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 :
- Store hierarchical data, like folder structure, organization structure, XML/HTML data.
- Binary Search Tree is a tree that allows fast search, insert, delete on a sorted data. It also allows finding closest item
- 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.
- Spanning Trees and shortest path trees are used in routers and bridges respectively in computer networks
- As a workflow for compositing digital images for visual effects.
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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 AND property
- Convert a given Binary tree to a tree that holds Logical OR property
- Check if a given Binary Tree is height balanced like a Red-Black Tree
- Construct XOR tree by Given leaf nodes of Perfect Binary Tree