Unlike Array and Linked List, which are linear data structures, tree is hierarchical (or non-linear) data structure.
- One reason to use trees might be because you want to store information that naturally forms a hierarchy. For example, the file system on a computer:
/ <-- root / \ ... home / \ ugrad course / / | \ ... cs101 cs112 cs113
- If we organize keys in form of a tree (with some ordering e.g., BST), we can search for a given key in moderate time (quicker than Linked List and slower than arrays). Self-balancing search trees like AVL and Red-Black trees guarantee an upper bound of O(Logn) for search.
- We can insert/delete keys in moderate time (quicker than Arrays and slower than Unordered Linked Lists). Self-balancing search trees like AVL and Red-Black trees guarantee an upper bound of O(Logn) for insertion/deletion.
- Like Linked Lists and unlike Arrays, Pointer implementation of trees don’t have an upper limit on number of nodes as nodes are linked using pointers.
Other Applications :
- Heap is a tree data structure which is implemented using arrays and used to implement priority queues.
- B-Tree and B+ Tree : They are used to implement indexing in databases.
- Syntax Tree: Used in Compilers.
- K-D Tree: A space partitioning tree used to organize points in K dimensional space.
- Trie : Used to implement dictionaries with prefix lookup.
- Suffix Tree : For quick pattern searching in a fixed text.
As per Wikipedia, following are the common uses of tree.
1. Manipulate hierarchical data.
2. Make information easy to search (see tree traversal).
3. Manipulate sorted lists of data.
4. As a workflow for compositing digital images for visual effects.
5. Router algorithms
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- Complexity of different operations in Binary tree, Binary Search Tree and AVL tree
- Given level order traversal of a Binary Tree, check if the Tree is a Min-Heap
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- Convert an arbitrary Binary Tree to a tree that holds Children Sum Property
- Convert a given Binary tree to a tree that holds Logical OR property
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- Convert a given Binary tree to a tree that holds Logical AND property
- Check if a given Binary Tree is height balanced like a Red-Black Tree
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