Trees in Data Structure — Structure, Operations & Applications
A Tree is a hierarchical, non-linear data structure consisting of nodes connected by edges, with one node designated as the root. Every node except the root has exactly one parent, and there are no cycles.
Key Terminology
- Root: the topmost node of the tree.
- Parent/Child: a node directly connected to another node below it.
- Leaf: a node with no children.
- Height: the length of the longest path from a node to a leaf.
- Depth: the length of the path from the root to a given node.
Common Operations
| Operation | Description |
|---|---|
| Insertion | Add a new node at the appropriate position. |
| Deletion | Remove a node while maintaining the tree structure. |
| Traversal | Visit all nodes (Inorder, Preorder, Postorder, Level Order). |
| Search | Find whether a value exists in the tree. |
Types of Trees
- Binary Tree — each node has at most two children.
- Binary Search Tree — a binary tree with an ordering property for fast search.
- AVL Tree / Red-Black Tree — self-balancing binary search trees.
- Heap — a complete binary tree satisfying the heap property.
- Trie — a tree specialized for storing strings.
Applications
- File system hierarchies (folders and files).
- Database indexing (B-Trees, B+ Trees).
- Parsing expressions in compilers (Abstract Syntax Trees).
- Decision-making models like decision trees in machine learning.
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