UVa 10652 - Board Wrapping

Accepted date: 2016-06-01
Run Time: 0.000
Ranking (as of 2016-06-01): 21 out of 490
Language: C++

/*
  UVa 10652 - Board Wrapping

  To build using Visual Studio 2012:
    cl -EHsc -O2 UVa_10652_Board_Wrapping.cpp
*/

#include <algorithm>
#include <vector>
#include <limits>
#include <cstdio>
#include <cmath>
using namespace std;

const double epsilon = numeric_limits<float>::epsilon();
const double pi = 2.0 * acos(0.0);

struct point {
  double x, y;

  point() : x(0.0), y(0.0) {}
  point(double _x, double _y) : x(_x), y(_y) {}
  point(const point &p) : x(p.x), y(p.y) {}
  bool operator==(const point& p) const {return x == p.x && y == p.y;}
};

/*
let (x0, y0) be the lower left corner of the rectangle, then:
center point: (x0 + w / 2, y0 + h / 2)
rotate the center point around (x0, y0), by (-a):
(
  x: cos(-a) * (x0 + w / 2 - x0) - sin(-a) * (y0 + h / 2 - y0) + x0
    = cos(a) * w / 2 + sin(a) * h / 2 + x0,
  y: sin(-a) * (x0 + w / 2 - x0) + cos(-a) * (y0 + h / 2 - y0) + y0
    = -sin(a) * w / 2 + cos(a) * h / 2 + y0
)

x0 = x - (cos(a) * w + sin(a) * h) / 2;
y0 = y + (sin(a) * w - cos(a) * h) / 2;

rotate the other 3 points:
  (x0, y0 + h):
    cos(-a) * (x0 - x0) - sin(-a) * (y0 + h - y0) + x0 = sin(a) * h + x0
    sin(-a) * (x0 - x0) + cos(-a) * (y0 + h - y0) + y0 = cos(a) * h + y0

  (x0 + w, y0):
    cos(-a) * (x0 + w - x0) - sin(-a) * (y0 - y0) + x0 = cos(a) * w + x0
    sin(-a) * (x0 + w - x0) + cos(-a) * (y0 - y0) + y0 = -sin(a) * w + y0

  (x0 + w, y0 + h):
    cos(-a) * (x0 + w - x0) - sin(-a) * (y0 + h - y0) + x0 = cos(a) * w + sin(a) * h + x0
    sin(-a) * (x0 + w - x0) + cos(-a) * (y0 + h - y0) + y0 = -sin(a) * w + cos(a) * h + y0

*/

void add_rectangle_points(double x, double y, double w, double h, double a,
  vector<point>& points)
{
  // lower left corner
  double x0 = x - (cos(a) * w + sin(a) * h) / 2, y0 = y + (sin(a) * w - cos(a) * h) / 2;
  points.push_back(point(x0, y0));
  points.push_back(point(sin(a) * h + x0, cos(a) * h + y0));
  points.push_back(point(cos(a) * w + x0, -sin(a) * w + y0));
  points.push_back(point(cos(a) * w + sin(a) * h + x0, -sin(a) * w + cos(a) * h + y0));
}

bool left_lower(const point& p1, const point& p2)
{
  if (p1.x < p2.x)
    return true;
  else if (p1.x > p2.x)
    return false;
  else if (p1.y < p2.y)
    return true;
  else
    return false;
}

void sort_and_remove_duplicates(vector<point>& points,
  bool (*compare)(const point&, const point&) /* = left_lower */)
{
  sort(points.begin(), points.end(), compare); // sort the points in leftmost-lowest order
  for (vector<point>::iterator i = points.begin(); i != points.end(); ) {
    // remove the duplicate points
    vector<point>::iterator j = i;
    j++;
    if (j != points.end() && *i == *j)
      i = points.erase(i);
    else
      i++;
  }
}

double signed_triangle_area(const point& a, const point& b, const point& c)
{
  return (a.x * b.y - a.y * b.x + a.y * c.x - a.x * c.y + b.x * c.y - c.x * b.y) / 2.0;
}

bool collinear(const point& a, const point& b, const point& c)
{
  return fabs(signed_triangle_area(a, b, c)) <= epsilon;
}

double euclidean_distance(const point& a, const point& b)
{
  double dx = a.x - b.x, dy = a.y - b.y;
  return sqrt(dx * dx + dy * dy);
}

bool ccw(const point& a, const point& b, const point& c)
{
  // see if the point c is to the left of a -> b (or, a - b - c are counterclockwise)
  return signed_triangle_area(a, b, c) > epsilon;
}

bool cw(const point& a, const point& b, const point& c)
{
  // see if the point c is to the right of a -> b (or, a - b - c are clockwise)
  return signed_triangle_area(a, b, c) < -epsilon;
}

struct smaller_angle {
  const point& first;

  smaller_angle(const point& _first) : first(_first) {}
  bool operator() (const point& p1, const point& p2) const;
};

bool smaller_angle::operator() (const point& p1, const point& p2) const
{
  if (collinear(first, p1, p2))
    return euclidean_distance(first, p1) <= euclidean_distance(first, p2);
  else
    return ccw(first, p1, p2);
}

int convex_hull(vector<point>& points, vector<point>& hull)
{
  sort_and_remove_duplicates(points, left_lower);
    // sort the points in leftmost-lowest order
  vector<point>::iterator i = points.begin();
  i++;
  sort(i, points.end(), smaller_angle(points[0]));
    // sort the second and later points in increasing angular order
  hull.resize(points.size());
  hull[0] = points[0]; hull[1] = points[1];
  int j = 1;
  for (int i = 2; i < points.size(); ) {
    if (cw(hull[j - 1], hull[j], points[i]))
      j--; // remove hulll[j]
    else {
      if (!collinear(hull[j - 1], hull[j], points[i]))
        j++;
      hull[j] = points[i++];
    }
  }
  if (cw(hull[j - 1], hull[j], points[0]))
    ;
  else
    j++;
  hull.resize(j);
  return hull.size();
}

double polygon_area(const vector<point>& polygon)
{
  double area = 0.0;
  for (int i = 0; i < polygon.size(); i++) {
    int j = (i + 1) % polygon.size();
    area += polygon[i].x * polygon[j].y - polygon[j].x * polygon[i].y;
  }
  return area / 2.0;
}

int main()
{
  int N;
  scanf("%d", &N);
  while (N--) {
    int n;
    scanf("%d", &n);
    vector<point> points;
    double ra = 0.0;
    for (int i = 0; i < n; i++) {
      double x, y, w, h, phi;
      scanf("%lf %lf %lf %lf %lf", &x, &y, &w, &h, &phi);
      add_rectangle_points(x, y, w, h, phi * pi / 180.0, points);
      ra += w * h;
    }
#ifdef DEBUG
    for (size_t i = 0; i < points.size(); i++)
      printf("%lf %lf\n", points[i].x, points[i].y);
#endif
    vector<point> hull(n * 4);
    convex_hull(points, hull);
#ifdef DEBUG
    for (size_t i = 0; i < hull.size(); i++)
      printf("%lf %lf\n", hull[i].x, hull[i].y);
#endif
    double area = polygon_area(hull);
    printf("%.1lf %%\n", ra * 100.0 / area);
  }
  return 0;
}