Binary Search Tree

• We’ve looked at a couple different search strategies so far:

  • Linked structures allowed easy insertion/deletion, but the best method for searching a linked list was sequential search
  • Binary search was fast, but required contiguous storage, making it expensive to modify the database

• Binary trees can be used to solve the problem

  • We can use the left/right ordering of subtrees to order our data (as required for binary search in contiguous storage)
  • We can use the linked structure to allow efficient updates

• Definition (from Aho, Hopcroft, Ullman): a binary search tree is a binary tree in which every node x satisfies the conditions:

  • Every node in the left subtree of x has a key < the key of x
  • Every node in the right subtree of x has a key > the key of x

• THE DEFINITION IN THE BOOK IS INCORRECT! Here’s a counterexample (not a binary search tree, but it meets book’s definition):

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