Binary Search Trees

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Binary Search Trees
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What are they?

• A Binary Search Tree (BST) is a special case of
  the generic binary tree.
• A Binary Search Tree is kept in sorted order,
  so that a value can be quickly found in the tree.
• An in-order traversal of the BST will return the
  elements in sorted order.

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Sorted Data

• A BST has to comply with the following rule All
  elements in the left subtree of any node in the
  tree must be less than that node, and all
  elements in the right subtree must be greater.
• In order to make this judgment, the items in a
  BST must be Comparable.

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What about duplicates?

• You can decide that your BST will allow
  duplicates, but if you do, it complicates
  matters. You must decide to consistently treat
  duplicates as either greater than, or less than,
  their duplicate value.
• You must also come up with a strategy for
  deleting duplicate values. Do you delete them
  all? Only the first?

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BST Operations

• public Comparable add(Comparable c)
• public Comparable remove(Comparable c)
• public boolean contains(Comparable c)
• public Comparable getEntry(Comparable c)
• public boolean isEmpty()
• public Iterator iterator()

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Efficiency of Operations

• When a tree is balanced, finding a node takes
  O(log n) time. However, at the worst case of an
  unbalanced tree, it can take O(n) time.
• When a tree is static, you can get good
  performance, but dynamic additions and removals
  can mess with a well balanced tree.
• Tips never add nodes in a sorted order. The
  ideal way is to add from the middle, but a random
  ordering is actually a pretty good way to get a
  tree set up.