SRM 250 Div1 Hard

2009-01-14

2つの多角形の共通部分の面積を求める問題．O(n + m)の解法もあるけれど，ここでは線分の交差点と一方の多角形に含まれる点をすべて列挙してそれらの点で凸包を構成する．

import java.util.*;

public class ConvexPolygons {
  class Point {
    double x, y;

    Point(double a, double b) {
      this.x = a;
      this.y = b;
    }

    @Override
    public String toString() {
      return x + " : " + y;
    }

    double norm() {
      return x * x + y * y;
    }
  }


  double cross(Point a, Point b, Point c) {
    double res = (b.x - a.x) * (c.y - a.y) - (b.y - a.y) * (c.x - a.x);
    return res;
  }
  double cmp(Point a , Point b){
    if(a.x != b.x)return a.x - b.x;
    return a.y - b.y;
  }
  List<Point> convexHull(List<Point> ps) {
    List<Point> res = new ArrayList<Point>();
    if(ps.size() < 3)return res;
    int N = ps.size();
    int p = 0;
    for(int i = 1 ; i < N ; i++)
      if(cmp(ps.get(i) , ps.get(p)) < 0)
        p = i;
    int st = p;
    do{
      int n = -1;
      for(int i = 0 ; i < N ; i++){
        if(i == p)continue;
        if(n == -1)n = i;
        double cross = cross(ps.get(p) , ps.get(i) , ps.get(n));
        if(cross < 0)
          n = i;
      }
      res.add(ps.get(p));
      p = n;
    }while(st != p);
    return res;
  }

  double area(List<Point> lst) {
    if(lst.size() < 3)return 0.0;
    double res = 0.0;
    for (int i = 0; i < lst.size(); i++) {
      Point p1 = lst.get(i);
      Point p2 = lst.get((i + 1) % lst.size());
      res += (p1.x - p2.x) * (p1.y + p2.y);
    }
    return Math.abs(res * 0.5);
  }

  boolean include(Point point , Point[] polygon){
    for(int i = 0 ; i < polygon.length ; i++){
      Point a = polygon[i];
      Point b = polygon[(i + 1) % polygon.length];      
      double ccw = cross(point , a , b);
      if(ccw < 0)return false;
    }
    return true;
  }
  Point intersect(Point p1 , Point p2 , Point q1 , Point q2){
    double a1 = p2.y - p1.y;
    double b1 = p1.x - p2.x;
    double c1 = a1 * p1.x + b1 * p1.y;
    double a2 = q2.y - q1.y;
    double b2 = q1.x - q2.x;
    double c2 = a2 * q1.x + b2 * q1.y;
    double det = a1 * b2 - a2 * b1;
    if(det == 0.0){
      return null;
    }else{
      double x = (b2 * c1 - b1 * c2) / det;
      double y = (a1 * c2 - a2 * c1) / det;
      if(inRange(x , p1.x , p2.x) && inRange(x , q1.x , q2.x) &&
         inRange(y , p1.y , p2.y) && inRange(y , q1.y , q2.y)    
          ){
        return new Point(x , y);
      }
      return null;
    }
  }
  boolean inRange(double x , double low , double up){
    if(low > up)return inRange(x , up , low);
    return low <= x && x <= up;
  }
  List<Point> hullPoint(Point[] polygon1 , Point[] polygon2){
    List<Point> res = new ArrayList<Point>();
    for(Point p1 : polygon1){
      if(include(p1, polygon2))
        res.add(p1);
    }
    for(Point p2 : polygon2){
      if(include(p2, polygon1))
        res.add(p2);      
    }
    for(int i = 0 ; i < polygon1.length ; i++){
      for(int j = 0 ; j < polygon2.length ; j++){
        Point a = polygon1[i];
        Point b = polygon1[(i+1) % polygon1.length];
        Point c = polygon2[j];
        Point d = polygon2[(j+1) % polygon2.length];
        Point ip = intersect(a, b, c, d);
        if(ip != null)
          res.add(ip);
      }
    }
    return res;
  }
  double overlap(Point[] polygon1 , Point[] polygon2){
    return area(convexHull(hullPoint(polygon1, polygon2)));
  }
  public double overlap(String[] polygon1, String[] polygon2) {    
    return overlap(toPolygon(polygon1), toPolygon(polygon2));
  }
  Point[] toPolygon(String[] poly){
    Point ps[] = new Point[poly.length];
    for(int i = 0 ; i < ps.length ; i++){
      String p = poly[i];
      String a[] = p.split("\\s+");
      Point pt = new Point(Integer.parseInt(a[0]) , Integer.parseInt(a[1]));
      ps[i] = pt;
    }
    return ps;
  }
}

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