Graham scan algorithm (#3903)

* Added Graham scan algorithm #3894

* Added Graham scan algorithm (#3894)

---------

Co-authored-by: Stronshade <diegobrocker1999@gmail.com>

src/main/java/com/thealgorithms/geometry/GrahamScan.java

@@ -0,0 +1,155 @@
+package com.thealgorithms.geometry;
+
+import java.util.Arrays;
+import java.util.Comparator;
+import java.util.Stack;
+
+/*
+ * A Java program that computes the convex hull using the Graham Scan algorithm
+ * In the best case, time complexity is O(n), while in the worst case, it is log(n).
+ * O(n) space complexity
+ *
+ * This algorithm is only applicable to integral coordinates.
+ *
+ * Reference:
+ * https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/geometry/graham_scan_algorithm.cpp
+ * https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/geometry/graham_scan_functions.hpp
+ * https://algs4.cs.princeton.edu/99hull/GrahamScan.java.html
+ */
+public class GrahamScan {
+    private final Stack<Point> hull = new Stack<>();
+
+    public GrahamScan(Point[] points) {
+
+        /*
+         * pre-process the points by sorting them with respect to the bottom-most point, then we'll push the
+         * first point in the array to be our first extreme point.
+         */
+        Arrays.sort(points);
+        Arrays.sort(points, 1, points.length, points[0].polarOrder());
+        hull.push(points[0]);
+
+        // find index of first point not equal to a[0] (indexPoint1) and the first point that's not
+        // collinear with either (indexPoint2).
+        int indexPoint1;
+        for (indexPoint1 = 1; indexPoint1 < points.length; indexPoint1++)
+            if (!points[0].equals(points[indexPoint1])) break;
+        if (indexPoint1 == points.length) return;
+
+        int indexPoint2;
+        for (indexPoint2 = indexPoint1+1; indexPoint2 < points.length; indexPoint2++)
+            if (Point.orientation(points[0], points[indexPoint1], points[indexPoint2]) != 0) break;
+        hull.push(points[indexPoint2-1]);
+
+        // Now we simply add the point to the stack based on the orientation.
+        for (int i = indexPoint2; i < points.length; i++) {
+            Point top = hull.pop();
+            while (Point.orientation(hull.peek(), top, points[i]) <= 0) {
+                top = hull.pop();
+            }
+            hull.push(top);
+            hull.push(points[i]);
+        }
+    }
+
+    /**
+     * @return A stack of points representing the convex hull.
+     */
+    public Iterable<Point> hull() {
+        Stack<Point> s = new Stack<>();
+        for (Point p : hull) s.push(p);
+        return s;
+    }
+
+    public record Point(int x, int y) implements Comparable<Point> {
+
+        /**
+         * Default constructor
+         * @param x x-coordinate
+         * @param y y-coordinate
+         */
+        public Point { }
+
+            /**
+             * @return the x-coordinate
+             */
+            @Override
+            public int x() {
+                return x;
+            }
+
+            /**
+             * @return the y-coordinate
+             */
+            @Override
+            public int y() { return y; }
+
+            /**
+             * Finds the orientation of ordered triplet.
+             *
+             * @param a Co-ordinates of point a <int, int>
+             * @param b Co-ordinates of point a <int, int>
+             * @param c Co-ordinates of point a <int, int>
+             * @return { -1, 0, +1 } if a -→ b -→ c is a { clockwise, collinear; counterclockwise } turn.
+             */
+            public static int orientation(Point a, Point b, Point c) {
+                int val = (b.x - a.x) * (c.y - a.y) - (b.y - a.y) * (c.x - a.x);
+                if (val == 0) {
+                    return 0;
+                }
+                return (val > 0) ? +1 : -1;
+            }
+
+            /**
+             * @param p2 Co-ordinate of point to compare to.
+             * This function will compare the points and will return a positive integer it the
+             * point is greater than the argument point and a negative integer if the point is
+             * less than the argument point.
+             */
+            public int compareTo(Point p2) {
+                if (this.y < p2.y) return -1;
+                if (this.y > p2.y) return +1;
+                if (this.x < p2.x) return -1;
+                if (this.x > p2.x) return +1;
+                return 0;
+            }
+
+            /**
+             * A helper function that will let us sort points by their polar order
+             * This function will compare the angle between 2 polar Co-ordinates
+             *
+             * @return the comparator
+             */
+            public Comparator<Point> polarOrder() {
+                return new PolarOrder();
+            }
+
+            private class PolarOrder implements Comparator<Point> {
+                public int compare(Point p1, Point p2) {
+                    int dx1 = p1.x - x;
+                    int dy1 = p1.y - y;
+                    int dx2 = p2.x - x;
+                    int dy2 = p2.y - y;
+
+                    if (dy1 >= 0 && dy2 < 0) return -1;    // q1 above; q2 below
+                    else if (dy2 >= 0 && dy1 < 0) return +1;    // q1 below; q2 above
+                    else if (dy1 == 0 && dy2 == 0) {            // 3-collinear and horizontal
+                        if (dx1 >= 0 && dx2 < 0) return -1;
+                        else if (dx2 >= 0 && dx1 < 0) return +1;
+                        else return 0;
+                    } else return -orientation(Point.this, p1, p2);     // both above or below
+                }
+            }
+
+            /**
+             * Override of the toString method, necessary to compute the difference
+             * between the expected result and the derived result
+             *
+             * @return a string representation of any given 2D point in the format (x, y)
+             */
+            @Override
+            public String toString() {
+                return "(" + x + ", " + y + ")";
+            }
+        }
+}

src/test/java/com/thealgorithms/geometry/GrahamScanTest.java

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+package com.thealgorithms.geometry;
+
+import org.junit.jupiter.api.Test;
+
+import static org.junit.jupiter.api.Assertions.assertEquals;
+
+public class GrahamScanTest {
+    @Test
+    void testGrahamScan() {
+        GrahamScan.Point[] points = {new GrahamScan.Point(0, 3), new GrahamScan.Point(1, 1),
+                new GrahamScan.Point(2, 2), new GrahamScan.Point(4, 4),
+                new GrahamScan.Point(0, 0), new GrahamScan.Point(1, 2),
+                new GrahamScan.Point(3, 1), new GrahamScan.Point(3, 3)};
+        String expectedResult = "[(0, 0), (3, 1), (4, 4), (0, 3)]";
+
+        GrahamScan graham = new GrahamScan(points);
+        assertEquals(expectedResult, graham.hull().toString());
+    }
+}