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Trees are hierarchical data structures with a root node and child nodes forming a hierarchy. Each node can have zero or more children, and there's exactly one path between any two nodes. Perfect for representing hierarchical relationships.
Hierarchical structure with parent-child relationships
Natural representation of hierarchical data
O(log n) search, insertion, and deletion in balanced trees
Each subtree is also a tree, enabling recursive algorithms
Various ways to visit nodes: inorder, preorder, postorder
Each node has at most two children
Left child < parent < right child
Self-balancing binary search tree
Balanced tree with color properties
Complete binary tree with heap property
Tree for storing strings efficiently
The topmost node with no parent
A node with no children
Maximum distance from root to any leaf
Distance from root to a specific node
Directory and file organization
B-trees for efficient database operations
Abstract syntax trees for compilers
Decision trees in AI and machine learning
| Operation | Average Case | Worst Case | Best Case |
|---|---|---|---|
| Search | O(log n) | O(n) | O(1) |
| Insertion | O(log n) | O(n) | O(1) |
| Deletion | O(log n) | O(n) | O(1) |
| Traversal | O(n) | O(n) | O(n) |
Space Complexity: O(n) where n is the number of nodes
Note: Balanced trees guarantee O(log n) for search, insertion, and deletion