結果

問題 No.132 点と平面との距離
ユーザー hamrayhamray
提出日時 2021-03-20 22:43:30
言語 C++14
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 37 ms / 5,000 ms
コード長 6,608 bytes
コンパイル時間 1,756 ms
コンパイル使用メモリ 173,132 KB
実行使用メモリ 5,248 KB
最終ジャッジ日時 2024-11-21 12:30:18
合計ジャッジ時間 2,471 ms
ジャッジサーバーID
（参考情報） 		judge5 / judge2
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ファイルパターン 結果
other AC * 3
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ソースコード

diff # 

#include <bits/stdc++.h>
//#include <atcoder/all>
//using namespace atcoder;
#pragma GCC target ("avx")
#pragma GCC optimization ("O3")
#pragma GCC optimization ("unroll-loops")

using namespace std;

typedef vector<int> VI;
typedef vector<VI> VVI;
typedef vector<string> VS;
typedef pair<int, int> PII;
typedef pair<int, int> pii;
typedef pair<long long, long long> PLL;
typedef pair<int, PII> TIII;

typedef long long ll;
typedef long double ld;
typedef unsigned long long ull;


#define FOR(i, s, n) for (int i = s; i < (int)n; ++i)
#define REP(i, n) FOR(i, 0, n)
#define rep(i, a, b) for (int i = a; i < (b); ++i)
#define trav(a, x) for (auto &a : x)
#define all(x) x.begin(), x.end()

#define MOD 1000000007

template<class T1, class T2> inline bool chmax(T1 &a, T2 b) {if (a < b) {a = b; return true;} return false;}
template<class T1, class T2> inline bool chmin(T1 &a, T2 b) {if (a > b) {a = b; return true;} return false;}
const double EPS = 1e-6, PI = acos(-1);
const double pi = 3.141592653589793238462643383279;
//ここから編集    
typedef string::const_iterator State;
ll GCD(ll a, ll b){
  return (b==0)?a:GCD(b, a%b);
}
ll LCM(ll a, ll b){
  return a/GCD(a, b) * b;
}
template< int mod >
struct ModInt {
  int x;

  ModInt() : x(0) {}

  ModInt(int64_t y) : x(y >= 0 ? y % mod : (mod - (-y) % mod) % mod) {}

  ModInt &operator+=(const ModInt &p) {
    if((x += p.x) >= mod) x -= mod;
    return *this;
  }

  ModInt &operator-=(const ModInt &p) {
    if((x += mod - p.x) >= mod) x -= mod;
    return *this;
  }

  ModInt &operator*=(const ModInt &p) {
    x = (int) (1LL * x * p.x % mod);
    return *this;
  }

  ModInt &operator/=(const ModInt &p) {
    *this *= p.inverse();
    return *this;
  }

  ModInt operator-() const { return ModInt(-x); }

  ModInt operator+(const ModInt &p) const { return ModInt(*this) += p; }

  ModInt operator-(const ModInt &p) const { return ModInt(*this) -= p; }

  ModInt operator*(const ModInt &p) const { return ModInt(*this) *= p; }

  ModInt operator/(const ModInt &p) const { return ModInt(*this) /= p; }

  bool operator==(const ModInt &p) const { return x == p.x; }

  bool operator!=(const ModInt &p) const { return x != p.x; }

  ModInt inverse() const {
    int a = x, b = mod, u = 1, v = 0, t;
    while(b > 0) {
      t = a / b;
      swap(a -= t * b, b);
      swap(u -= t * v, v);
    }
    return ModInt(u);
  }

  ModInt pow(int64_t n) const {
    ModInt ret(1), mul(x);
    while(n > 0) {
      if(n & 1) ret *= mul;
      mul *= mul;
      n >>= 1;
    }
    return ret;
  }

  friend ostream &operator<<(ostream &os, const ModInt &p) {
    return os << p.x;
  }

  friend istream &operator>>(istream &is, ModInt &a) {
    int64_t t;
    is >> t;
    a = ModInt< mod >(t);
    return (is);
  }

  static int get_mod() { return mod; }
};

using modint = ModInt< 998244353 >;
template< typename T >
struct Combination {
  vector< T > _fact, _rfact, _inv;

  Combination(int sz) : _fact(sz + 1), _rfact(sz + 1), _inv(sz + 1) {
    _fact[0] = _rfact[sz] = _inv[0] = 1;
    for(int i = 1; i <= sz; i++) _fact[i] = _fact[i - 1] * i;
    _rfact[sz] /= _fact[sz];
    for(int i = sz - 1; i >= 0; i--) _rfact[i] = _rfact[i + 1] * (i + 1);
    for(int i = 1; i <= sz; i++) _inv[i] = _rfact[i] * _fact[i - 1];
  }

  inline T fact(int k) const { return _fact[k]; }

  inline T rfact(int k) const { return _rfact[k]; }

  inline T inv(int k) const { return _inv[k]; }

  T P(int n, int r) const {
    if(r < 0 || n < r) return 0;
    return fact(n) * rfact(n - r);
  }

  T C(int p, int q) const {
    if(q < 0 || p < q) return 0;
    return fact(p) * rfact(q) * rfact(p - q);
  }

  T H(int n, int r) const {
    if(n < 0 || r < 0) return (0);
    return r == 0 ? 1 : C(n + r - 1, r);
  }
};

int modpow(ll x, ll n, int mod) {
  if(x == 0) return 0;
  
  ll res = 1;
  while(n) {
    if(n&1) res = res*x % mod;
    x = x*x%mod;
    n >>= 1;
  }
  return res;
}

using DD = double;
struct Point3{
  DD x, y, z;
  Point3(DD x=0.0, DD y=0.0, DD z=0.0): x(x), y(y), z(z){}
  friend ostream& operator << (ostream &s, const Point3 &p) {return s << p.x << " " << p.y << " " << p.z;}

};
inline Point3 operator + (const Point3 &p, const Point3 &q) {return Point3(p.x + q.x, p.y + q.y, p.z + q.z);}
inline Point3 operator - (const Point3 &p, const Point3 &q) {return Point3(p.x - q.x, p.y - q.y, p.z - q.z);}
inline Point3 operator * (const Point3 &p, DD a) {return Point3(p.x * a, p.y * a, p.z * a);}
inline Point3 operator * (DD a, const Point3 &p) {return Point3(a * p.x, a * p.y, a * p.z);}
//inline Point3 operator * (const Point3 &p, const Point3 &q) {return Point3(p.x * q.x - p.y * q.y, p.x * q.y + p.y * q.x);}
inline Point3 operator / (const Point3 &p, DD a) {return Point3(p.x / a, p.y / a, p.z / a);}
//inline Point3 conj(const Point3 &p) {return Point3(p.x, -p.y);}
//inline Point3 rot(const Point3 &p, DD ang) {return Point3(cos(ang) * p.x - sin(ang) * p.y, sin(ang) * p.x + cos(ang) * p.y);}
//inline Point3 rot90(const Point3 &p) {return Point3(-p.y, p.x);}
inline Point3 cross(const Point3 &p, const Point3 &q) {return Point3(p.y * q.z - p.z * q.y, p.z * q.x - p.x * q.z, p.x * q.y - p.y * q.x);}
inline DD dot(const Point3 &p, const Point3 &q) {return p.x * q.x + p.y * q.y + p.z * q.z;}

inline DD norm(const Point3 &p) {return dot(p, p);}
inline DD abs(const Point3 &p) {return sqrt(dot(p, p));}

//inline DD amp(const Point3 &p) {DD res = atan2(p.y, p.x); if (res < 0) res += PI*2; return res;}

inline bool eq(const Point3 &p, const Point3 &q) {return abs(p - q) < EPS;}
//inline bool operator < (const Point3 &p, const Point3 &q) {return (abs(p.x - q.x) > EPS ? p.x < q.x : p.y < q.y);}
//inline bool operator > (const Point3 &p, const Point3 &q) {return (abs(p.x - q.x) > EPS ? p.x > q.x : p.y > q.y);}

// 参考 http://www.math.s.chiba-u.ac.jp/~yasuda/Chiba/Lec/naiseki.pdf

istream& operator>> (istream &is, Point3 &p) { 
  DD x, y, z;
  is >> x >> y >> z;
  p = Point3(x, y, z);
  return is;
}
int main() {
  cin.tie(0);
  ios::sync_with_stdio(false);
  cout << fixed << setprecision(11);
  
  ll n; cin >> n;
  Point3 P;
  cin >> P;
  vector<Point3> X(n);
  REP(i,n) {
    cin >> X[i];
  }
  double ans = 0;
  for(int i=0; i<n; i++) {
    for(int j=i+1; j<n; j++) {
      for(int k=j+1; k<n; k++) {        
        Point3 ab = X[j]-X[i];
        Point3 ac = X[k]-X[i];

        Point3 norm = cross(ab, ac);
        double a = norm.x, b = norm.y, c = norm.z;
        double d = - a * X[i].x - b * X[i].y - c * X[i].z;

        ans += abs(a*P.x+b*P.y+c*P.z+d)/abs(norm);
      }
    }
  }
  cout << ans << endl;
  return 0;
}
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