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