# [Algorithms]Binary Tree, Quadtree and Octree

keywords: Algorithms, Binary Tree, Quadtree and Octree

##### Wikipedia

Binary tree

https://en.wikipedia.org/wiki/Binary_tree

Quadtree

https://en.wikipedia.org/wiki/Quadtree

Octree

https://en.wikipedia.org/wiki/Octree

### Applications

##### Binary Tree Applications

- Binary Search Tree - Used in many search applications where data is constantly entering/leaving, such as the map and set objects in many languages’ libraries.
- Binary Space Partition - Used in almost every 3D video game to determine what objects need to be rendered.
- Binary Tries - Used in almost every high-bandwidth router for storing router-tables.
- Hash Trees - used in p2p programs and specialized image-signatures in which a hash needs to be verified, but the whole file is not available.
- Heaps - Used in implementing efficient priority-queues, which in turn are used for scheduling processes in many operating systems, Quality-of-Service in routers, and A* (path-finding algorithm used in AI applications, including robotics and video games). Also used in heap-sort.
- Huffman Coding Tree (Chip Uni) - used in compression algorithms, such as those used by the .jpeg and .mp3 file-formats.
- GGM Trees - Used in cryptographic applications to generate a tree of pseudo-random numbers.
- Syntax Tree - Constructed by compilers and (implicitly) calculators to parse expressions.
- Treap - Randomized data structure used in wireless networking and memory allocation.
- T-tree - Though most databases use some form of B-tree to store data on the drive, databases which keep all (most) their data in memory often use T-trees to do so.

Reference:

What are the applications of binary trees?

https://stackoverflow.com/questions/2130416/what-are-the-applications-of-binary-trees

##### Quadtree Applications

- Image processing
- Mesh generation
- Spatial indexing, point location queries, and range queries
- Efficient collision detection in two dimensions
- View frustum culling of terrain data
- Storing sparse data, such as a formatting information for a spreadsheet or for some matrix calculations
- Solution of multidimensional fields (computational fluid dynamics, electromagnetism)
- Conway’s Game of Life simulation program.
- State estimation
- Quadtrees are also used in the area of fractal image analysis
- Maximum disjoint sets

##### Octree Applications

- Level of detail rendering in 3D computer graphics
- Spatial indexing
- Nearest neighbor search
- Efficient collision detection in three dimensions
- View frustum culling
- Fast multipole method
- Unstructured grid
- Finite element analysis
- Sparse voxel octree
- State estimation
- Set estimation

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