int128_t &x) {
  string S;
  is >> S;
  x = 0;
  int flag = 0;
  for (auto &c : S) {
    if (c == '-') {
      flag = true;
      continue;
    }
    x *= 10;
    x += c - '0';
  }
  if (flag) x = -x;
  return is;
}
istream &operator>>(istream &is, __uint128_t &x) {
  string S;
  is >> S;
  x = 0;
  for (auto &c : S) {
    x *= 10;
    x += c - '0';
  }
  return is;
}
ostream &operator<<(ostream &os, __int128_t x) {
  if (x == 0) return os << 0;
  if (x < 0) os << '-', x = -x;
  string S;
  while (x) S.push_back('0' + x % 10), x /= 10;
  reverse(begin(S), end(S));
  return os << S;
}
ostream &operator<<(ostream &os, __uint128_t x) {
  if (x == 0) return os << 0;
  string S;
  while (x) S.push_back('0' + x % 10), x /= 10;
  reverse(begin(S), end(S));
  return os << S;
}
void in() {}
template <typename T, class... U>
void in(T &t, U &...u) {
  cin >> t;
  in(u...);
}
void out() { cout << "\n"; }
template <typename T, class... U, char sep = ' '>
void out(const T &t, const U &...u) {
  cout << t;
  if (sizeof...(u)) cout << sep;
  out(u...);
}
void outr() {}
template <typename T, class... U, char sep = ' '>
void outr(const T &t, const U &...u) {
  cout << t;
  outr(u...);
}
struct IoSetupNya {
  IoSetupNya() {
    cin.tie(nullptr);
    ios::sync_with_stdio(false);
    cout << fixed << setprecision(15);
    cerr << fixed << setprecision(7);
  }
} iosetupnya;
}  // namespace Nyaan
// debug
#ifdef NyaanDebug
#define trc(...) (void(0))
#else
#define trc(...) (void(0))
#endif
#ifdef NyaanLocal
#define trc2(...) (void(0))
#else
#define trc2(...) (void(0))
#endif
// macro
#define each(x, v) for (auto&& x : v)
#define each2(x, y, v) for (auto&& [x, y] : v)
#define all(v) (v).begin(), (v).end()
#define rep(i, N) for (long long i = 0; i < (long long)(N); i++)
#define repr(i, N) for (long long i = (long long)(N)-1; i >= 0; i--)
#define rep1(i, N) for (long long i = 1; i <= (long long)(N); i++)
#define repr1(i, N) for (long long i = (N); (long long)(i) > 0; i--)
#define reg(i, a, b) for (long long i = (a); i < (b); i++)
#define regr(i, a, b) for (long long i = (b)-1; i >= (a); i--)
#define fi first
#define se second
#define ini(...)   \
  int __VA_ARGS__; \
  in(__VA_ARGS__)
#define inl(...)         \
  long long __VA_ARGS__; \
  in(__VA_ARGS__)
#define ins(...)      \
  string __VA_ARGS__; \
  in(__VA_ARGS__)
#define in2(s, t)                           \
  for (int i = 0; i < (int)s.size(); i++) { \
    in(s[i], t[i]);                         \
  }
#define in3(s, t, u)                        \
  for (int i = 0; i < (int)s.size(); i++) { \
    in(s[i], t[i], u[i]);                   \
  }
#define in4(s, t, u, v)                     \
  for (int i = 0; i < (int)s.size(); i++) { \
    in(s[i], t[i], u[i], v[i]);             \
  }
#define die(...)             \
  do {                       \
    Nyaan::out(__VA_ARGS__); \
    return;                  \
  } while (0)
namespace Nyaan {
void solve();
}
int main() { Nyaan::solve(); }
//
using namespace Nyaan;
using po = pair<double, double>;
using li = array<double, 3>;
int dp[1 << 13][13][13];
li line(po p1, po p2) {
  assert(p1 != p2);
  if (p1.fi == p2.fi) return li{{1, 0, -p1.fi}};
  if (p1.se == p2.se) return li{{0, 1, -p1.se}};
  double b = p1.fi - p2.fi;
  double a = -(p1.se - p2.se);
  double c = -(a * p1.fi + b * p1.se);
  // trc(p1,p2,a,b,c);
  double s = sqrt(a * a + b * b);
  a /= s, b /= s, c /= s;
  if (a < 0) a = -a, b = -b, c = -c;
  return li{{a, b, c}};
}
bool on(li l, po p) { return abs(l[0] * p.fi + l[1] * p.se + l[2]) <= 1e-8; }
bool parallel(li l1, li l2) {
  return abs(l1[0] - l2[0]) < 1e-8 and abs(l1[1] - l2[1]) < 1e-8;
}
void q() {
  inl(N);
  V<po> ps(N);
  in(ps);
  if (N <= 2) die(1);
  vi ok(1 << N);
  V<li> lines(1 << N);
  rep(i, 1 << N) {
    if (popcnt(i) < 2) continue;
    vi bits;
    rep(j, N) if (gbit(i, j)) bits.push_back(j);
    li l = line(ps[bits[0]], ps[bits[1]]);
    assert(on(l, ps[bits[0]]));
    assert(on(l, ps[bits[1]]));
    int flag = 1;
    reg(j, 2, sz(bits)) {
      if (!on(l, ps[bits[j]])) flag = 0;
    }
    if (flag) {
      ok[i] = 1, lines[i] = l;
      trc(bits, l);
    }
  }
  rep(i, 1 << N) rep(j, N) rep(k, N) { dp[i][j][k] = inf; }
  rep(i, 1 << N) {
    if (popcnt(i) == 1) {
      int t = msb(i);
      dp[i][t][t] = 1;
    }
    if (ok[i]) {
      int t = msb(i);
      int ii = i - (1 << t);
      int u = msb(ii);
      dp[i][t][u] = 1;
    }
  }
  rep(i, 1 << N) {
    rep(i1, 1 << N) {
      if ((i & i1) != i1) continue;
      int i2 = i ^ i1;
      // if(i1 > i2) break;
      int need = popcnt(i1) >= 2 and popcnt(i2) >= 2;
      rep(j1, N) rep(k1, N) {
        if (dp[i1][j1][k1] == inf) continue;
        rep(j2, N) rep(k2, N) {
          if (dp[i2][j2][k2] == inf) continue;
          if (need and j1!=k1 and j2!=k2) {
            li& l1 = lines[(1 << j1) + (1 << k1)];
            li& l2 = lines[(1 << j2) + (1 << k2)];
            if (parallel(l1, l2)) continue;
          }
          amin(dp[i][j1][k1], dp[i1][j1][k1] + dp[i2][j2][k2]);
          amin(dp[i][j2][k2], dp[i1][j1][k1] + dp[i2][j2][k2]);
        }
      }
    }
  }
  int ans = inf;
  rep(j, N) rep(k, N) amin(ans, dp[(1<<N)-1][j][k]);
  out(ans);
}
void Nyaan::solve() {
  int t = 1;
  // in(t);
  while (t--) q();
}
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