Binary Tree Comparisons

Comparison Chart

Feature	Binary Tree	AVL Tree	Red-Black Tree
Structure	Nodes have 0 or 2 children	Self-balancing, height difference between subtrees <= 1	Self-balancing, specific color properties to maintain balance
Data Organization	Can hold any type of data	Usually holds comparable data for efficient search	Can hold any type of data
Search Performance	O(n) in worst case, O(log n) on average	O(log n) guaranteed	O(log n) guaranteed
Insertion/Deletion Performance	O(n) in worst case, O(log n) on average	O(log n) guaranteed, more complex operations	O(log n) guaranteed, simpler operations than AVL
Memory Usage	Minimum, only 2 pointers per node	Slightly higher than binary tree, stores balance factor	Slightly higher than binary tree, stores color information
Applications	Simple data structures, expression trees	Efficient search and sorting, databases	General purpose, good balance between performance and complexity
Pros	Simple to implement, efficient for small datasets	Fast search and guaranteed balance	Faster insertions than AVL, simpler operations
Cons	Can become unbalanced, leading to poor performance	More complex to implement than binary tree	Not as strictly balanced as AVL trees, potentially impacting search performance in rare cases