/************************************************************************* * Compilation: javac GrahamaScan.java * Execution: java GrahamScan < input.txt * Dependencies: Point2D.java * * Create points from standard input and compute the convex hull using * Graham scan algorithm. * * May be floating-point issues if x- and y-coordinates are not integers. * *************************************************************************/ import java.util.Arrays; import edu.princeton.cs.introcs.StdIn; import edu.princeton.cs.introcs.StdOut; public class GrahamScan { private Stack hull = new Stack(); public GrahamScan(Point2D[] pts) { // defensive copy int N = pts.length; Point2D[] points = new Point2D[N]; for (int i = 0; i < N; i++) points[i] = pts[i]; // preprocess so that points[0] has lowest y-coordinate; break ties by x-coordinate // points[0] is an extreme point of the convex hull // (alternatively, could do easily in linear time) Arrays.sort(points); // sort by polar angle with respect to base point points[0], // breaking ties by distance to points[0] Arrays.sort(points, 1, N, points[0].POLAR_ORDER); hull.push(points[0]); // p[0] is first extreme point // find index k1 of first point not equal to points[0] int k1; for (k1 = 1; k1 < N; k1++) if (!points[0].equals(points[k1])) break; if (k1 == N) return; // all points equal // find index k2 of first point not collinear with points[0] and points[k1] int k2; for (k2 = k1 + 1; k2 < N; k2++) if (Point2D.ccw(points[0], points[k1], points[k2]) != 0) break; hull.push(points[k2-1]); // points[k2-1] is second extreme point // Graham scan; note that points[N-1] is extreme point different from points[0] for (int i = k2; i < N; i++) { Point2D top = hull.pop(); while (Point2D.ccw(hull.peek(), top, points[i]) <= 0) { top = hull.pop(); } hull.push(top); hull.push(points[i]); } assert isConvex(); } // return extreme points on convex hull in counterclockwise order as an Iterable public Iterable hull() { Stack s = new Stack(); for (Point2D p : hull) s.push(p); return s; } // check that boundary of hull is strictly convex private boolean isConvex() { int N = hull.size(); if (N <= 2) return true; Point2D[] points = new Point2D[N]; int n = 0; for (Point2D p : hull()) { points[n++] = p; } for (int i = 0; i < N; i++) { if (Point2D.ccw(points[i], points[(i+1) % N], points[(i+2) % N]) <= 0) { return false; } } return true; } // test client 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); } GrahamScan graham = new GrahamScan(points); for (Point2D p : graham.hull()) StdOut.println(p); } }