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Add QuadTree data structure (#5681)
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‎DIRECTORY.md

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* [PostOrderTraversal](https://github.com/TheAlgorithms/Java/blob/master/src/main/java/com/thealgorithms/datastructures/trees/PostOrderTraversal.java)
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* [PreOrderTraversal](https://github.com/TheAlgorithms/Java/blob/master/src/main/java/com/thealgorithms/datastructures/trees/PreOrderTraversal.java)
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* [PrintTopViewofTree](https://github.com/TheAlgorithms/Java/blob/master/src/main/java/com/thealgorithms/datastructures/trees/PrintTopViewofTree.java)
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* [QuadTree](https://github.com/TheAlgorithms/Java/blob/master/src/main/java/com/thealgorithms/datastructures/trees/QuadTree.java)
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* [RedBlackBST](https://github.com/TheAlgorithms/Java/blob/master/src/main/java/com/thealgorithms/datastructures/trees/RedBlackBST.java)
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* [SameTreesCheck](https://github.com/TheAlgorithms/Java/blob/master/src/main/java/com/thealgorithms/datastructures/trees/SameTreesCheck.java)
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* [SegmentTree](https://github.com/TheAlgorithms/Java/blob/master/src/main/java/com/thealgorithms/datastructures/trees/SegmentTree.java)

‎src/main/java/com/thealgorithms/datastructures/trees/QuadTree.java

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package com.thealgorithms.datastructures.trees;
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import java.util.ArrayList;
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import java.util.List;
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/**
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* Point is a simple class that represents a point in 2D space.
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*
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* @see <a href="https://en.wikipedia.org/wiki/Point_(geometry)">Point</a>
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* @author <a href="https://github.com/sailok">Sailok Chinta</a>
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*/
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class Point {
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public double x;
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public double y;
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Point(double x, double y) {
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this.x = x;
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this.y = y;
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}
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}
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/**
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* BoundingBox is a simple class that represents a bounding box in 2D space.
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*
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* @see <a href="https://en.wikipedia.org/wiki/Bounding_box">Bounding Box</a>
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* @author <a href="https://github.com/sailok">Sailok Chinta</a>
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*/
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class BoundingBox {
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public Point center;
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public double halfWidth;
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BoundingBox(Point center, double halfWidth) {
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this.center = center;
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this.halfWidth = halfWidth;
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}
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/**
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* Checks if the point is inside the bounding box
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*
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* @param point The point to check
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* @return true if the point is inside the bounding box, false otherwise
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*/
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public boolean containsPoint(Point point) {
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return point.x >= center.x - halfWidth && point.x <= center.x + halfWidth && point.y >= center.y - halfWidth && point.y <= center.y + halfWidth;
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}
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/**
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* Checks if the bounding box intersects with the other bounding box
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*
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* @param otherBoundingBox The other bounding box
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* @return true if the bounding box intersects with the other bounding box, false otherwise
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*/
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public boolean intersectsBoundingBox(BoundingBox otherBoundingBox) {
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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
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&& otherBoundingBox.center.y + otherBoundingBox.halfWidth >= center.y - halfWidth;
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}
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}
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/**
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* QuadTree is a tree data structure that is used to store spatial information
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* in an efficient way.
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*
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* This implementation is specific to Point QuadTrees
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*
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* @see <a href="https://en.wikipedia.org/wiki/Quadtree">Quad Tree</a>
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* @author <a href="https://github.com/sailok">Sailok Chinta</a>
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*/
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public class QuadTree {
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private final BoundingBox boundary;
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private final int capacity;
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private List<Point> pointList;
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private boolean divided;
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private QuadTree northWest;
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private QuadTree northEast;
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private QuadTree southWest;
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private QuadTree southEast;
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public QuadTree(BoundingBox boundary, int capacity) {
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this.boundary = boundary;
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this.capacity = capacity;
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this.pointList = new ArrayList<>();
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this.divided = false;
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this.northWest = null;
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this.northEast = null;
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this.southWest = null;
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this.southEast = null;
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}
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/**
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* Inserts a point into the tree
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*
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* @param point The point to insert
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* @return true if the point is successfully inserted, false otherwise
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*/
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public boolean insert(Point point) {
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if (point == null) {
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return false;
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}
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// Ignore points that don't belong to this quad tree
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if (!boundary.containsPoint(point)) {
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return false;
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}
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// if the space is not already occupied, add it to the list
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if (pointList.size() < capacity) {
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pointList.add(point);
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return true;
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}
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// if subdivision hasn't happened, divide the tree
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if (!divided) {
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subDivide();
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}
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// try to add the point in one of the four quadrants
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if (northWest.insert(point)) {
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return true;
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}
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if (northEast.insert(point)) {
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return true;
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}
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if (southWest.insert(point)) {
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return true;
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}
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if (southEast.insert(point)) {
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return true;
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}
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return false;
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}
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/**
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* Create four children that fully divide this quad into four quads of equal area
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*/
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private void subDivide() {
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double quadrantHalfWidth = boundary.halfWidth / 2;
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northWest = new QuadTree(new BoundingBox(new Point(boundary.center.x - quadrantHalfWidth, boundary.center.y + quadrantHalfWidth), quadrantHalfWidth), this.capacity);
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northEast = new QuadTree(new BoundingBox(new Point(boundary.center.x + quadrantHalfWidth, boundary.center.y + quadrantHalfWidth), quadrantHalfWidth), this.capacity);
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southWest = new QuadTree(new BoundingBox(new Point(boundary.center.x - quadrantHalfWidth, boundary.center.y - quadrantHalfWidth), quadrantHalfWidth), this.capacity);
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southEast = new QuadTree(new BoundingBox(new Point(boundary.center.x + quadrantHalfWidth, boundary.center.y - quadrantHalfWidth), quadrantHalfWidth), this.capacity);
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divided = true;
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}
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/**
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* Queries all the points that intersect with the other bounding box
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*
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* @param otherBoundingBox The other bounding box
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* @return List of points that intersect with the other bounding box
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*/
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public List<Point> query(BoundingBox otherBoundingBox) {
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List<Point> points = new ArrayList<>();
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if (!boundary.intersectsBoundingBox(otherBoundingBox)) {
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return points;
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}
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// filter the points that intersect with the other bounding box
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points.addAll(pointList.stream().filter(otherBoundingBox::containsPoint).toList());
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if (divided) {
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points.addAll(northWest.query(otherBoundingBox));
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points.addAll(northEast.query(otherBoundingBox));
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points.addAll(southWest.query(otherBoundingBox));
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points.addAll(southEast.query(otherBoundingBox));
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}
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return points;
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}
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}

‎src/test/java/com/thealgorithms/datastructures/trees/QuadTreeTest.java

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package com.thealgorithms.datastructures.trees;
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import java.util.List;
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import org.junit.jupiter.api.Assertions;
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import org.junit.jupiter.api.Test;
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public class QuadTreeTest {
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int quadTreeCapacity = 4;
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BoundingBox boundingBox = new BoundingBox(new Point(0, 0), 500);
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QuadTree quadTree = new QuadTree(boundingBox, quadTreeCapacity);
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@Test
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public void testNullPointInsertIntoQuadTree() {
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Assertions.assertFalse(quadTree.insert(null));
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}
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@Test
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public void testInsertIntoQuadTree() {
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Assertions.assertTrue(quadTree.insert(new Point(10, -10)));
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Assertions.assertTrue(quadTree.insert(new Point(-10, 10)));
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Assertions.assertTrue(quadTree.insert(new Point(-10, -10)));
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Assertions.assertTrue(quadTree.insert(new Point(10, 10)));
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Assertions.assertFalse(quadTree.insert(new Point(1050, 1050)));
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}
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@Test
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public void testInsertIntoQuadTreeAndSubDivide() {
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Assertions.assertTrue(quadTree.insert(new Point(10, -10)));
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Assertions.assertTrue(quadTree.insert(new Point(-10, 10)));
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Assertions.assertTrue(quadTree.insert(new Point(-10, -10)));
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Assertions.assertTrue(quadTree.insert(new Point(10, 10)));
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Assertions.assertTrue(quadTree.insert(new Point(-100, 100)));
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Assertions.assertTrue(quadTree.insert(new Point(100, -101)));
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Assertions.assertTrue(quadTree.insert(new Point(-100, -100)));
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Assertions.assertTrue(quadTree.insert(new Point(100, 100)));
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}
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@Test
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public void testQueryInQuadTree() {
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quadTree.insert(new Point(10, -10));
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quadTree.insert(new Point(-10, 10));
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quadTree.insert(new Point(-10, -10));
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quadTree.insert(new Point(10, 10));
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quadTree.insert(new Point(-100, 100));
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quadTree.insert(new Point(100, -100));
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quadTree.insert(new Point(-100, -100));
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quadTree.insert(new Point(100, 100));
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List<Point> points = quadTree.query(new BoundingBox(new Point(0, 0), 100));
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Assertions.assertEquals(8, points.size());
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points = quadTree.query(new BoundingBox(new Point(5, 5), 5));
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Assertions.assertEquals(1, points.size());
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points = quadTree.query(new BoundingBox(new Point(-200, -200), 5));
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Assertions.assertEquals(0, points.size());
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}
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}

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