Merge branch 'master' into add-graham-scan-convex-hull

Author: poyea

geometry/jarvis_march.py

@@ -0,0 +1,187 @@
+"""
+Jarvis March (Gift Wrapping) algorithm for finding the convex hull of a set of points.
+
+The convex hull is the smallest convex polygon that contains all the points.
+
+Time Complexity: O(n*h) where n is the number of points and h is the number of
+hull points.
+Space Complexity: O(h) where h is the number of hull points.
+
+USAGE:
+    -> Import this file into your project.
+    -> Use the jarvis_march() function to find the convex hull of a set of points.
+    -> Parameters:
+        -> points: A list of Point objects representing 2D coordinates
+
+REFERENCES:
+    -> Wikipedia reference: https://en.wikipedia.org/wiki/Gift_wrapping_algorithm
+    -> GeeksforGeeks:
+       https://www.geeksforgeeks.org/convex-hull-set-1-jarviss-algorithm-or-wrapping/
+"""
+
+from __future__ import annotations
+
+
+class Point:
+    """Represents a 2D point with x and y coordinates."""
+
+    def __init__(self, x_coordinate: float, y_coordinate: float) -> None:
+        self.x = x_coordinate
+        self.y = y_coordinate
+
+    def __eq__(self, other: object) -> bool:
+        if not isinstance(other, Point):
+            return NotImplemented
+        return self.x == other.x and self.y == other.y
+
+    def __repr__(self) -> str:
+        return f"Point({self.x}, {self.y})"
+
+    def __hash__(self) -> int:
+        return hash((self.x, self.y))
+
+
+def _cross_product(origin: Point, point_a: Point, point_b: Point) -> float:
+    """
+    Calculate the cross product of vectors OA and OB.
+
+    Returns:
+        > 0: Counter-clockwise turn (left turn)
+        = 0: Collinear
+        < 0: Clockwise turn (right turn)
+    """
+    return (point_a.x - origin.x) * (point_b.y - origin.y) - (point_a.y - origin.y) * (
+        point_b.x - origin.x
+    )
+
+
+def _is_point_on_segment(p1: Point, p2: Point, point: Point) -> bool:
+    """Check if a point lies on the line segment between p1 and p2."""
+    # Check if point is collinear with segment endpoints
+    cross = (point.y - p1.y) * (p2.x - p1.x) - (point.x - p1.x) * (p2.y - p1.y)
+
+    if abs(cross) > 1e-9:
+        return False
+
+    # Check if point is within the bounding box of the segment
+    return min(p1.x, p2.x) <= point.x <= max(p1.x, p2.x) and min(
+        p1.y, p2.y
+    ) <= point.y <= max(p1.y, p2.y)
+
+
+def _find_leftmost_point(points: list[Point]) -> int:
+    """Find index of leftmost point (and bottom-most in case of tie)."""
+    left_idx = 0
+    for i in range(1, len(points)):
+        if points[i].x < points[left_idx].x or (
+            points[i].x == points[left_idx].x and points[i].y < points[left_idx].y
+        ):
+            left_idx = i
+    return left_idx
+
+
+def _find_next_hull_point(points: list[Point], current_idx: int) -> int:
+    """Find the next point on the convex hull."""
+    next_idx = (current_idx + 1) % len(points)
+    # Ensure next_idx is not the same as current_idx
+    while next_idx == current_idx:
+        next_idx = (next_idx + 1) % len(points)
+
+    for i in range(len(points)):
+        if i == current_idx:
+            continue
+        cross = _cross_product(points[current_idx], points[i], points[next_idx])
+        if cross > 0:
+            next_idx = i
+
+    return next_idx
+
+
+def _is_valid_polygon(hull: list[Point]) -> bool:
+    """Check if hull forms a valid polygon (has at least one non-collinear turn)."""
+    for i in range(len(hull)):
+        p1 = hull[i]
+        p2 = hull[(i + 1) % len(hull)]
+        p3 = hull[(i + 2) % len(hull)]
+        if abs(_cross_product(p1, p2, p3)) > 1e-9:
+            return True
+    return False
+
+
+def _add_point_to_hull(hull: list[Point], point: Point) -> None:
+    """Add a point to hull, removing collinear intermediate points."""
+    last = len(hull) - 1
+    if len(hull) > 1 and _is_point_on_segment(hull[last - 1], hull[last], point):
+        hull[last] = Point(point.x, point.y)
+    else:
+        hull.append(Point(point.x, point.y))
+
+
+def jarvis_march(points: list[Point]) -> list[Point]:
+    """
+    Find the convex hull of a set of points using the Jarvis March algorithm.
+
+    The algorithm starts with the leftmost point and wraps around the set of
+    points, selecting the most counter-clockwise point at each step.
+
+    Args:
+        points: List of Point objects representing 2D coordinates
+
+    Returns:
+        List of Points that form the convex hull in counter-clockwise order.
+        Returns empty list if there are fewer than 3 non-collinear points.
+    """
+    if len(points) <= 2:
+        return []
+
+    # Remove duplicate points to avoid infinite loops
+    unique_points = list(set(points))
+
+    if len(unique_points) <= 2:
+        return []
+
+    convex_hull: list[Point] = []
+
+    # Find the leftmost point
+    left_point_idx = _find_leftmost_point(unique_points)
+    convex_hull.append(
+        Point(unique_points[left_point_idx].x, unique_points[left_point_idx].y)
+    )
+
+    current_idx = left_point_idx
+    while True:
+        # Find the next counter-clockwise point
+        next_idx = _find_next_hull_point(unique_points, current_idx)
+
+        if next_idx == left_point_idx:
+            break
+
+        if next_idx == current_idx:
+            break
+
+        current_idx = next_idx
+        _add_point_to_hull(convex_hull, unique_points[current_idx])
+
+    # Check for degenerate cases
+    if len(convex_hull) <= 2:
+        return []
+
+    # Check if last point is collinear with first and second-to-last
+    last = len(convex_hull) - 1
+    if _is_point_on_segment(convex_hull[last - 1], convex_hull[last], convex_hull[0]):
+        convex_hull.pop()
+        if len(convex_hull) == 2:
+            return []
+
+    # Verify the hull forms a valid polygon
+    if not _is_valid_polygon(convex_hull):
+        return []
+
+    return convex_hull
+
+
+if __name__ == "__main__":
+    # Example usage
+    points = [Point(0, 0), Point(1, 1), Point(0, 1), Point(1, 0), Point(0.5, 0.5)]
+    hull = jarvis_march(points)
+    print(f"Convex hull: {hull}")

geometry/tests/test_jarvis_march.py

@@ -0,0 +1,115 @@
+"""
+Unit tests for Jarvis March (Gift Wrapping) algorithm.
+"""
+
+from geometry.jarvis_march import Point, jarvis_march
+
+
+class TestPoint:
+    """Tests for the Point class."""
+
+    def test_point_creation(self) -> None:
+        """Test Point initialization."""
+        p = Point(1.0, 2.0)
+        assert p.x == 1.0
+        assert p.y == 2.0
+
+    def test_point_equality(self) -> None:
+        """Test Point equality comparison."""
+        p1 = Point(1.0, 2.0)
+        p2 = Point(1.0, 2.0)
+        p3 = Point(2.0, 1.0)
+        assert p1 == p2
+        assert p1 != p3
+
+    def test_point_repr(self) -> None:
+        """Test Point string representation."""
+        p = Point(1.5, 2.5)
+        assert repr(p) == "Point(1.5, 2.5)"
+
+    def test_point_hash(self) -> None:
+        """Test Point hashing."""
+        p1 = Point(1.0, 2.0)
+        p2 = Point(1.0, 2.0)
+        assert hash(p1) == hash(p2)
+
+
+class TestJarvisMarch:
+    """Tests for the jarvis_march function."""
+
+    def test_triangle(self) -> None:
+        """Test convex hull of a triangle."""
+        p1, p2, p3 = Point(1, 1), Point(2, 1), Point(1.5, 2)
+        hull = jarvis_march([p1, p2, p3])
+        assert len(hull) == 3
+        assert all(p in hull for p in [p1, p2, p3])
+
+    def test_collinear_points(self) -> None:
+        """Test that collinear points return empty hull."""
+        points = [Point(i, 0) for i in range(5)]
+        hull = jarvis_march(points)
+        assert hull == []
+
+    def test_rectangle_with_interior_point(self) -> None:
+        """Test rectangle with interior point - interior point excluded."""
+        p1, p2 = Point(1, 1), Point(2, 1)
+        p3, p4 = Point(2, 2), Point(1, 2)
+        p5 = Point(1.5, 1.5)
+        hull = jarvis_march([p1, p2, p3, p4, p5])
+        assert len(hull) == 4
+        assert p5 not in hull
+
+    def test_star_shape(self) -> None:
+        """Test star shape - only tips are in hull."""
+        tips = [
+            Point(-5, 6),
+            Point(-11, 0),
+            Point(-9, -8),
+            Point(4, 4),
+            Point(6, -7),
+        ]
+        interior = [Point(-7, -2), Point(-2, -4), Point(0, 1)]
+        hull = jarvis_march(tips + interior)
+        assert len(hull) == 5
+        assert all(p in hull for p in tips)
+        assert not any(p in hull for p in interior)
+
+    def test_empty_list(self) -> None:
+        """Test empty list returns empty hull."""
+        assert jarvis_march([]) == []
+
+    def test_single_point(self) -> None:
+        """Test single point returns empty hull."""
+        assert jarvis_march([Point(0, 0)]) == []
+
+    def test_two_points(self) -> None:
+        """Test two points return empty hull."""
+        assert jarvis_march([Point(0, 0), Point(1, 1)]) == []
+
+    def test_square(self) -> None:
+        """Test convex hull of a square."""
+        p1, p2 = Point(0, 0), Point(1, 0)
+        p3, p4 = Point(1, 1), Point(0, 1)
+        hull = jarvis_march([p1, p2, p3, p4])
+        assert len(hull) == 4
+        assert all(p in hull for p in [p1, p2, p3, p4])
+
+    def test_duplicate_points(self) -> None:
+        """Test handling of duplicate points."""
+        p1, p2, p3 = Point(0, 0), Point(1, 0), Point(0, 1)
+        points = [p1, p2, p3, p1, p2]  # Include duplicates
+        hull = jarvis_march(points)
+        assert len(hull) == 3
+
+    def test_pentagon(self) -> None:
+        """Test convex hull of a pentagon."""
+        points = [
+            Point(0, 1),
+            Point(1, 2),
+            Point(2, 1),
+            Point(1.5, 0),
+            Point(0.5, 0),
+        ]
+        hull = jarvis_march(points)
+        assert len(hull) == 5
+        assert all(p in hull for p in points)