Data Structures and Algorithms in Java[1].pdf - Fulvio Frisone

Analysis of Binary Tree Searching
The analysis of the worst-case running time of searching in a binary search tree T
is simple. Algorithm TreeSearch is recursive and executes a constant number
of primitive operations for each recursive call. Each recursive call of
TreeSearch is made on a child of the previous node. That is, TreeSearch is
called on the nodes of a path of T that starts at the root and goes down one level at
a time. Thus, the number of such nodes is bounded by h + 1, where h is the height
of T. In other words, since we spend O(1) time per node encountered in the
search, method find on dictionary D runs in O(h) time, where h is the height of
the binary search tree T used to implement D. (See Figure 10.2.)
Figure 10.2: Illustrating the running time of
searching in a binary search tree. The figure uses
standard visualization shortcuts of viewing a binary
search tree as a big triangle and a path from the root
as a zig-zag line.
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