(Latest Revision: 05/09/2006)

Binary Search Trees

• binary trees, tables, and binary search trees.
  • ADT binary tree -- the ADT is determined by these properties
    • Organization -- A binary tree is empty, or consists of a root with a left subtree and a right subtree. The subtrees are binary trees.
    • Elements -- any given homogeneous set
    • Operations -- see the file BinaryTree.h in Carrano (pp. 520-522) for the list and the specs.
  • ADT table -- see the specs in Carrano, Chapter 11.
    • The table is important -- a basic data type for representing many kinds of databases.
    • We can use a simple array-based list or linked list to implement a table, but neither of these implementations will be very efficient if the number of items to be stored is large. (Discuss)
    • The table ADT can be implemented quite efficiently as a binary search tree. This explains the importance of binary search trees.
    • Organization of the Table data type -- There is a totally ordered set of keys. Each element of the table contains a data field. Each element is also assigned a unique key. Elements and the data in them are accessed by key value.
    • Elements of a Table data type -- data fields from any homogeneos set -- typically each element of the table is a certain kind of record which may contain many different information fields -- an employee record for example.
    • Major Table data type Operations
      • Insert by key value
      • Delete by key value
      • Retrieve by key value
      • Traverse Table
  • What is the reason for using BST's? -- they provide a hybrid of the array and linked list versions of a table in which all major operations can be implemented efficiently.
  • ADT binary search tree
    • Organization -- A binary search tree is a binary tree in which each node contains a key that is an element of a totally ordered set. For every node N in the tree, all keys in the left subtree of N are less than the key in N, and all keys in the right subtree of N are greater than the key in N.
    • Elements -- any given homogeneous set
    • Operations -- see the file BST2.h for the list and the specs.
      • Discuss implementation of retrieval.
      • Discuss implementation of insertion.
      • Discuss implementation of traversal.
      • Discuss implementation of deletion.
        • -- when the delete node is a leaf
        • -- when the delete node has one child
        • -- when the delete node has two children

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