diff --git a/DIRECTORY.md b/DIRECTORY.md index dea06ca10f4f..3dbd1519ff08 100644 --- a/DIRECTORY.md +++ b/DIRECTORY.md @@ -218,6 +218,7 @@ * [PostOrderTraversal](https://github.com/TheAlgorithms/Java/blob/master/src/main/java/com/thealgorithms/datastructures/trees/PostOrderTraversal.java) * [PreOrderTraversal](https://github.com/TheAlgorithms/Java/blob/master/src/main/java/com/thealgorithms/datastructures/trees/PreOrderTraversal.java) * [PrintTopViewofTree](https://github.com/TheAlgorithms/Java/blob/master/src/main/java/com/thealgorithms/datastructures/trees/PrintTopViewofTree.java) + * [QuadTree](https://github.com/TheAlgorithms/Java/blob/master/src/main/java/com/thealgorithms/datastructures/trees/QuadTree.java) * [RedBlackBST](https://github.com/TheAlgorithms/Java/blob/master/src/main/java/com/thealgorithms/datastructures/trees/RedBlackBST.java) * [SameTreesCheck](https://github.com/TheAlgorithms/Java/blob/master/src/main/java/com/thealgorithms/datastructures/trees/SameTreesCheck.java) * [SegmentTree](https://github.com/TheAlgorithms/Java/blob/master/src/main/java/com/thealgorithms/datastructures/trees/SegmentTree.java) diff --git a/src/main/java/com/thealgorithms/datastructures/trees/QuadTree.java b/src/main/java/com/thealgorithms/datastructures/trees/QuadTree.java new file mode 100644 index 000000000000..e0d255b1e784 --- /dev/null +++ b/src/main/java/com/thealgorithms/datastructures/trees/QuadTree.java @@ -0,0 +1,176 @@ +package com.thealgorithms.datastructures.trees; + +import java.util.ArrayList; +import java.util.List; + +/** + * Point is a simple class that represents a point in 2D space. + * + * @see Point + * @author Sailok Chinta + */ +class Point { + public double x; + public double y; + + Point(double x, double y) { + this.x = x; + this.y = y; + } +} + +/** + * BoundingBox is a simple class that represents a bounding box in 2D space. + * + * @see Bounding Box + * @author Sailok Chinta + */ +class BoundingBox { + public Point center; + public double halfWidth; + + BoundingBox(Point center, double halfWidth) { + this.center = center; + this.halfWidth = halfWidth; + } + + /** + * Checks if the point is inside the bounding box + * + * @param point The point to check + * @return true if the point is inside the bounding box, false otherwise + */ + public boolean containsPoint(Point point) { + return point.x >= center.x - halfWidth && point.x <= center.x + halfWidth && point.y >= center.y - halfWidth && point.y <= center.y + halfWidth; + } + + /** + * Checks if the bounding box intersects with the other bounding box + * + * @param otherBoundingBox The other bounding box + * @return true if the bounding box intersects with the other bounding box, false otherwise + */ + public boolean intersectsBoundingBox(BoundingBox otherBoundingBox) { + return otherBoundingBox.center.x - otherBoundingBox.halfWidth <= center.x + halfWidth && otherBoundingBox.center.x + otherBoundingBox.halfWidth >= center.x - halfWidth && otherBoundingBox.center.y - otherBoundingBox.halfWidth <= center.y + halfWidth + && otherBoundingBox.center.y + otherBoundingBox.halfWidth >= center.y - halfWidth; + } +} + +/** + * QuadTree is a tree data structure that is used to store spatial information + * in an efficient way. + * + * This implementation is specific to Point QuadTrees + * + * @see Quad Tree + * @author Sailok Chinta + */ +public class QuadTree { + private final BoundingBox boundary; + private final int capacity; + + private List pointList; + private boolean divided; + private QuadTree northWest; + private QuadTree northEast; + private QuadTree southWest; + private QuadTree southEast; + + public QuadTree(BoundingBox boundary, int capacity) { + this.boundary = boundary; + this.capacity = capacity; + + this.pointList = new ArrayList<>(); + this.divided = false; + this.northWest = null; + this.northEast = null; + this.southWest = null; + this.southEast = null; + } + + /** + * Inserts a point into the tree + * + * @param point The point to insert + * @return true if the point is successfully inserted, false otherwise + */ + public boolean insert(Point point) { + if (point == null) { + return false; + } + + // Ignore points that don't belong to this quad tree + if (!boundary.containsPoint(point)) { + return false; + } + + // if the space is not already occupied, add it to the list + if (pointList.size() < capacity) { + pointList.add(point); + return true; + } + + // if subdivision hasn't happened, divide the tree + if (!divided) { + subDivide(); + } + + // try to add the point in one of the four quadrants + if (northWest.insert(point)) { + return true; + } + + if (northEast.insert(point)) { + return true; + } + + if (southWest.insert(point)) { + return true; + } + + if (southEast.insert(point)) { + return true; + } + + return false; + } + + /** + * Create four children that fully divide this quad into four quads of equal area + */ + private void subDivide() { + double quadrantHalfWidth = boundary.halfWidth / 2; + + northWest = new QuadTree(new BoundingBox(new Point(boundary.center.x - quadrantHalfWidth, boundary.center.y + quadrantHalfWidth), quadrantHalfWidth), this.capacity); + northEast = new QuadTree(new BoundingBox(new Point(boundary.center.x + quadrantHalfWidth, boundary.center.y + quadrantHalfWidth), quadrantHalfWidth), this.capacity); + southWest = new QuadTree(new BoundingBox(new Point(boundary.center.x - quadrantHalfWidth, boundary.center.y - quadrantHalfWidth), quadrantHalfWidth), this.capacity); + southEast = new QuadTree(new BoundingBox(new Point(boundary.center.x + quadrantHalfWidth, boundary.center.y - quadrantHalfWidth), quadrantHalfWidth), this.capacity); + divided = true; + } + + /** + * Queries all the points that intersect with the other bounding box + * + * @param otherBoundingBox The other bounding box + * @return List of points that intersect with the other bounding box + */ + public List query(BoundingBox otherBoundingBox) { + List points = new ArrayList<>(); + + if (!boundary.intersectsBoundingBox(otherBoundingBox)) { + return points; + } + + // filter the points that intersect with the other bounding box + points.addAll(pointList.stream().filter(otherBoundingBox::containsPoint).toList()); + + if (divided) { + points.addAll(northWest.query(otherBoundingBox)); + points.addAll(northEast.query(otherBoundingBox)); + points.addAll(southWest.query(otherBoundingBox)); + points.addAll(southEast.query(otherBoundingBox)); + } + + return points; + } +} diff --git a/src/test/java/com/thealgorithms/datastructures/trees/QuadTreeTest.java b/src/test/java/com/thealgorithms/datastructures/trees/QuadTreeTest.java new file mode 100644 index 000000000000..62b86da214db --- /dev/null +++ b/src/test/java/com/thealgorithms/datastructures/trees/QuadTreeTest.java @@ -0,0 +1,58 @@ +package com.thealgorithms.datastructures.trees; + +import java.util.List; +import org.junit.jupiter.api.Assertions; +import org.junit.jupiter.api.Test; + +public class QuadTreeTest { + int quadTreeCapacity = 4; + BoundingBox boundingBox = new BoundingBox(new Point(0, 0), 500); + QuadTree quadTree = new QuadTree(boundingBox, quadTreeCapacity); + + @Test + public void testNullPointInsertIntoQuadTree() { + Assertions.assertFalse(quadTree.insert(null)); + } + + @Test + public void testInsertIntoQuadTree() { + Assertions.assertTrue(quadTree.insert(new Point(10, -10))); + Assertions.assertTrue(quadTree.insert(new Point(-10, 10))); + Assertions.assertTrue(quadTree.insert(new Point(-10, -10))); + Assertions.assertTrue(quadTree.insert(new Point(10, 10))); + Assertions.assertFalse(quadTree.insert(new Point(1050, 1050))); + } + + @Test + public void testInsertIntoQuadTreeAndSubDivide() { + Assertions.assertTrue(quadTree.insert(new Point(10, -10))); + Assertions.assertTrue(quadTree.insert(new Point(-10, 10))); + Assertions.assertTrue(quadTree.insert(new Point(-10, -10))); + Assertions.assertTrue(quadTree.insert(new Point(10, 10))); + Assertions.assertTrue(quadTree.insert(new Point(-100, 100))); + Assertions.assertTrue(quadTree.insert(new Point(100, -101))); + Assertions.assertTrue(quadTree.insert(new Point(-100, -100))); + Assertions.assertTrue(quadTree.insert(new Point(100, 100))); + } + + @Test + public void testQueryInQuadTree() { + quadTree.insert(new Point(10, -10)); + quadTree.insert(new Point(-10, 10)); + quadTree.insert(new Point(-10, -10)); + quadTree.insert(new Point(10, 10)); + quadTree.insert(new Point(-100, 100)); + quadTree.insert(new Point(100, -100)); + quadTree.insert(new Point(-100, -100)); + quadTree.insert(new Point(100, 100)); + + List points = quadTree.query(new BoundingBox(new Point(0, 0), 100)); + Assertions.assertEquals(8, points.size()); + + points = quadTree.query(new BoundingBox(new Point(5, 5), 5)); + Assertions.assertEquals(1, points.size()); + + points = quadTree.query(new BoundingBox(new Point(-200, -200), 5)); + Assertions.assertEquals(0, points.size()); + } +}