Binary Search Trees

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Binary Search Trees

• Chapter 9

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Binary Search Trees

• A binary tree that is built such that
• every node's left subtree has key values less
  than the node's key value, and the nodes right
  subtree has key values greater than the nodes
  key value. A new node is added as a leaf.
• Above is NISTs (National Institute of Standards
  and Technology) definition
• We will add a constraint that the key will be
  unique.

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Binary Search Tree

• We will define the operations of binary search
  tree.
• We will use the simple binary tree that we
  designed earlier.
• The semantics of the operation are loosely based
  on Chapter 9s discussion on binary search trees.

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BST server side
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BST Client side
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Insert, and Search methods

• Insert (key, element)
• (Non_empty tree) Locate position (cursor) to
  insert. This will be parent of new node
  (key-element pair) to be inserted.
• 1.1 If key lt cursors key, insert as left leaf
• 1.2 Else if key gtcursors key, insert as right
  leaf
• 1.3 Else replace value of element with new value.
• (Empty tree) Create a tree with node with an item
  made up of key,element.

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Search(key)

• Locate the node with the given key.
• 1.1 If one exists return element of the node
• 1.2 Else return null.
• Both insert and search method use a utility
  method
• boolean locate(Key k, Btree b)
• That return true, if key is found and sets a
  cursor to the location where it was found.
• Returns false if not found, cursor has the
  location of parent for insert.

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Object remove(Comparable key)

• Empty case throw exception
• NonEmpty case locate the key in the tree
• found key at cursor
• 2.1 Left sub tree of cursor empty set the
  cursors parents left or right sub tree with
  cursors right sub tree.
• 2.2 Left sub tree nonempty right sub tree
  empty or non empty
• 2.2.1 find the rightmost node
• 2.2.2 replace cursor data with
  rightmost nodes data
• 2.2.3 remove rightmost node
• return Item found at the node
• Not found Throw exception

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Examples

• Lets look at some representative examples using
  the animation tool.

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