Why Binary Search Trees?

• Implementing a keyed list as an array (maintained in key-order):
  • Advantages:
    • Fast, O(log(Size)) worst case, binary search (faster than in a BST)
    • Fast, O(Size) worst case, in-order traversal (faster than in a BST)
  • Disadvantages:
    • Slow, O(Size) on average, insertion and deletion operations (moves required).
    • Static Memory Allocation -- size limits -- wasted space.
  
  
  
• Implementing a keyed list as a linked list (maintained in key-order):
  • Advantages:
    • Dynamic memory allocation -- uses only the memory needed (some extra for pointers).
    • Fast, O(Size) worst case, in-order traversal (faster than in a BST).
  • Disadvantages:
    • Slow, O(Size) on average, linear search. (Binary search is not an option.)
    • Slow, O(Size) average, insertion and deletion (linear search required).
  
  
  
• Implementing a keyed list as a BST with nodes and links:
  • Advantages:
    • Average O(log(Size)) binary search
    • Average O(log(Size)) insertion and deletion (find position with binary search -- no moves required).
    • Dynamic memory allocation -- uses only the memory needed (some extra for pointers).
    • Worst case O(Size), in-order, pre-order, and post-order traversals.
  • Disadvantages:
    • The worst case of search, insertion, and deletion is O(Size) -- (This happens when the tree has near-maximum height.)