Data Structures and Algorithms with Object-Oriented Design Patterns in C#
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Find Method

Program gif gives the code for the Find method of the BinarySearchTree class. The Find method takes as its argument any ComparableObject. The purpose of the method is to search the tree for an object which matches the argument. If a match is found, Find returns the matching object. Otherwise, Find returns null.

   program18661
Program: BinarySearchTree class Find and Min methods.

The recursive Find method starts its search at the root and descends one level in the tree for each recursive call. At each level at most one object comparison is made (line 7). The worst case running time for a search is

displaymath63919

where tex2html_wrap_inline63301 is the time to compare two objects and n is the number of internal nodes in the tree. The same asymptotic running time applies for both successful and unsuccessful searches.

The average running time for a successful search is tex2html_wrap_inline63925, where tex2html_wrap_inline63927 is the average depth of an internal node in a binary search tree. If tex2html_wrap_inline63929, the average time of a successful search is tex2html_wrap_inline59121.

The average running time for an unsuccessful search is tex2html_wrap_inline63933, where tex2html_wrap_inline63935 is the average depth of an external node in a binary search tree. If tex2html_wrap_inline63929, the average time of an unsuccessful search is tex2html_wrap_inline59121.


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