結果

問題 No.132 点と平面との距離
ユーザー fumiphysfumiphys
提出日時 2019-05-24 19:08:11
言語 C++14
(gcc 12.3.0 + boost 1.83.0)
結果
AC  
実行時間 35 ms / 5,000 ms
コード長 5,831 bytes
コンパイル時間 1,429 ms
コンパイル使用メモリ 172,024 KB
実行使用メモリ 5,376 KB
最終ジャッジ日時 2024-09-17 10:11:45
合計ジャッジ時間 1,833 ms
ジャッジサーバーID
（参考情報） 		judge3 / judge2
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テストケース

テストケース表示
入力 結果 実行時間
実行使用メモリ
testcase_00 AC 4 ms
5,248 KB
testcase_01 AC 12 ms
5,376 KB
testcase_02 AC 35 ms
5,376 KB
権限があれば一括ダウンロードができます

ソースコード

diff # 

// includes
#include <bits/stdc++.h>

// macros
#define ll long long int
#define pb emplace_back
#define mk make_pair
#define pq priority_queue
#define FOR(i, a, b) for(int i=(a);i<(b);++i)
#define rep(i, n) FOR(i, 0, n)
#define rrep(i, n) for(int i=((int)(n)-1);i>=0;i--)
#define irep(itr, st) for(auto itr = (st).begin(); itr != (st).end(); ++itr)
#define irrep(itr, st) for(auto itr = (st).rbegin(); itr != (st).rend(); ++itr)
#define vrep(v, i) for(int i = 0; i < (v).size(); i++)
#define all(x) (x).begin(),(x).end()
#define sz(x) ((int)(x).size())
#define UNIQUE(v) v.erase(unique(v.begin(), v.end()), v.end())
#define FI first
#define SE second
#define dump(a, n) for(int i = 0; i < n; i++)cout << a[i] << "\n "[i + 1 != n];
#define dump2(a, n, m) for(int i = 0; i < n; i++)for(int j = 0; j < m; j++)cout << a[i][j] << "\n "[j + 1 != m];
#define bit(n) (1LL<<(n))
#define INT(n) int n; cin >> n;
#define LL(n) ll n; cin >> n;
#define DOUBLE(n) double n; cin >> n;
using namespace std;

//  types
typedef pair<int, int> P;
typedef pair<ll, int> Pl;
typedef pair<ll, ll> Pll;
typedef pair<double, double> Pd;
typedef complex<double> cd;
 
// constants
const int inf = 1e9;
const ll linf = 1LL << 50;
const double EPS = 1e-10;
const int mod = 1e9 + 7;
const int dx[4] = {-1, 0, 1, 0};
const int dy[4] = {0, -1, 0, 1};

// solve
template <class T>bool chmax(T &a, const T &b){if(a < b){a = b; return 1;} return 0;}
template <class T>bool chmin(T &a, const T &b){if(a > b){a = b; return 1;} return 0;}
template <typename T> istream &operator>>(istream &is, vector<T> &vec){for(auto &v: vec)is >> v; return is;}
template <typename T> ostream &operator<<(ostream &os, const vector<T>& vec){for(int i = 0; i < vec.size(); i++){ os << vec[i]; if(i + 1 != vec.size())os << " ";} return os;}
template <typename T> ostream &operator<<(ostream &os, const set<T>& st){for(auto itr = st.begin(); itr != st.end(); ++itr){ os << *itr; auto titr = itr; if(++titr != st.end())os << " ";} return os;}
template <typename T> ostream &operator<<(ostream &os, const unordered_set<T>& st){for(auto itr = st.begin(); itr != st.end(); ++itr){ os << *itr; auto titr = itr; if(++titr != st.end())os << " ";} return os;}
template <typename T> ostream &operator<<(ostream &os, const multiset<T>& st){for(auto itr = st.begin(); itr != st.end(); ++itr){ os << *itr; auto titr = itr; if(++titr != st.end())os << " ";} return os;}
template <typename T> ostream &operator<<(ostream &os, const unordered_multiset<T>& st){for(auto itr = st.begin(); itr != st.end(); ++itr){ os << *itr; auto titr = itr; if(++titr != st.end())os << " ";} return os;}
template <typename T1, typename T2> ostream &operator<<(ostream &os, const pair<T1, T2> &p){os << p.first << " " << p.second; return os;}
template <typename T1, typename T2> ostream &operator<<(ostream &os, const map<T1, T2> &mp){for(auto itr = mp.begin(); itr != mp.end(); ++itr){ os << itr->first << ":" << itr->second; auto titr = itr; if(++titr != mp.end())os << " "; } return os;}
template <typename T1, typename T2> ostream &operator<<(ostream &os, const unordered_map<T1, T2> &mp){for(auto itr = mp.begin(); itr != mp.end(); ++itr){ os << itr->first << ":" << itr->second; auto titr = itr; if(++titr != mp.end())os << " "; } return os;}

struct point3d{
  double x, y, z;
  point3d(){}
  point3d(double x, double y, double z): x(x), y(y), z(z){}
  point3d operator+(const point3d &r) const{
    return point3d(x + r.x, y + r.y, z + r.z);
  }
  point3d operator-(const point3d &r) const{
    return point3d(x - r.x, y - r.y, z - r.z);
  }
  point3d& operator+=(const point3d &r){
    *this = *this + r;
    return *this;
  }
  point3d& operator-=(const point3d &r){
    *this = *this - r;
    return *this;
  }
  bool operator==(const point3d &r) const{
    return abs(x - r.x) < EPS && abs(y - r.y) < EPS && abs(z - r.z) < EPS;
  }
  bool operator!=(const point3d &r) const{
    return !(*this == r);
  }
  bool operator<(const point3d &r) const{
    if(abs(x - r.x) >= EPS)return x < r.x;
    if(abs(y - r.y) >= EPS)return y < r.y;
    return z < r.z;
  }
};

point3d operator*(double x, const point3d &p){
  return point3d(x * p.x, x * p.y, x * p.z);
}

point3d operator/(const point3d &p, double x){
  return point3d(p.x / x, p.y / x, p.z / x);
}

double norm(const point3d &a){
  return sqrt(a.x * a.x + a.y * a.y + a.z * a.z);
}

double dis(const point3d &a, const point3d &b){
  point3d c = a - b;
  return norm(c);
}

double inner_product(const point3d &a, const point3d &b){
  return a.x * b.x + a.y * b.y + a.z * b.z;
}

point3d outer_product(const point3d &a, const point3d &b){
  return point3d(a.y * b.z - a.z * b.y,
      a.z * b.x - a.x * b.z, a.x * b.y - a.y * b.x);
}

double cosine(const point3d &a, const point3d &b){
  return inner_product(a, b) / norm(a) / norm(b);
}

struct plane3d{
  double a, b, c, d;
  double norm = 1.;
  plane3d(){}
  plane3d(double a, double b, double c, double d): a(a), b(b), c(c), d(d){
    build();
  }
  void build(){
    norm = sqrt(a * a + b * b + c * c);
  }
  double dis(point3d p){
    return abs(a * p.x + b * p.y + c * p.z + d) / norm;
  }
};

plane3d get_eq(point3d pa, point3d pb, point3d pc){
  point3d re = outer_product(pb - pa, pc - pa);
  plane3d res;
  res.a = re.x, res.b = re.y, res.c = re.z;
  res.d = - (res.a * pa.x + res.b * pa.y + res.c * pa.z);
  res.build();
  return res;
}

int main(int argc, char const* argv[])
{
  ios_base::sync_with_stdio(false);
  cin.tie(0);
  INT(n);
  point3d p;
  cin >> p.x >> p.y >> p.z;
  vector<point3d> q(n);
  rep(i, n){
    cin >> q[i].x >> q[i].y >> q[i].z;
  }
  double res = 0.;
  rep(i, n){
    FOR(j, i + 1, n){
      FOR(k, j + 1, n){
        plane3d pl = get_eq(q[i], q[j], q[k]);
        res += pl.dis(p);
      }
    }
  }
  cout << setprecision(20);
  cout << res << endl;
  return 0;
}
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