100 lines
3.2 KiB
Java
100 lines
3.2 KiB
Java
|
|
||
|
|
|
||
|
|
import edu.princeton.cs.introcs.StdIn;
|
||
|
|
import edu.princeton.cs.introcs.StdOut;
|
||
|
|
|
||
|
|
/*************************************************************************
|
||
|
|
* Compilation: javac FarthestPair.java
|
||
|
|
* Execution: java FarthestPair < input.txt
|
||
|
|
* Dependencies: GrahamScan.java Point2D.java
|
||
|
|
*
|
||
|
|
* Given a set of N points in the plane, find the farthest pair
|
||
|
|
* (equivalently, compute the diameter of the set of points).
|
||
|
|
*
|
||
|
|
* Computes the convex hull of the set of points and using the
|
||
|
|
* rotating callipers method to find all antipodal point pairs
|
||
|
|
* and the farthest pair.
|
||
|
|
*
|
||
|
|
*************************************************************************/
|
||
|
|
|
||
|
|
public class FarthestPair {
|
||
|
|
|
||
|
|
// farthest pair of points and distance
|
||
|
|
private Point2D best1, best2;
|
||
|
|
private double bestDistance = Double.NEGATIVE_INFINITY;
|
||
|
|
|
||
|
|
public FarthestPair(Point2D[] points) {
|
||
|
|
GrahamScan graham = new GrahamScan(points);
|
||
|
|
|
||
|
|
// single point
|
||
|
|
if (points.length <= 1) return;
|
||
|
|
|
||
|
|
// number of points on the hull
|
||
|
|
int M = 0;
|
||
|
|
for (Point2D p : graham.hull())
|
||
|
|
M++;
|
||
|
|
|
||
|
|
// the hull, in counterclockwise order
|
||
|
|
Point2D[] hull = new Point2D[M+1];
|
||
|
|
int m = 1;
|
||
|
|
for (Point2D p : graham.hull()) {
|
||
|
|
hull[m++] = p;
|
||
|
|
}
|
||
|
|
|
||
|
|
// all points are equal
|
||
|
|
if (M == 1) return;
|
||
|
|
|
||
|
|
// points are collinear
|
||
|
|
if (M == 2) {
|
||
|
|
best1 = hull[1];
|
||
|
|
best2 = hull[2];
|
||
|
|
bestDistance = best1.distanceTo(best2);
|
||
|
|
return;
|
||
|
|
}
|
||
|
|
|
||
|
|
// k = farthest vertex from edge from hull[1] to hull[M]
|
||
|
|
int k = 2;
|
||
|
|
while (Point2D.area2(hull[M], hull[k+1], hull[1]) > Point2D.area2(hull[M], hull[k], hull[1])) {
|
||
|
|
k++;
|
||
|
|
}
|
||
|
|
|
||
|
|
int j = k;
|
||
|
|
for (int i = 1; i <= k; i++) {
|
||
|
|
// StdOut.println("hull[i] + " and " + hull[j] + " are antipodal");
|
||
|
|
if (hull[i].distanceTo(hull[j]) > bestDistance) {
|
||
|
|
best1 = hull[i];
|
||
|
|
best2 = hull[j];
|
||
|
|
bestDistance = hull[i].distanceTo(hull[j]);
|
||
|
|
}
|
||
|
|
while ((j < M) && Point2D.area2(hull[i], hull[j+1], hull[i+1]) > Point2D.area2(hull[i], hull[j], hull[i+1])) {
|
||
|
|
j++;
|
||
|
|
// StdOut.println(hull[i] + " and " + hull[j] + " are antipodal");
|
||
|
|
double distance = hull[i].distanceTo(hull[j]);
|
||
|
|
if (distance > bestDistance) {
|
||
|
|
best1 = hull[i];
|
||
|
|
best2 = hull[j];
|
||
|
|
bestDistance = hull[i].distanceTo(hull[j]);
|
||
|
|
}
|
||
|
|
}
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
public Point2D either() { return best1; }
|
||
|
|
public Point2D other() { return best2; }
|
||
|
|
public double distance() { return bestDistance; }
|
||
|
|
|
||
|
|
|
||
|
|
public static void main(String[] args) {
|
||
|
|
int N = StdIn.readInt();
|
||
|
|
Point2D[] points = new Point2D[N];
|
||
|
|
for (int i = 0; i < N; i++) {
|
||
|
|
int x = StdIn.readInt();
|
||
|
|
int y = StdIn.readInt();
|
||
|
|
points[i] = new Point2D(x, y);
|
||
|
|
}
|
||
|
|
FarthestPair farthest = new FarthestPair(points);
|
||
|
|
StdOut.println(farthest.distance() + " from " + farthest.either() + " to " + farthest.other());
|
||
|
|
}
|
||
|
|
|
||
|
|
}
|