Cod sursa(job #2080043)

Utilizator andrei.arnautuAndi Arnautu andrei.arnautu Data 2 decembrie 2017 12:52:51
Problema Rubarba Scor 70
Compilator cpp Status done
Runda Arhiva de probleme Marime 1.3 kb
/**
  *  Worg
  */
#include <cmath>
#include <cstdio>
#include <vector>
#include <algorithm>

#define x first
#define y second

FILE *fin = freopen("rubarba.in", "r", stdin); FILE *fout = freopen("rubarba.out", "w", stdout);

const double eps = 5e-14;
const double pi = std::acos(-1.0);
const double maxC = 1e12;

/*--------- Data --------*/
int N;
std::vector<std::pair<double, double > > points;
/*--------- --------*/

double Compute(double alfa) {
  double sin = std::sin(alfa), cos = std::cos(alfa);
  double maxX = -maxC, maxY = -maxC, minX = maxC, minY = maxC;

  for(auto& p : points) {
    double x = p.x * cos - p.y * sin;
    double y = p.x * sin + p.y * cos;

    minX = std::min(minX, x);
    maxX = std::max(maxX, x);
    minY = std::min(minY, y);
    maxY = std::max(maxY, y);
  }

  return (maxY - minY) * (maxX - minX);
}

int main() {
  scanf("%d", &N);
  for(int i = 0; i < N; i++) {
    double a, b; scanf("%lf%lf", &a, &b);
    points.emplace_back(a, b);
  }

  //printf("%.15f\n", pi);

  double left = 0, right = pi / 2, mid;

  while(right - left >= eps) {
    mid = left + (right - left) / 2;

    if(Compute(mid) >= Compute(mid + eps)) {
      left = mid;
    } else {
      right = mid;
    }
  }

  printf("%.6f", Compute(mid));

  return 0;
}