Explanation:
- A **Quadtree** is a tree data structure used to partition a two-dimensional space by recursively subdividing it into four quadrants or regions.
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- It is particularly useful in applications such as image processing, spatial indexing, and computer graphics.
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Steps:
- The space is recursively divided into four quadrants until a predefined condition is met (such as a maximum number of points in a quadrant or a minimum size of the region).
- Each node in the tree represents a quadrant, and each child node corresponds to a subdivision of the parent quadrant.
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Time Complexity:
- Insertion: O(log n) for balanced trees, or O(n) in the worst case if all points are in the same quadrant.
- Querying: O(log n) for searching in balanced structures.