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CSC 263H               Tutorial Outline for Week  3             Winter 2004
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Binary Search Trees  [section 3.1]
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You've all seen binary search trees in CSC148H/A58H before, but let's
review their definition and how to perform SEARCH, INSERT, and DELETE
operations on them.

Assume each node x of a binary tree has fields parent[x], left[x],
right[x], and key[x], and a tree T is given by a pointer to its root
(root[T]).

A binary tree is a BST if it satisfies the "BST property":
 [[Q: state the ordering property for BST's.]]

 [[Q: describe the SEARCH algorithm for BST's.]]

Running time?  In the worst-case, since the algorithm only examines nodes
in a single path from the root down to a leaf, it's O(height of the tree).

 [[Q: describe INSERT algorithm for BST's.]]

 [[Q: describe DELETE algorithm for BST's.]]

 [[Q: think of algorithms for operations MIN/MAX (find smallest/largest
      value in tree) and PRED/SUCC (find predecessor/successor of any value
      in tree).]]

Worst-case running time for all these operations is O(height(T)).
Unfortunately, height(T) can be as bad as n so in the worst-case, all
operations could take time Omega(n).