What is a Tree?
A Tree is a hierarchical data structure composed of nodes connected by edges. It has a root node and zero or more subtrees, each with its own subtree structure.
Unlike arrays or linked lists, trees are non-linear, offering a more diversified set of use-cases.
Structure of a Tree
- Node: Basic unit containing data.
- Root: The topmost node.
- Child: Node directly connected to another node when moving away from the root.
- Parent: Node directly connected to another node when moving towards the root.
- Leaf: Node with no children.
Example:
10
/ \
5 15
/ \ / \
3 7 12 18
/ \ \
1 4 20
- Root Node:
10is the root of the tree. - Parent-Child Relationship: Node
5is a child of node10, and node10is a parent of node5. - Leaf Nodes:
1,4,7,12, and20are leaf nodes as they don’t have any children. - Internal Nodes: Nodes
10,5,15,3, and18are internal nodes as they have at least one child.
Types of Trees
- Binary Trees: Each node has at most two children.
- Binary Search Trees: Left child is smaller, and right child is greater than the parent node.
- Heaps: Specialized trees for priority queue implementations.
- B-Trees: Used in databases for indexing purposes.
- Trie: Used in dictionaries and text auto-completion.
Basic Operations
- Insertion: Add a node.
- Deletion: Remove a node.
- Traversal: Visit all nodes in a specific order.
- Search: Find the existence of data in the tree.
Importance of Trees
- Hierarchical Data: Model organizational structures or file systems.
- Efficient Search: Faster search algorithms, especially in balanced trees.
- Priority Queues: Used in algorithms like heap sort.
- Spell-Check: Trie trees are used in dictionary implementations.
- Networking: Trees are used in algorithms for network routing.
Summary
Trees are a fundamental data structure used in various applications, from databases and file systems to networking and natural language processing. They offer an effective way to organize, manage, and search complex data sets efficiently.