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