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

10.1.1 Searching
To perform operation find(k) in a dictionary D that is represented with a binary
search tree T, we view the tree T as a decision tree (recall Figure 7.10). In this case,
the question asked at each internal node v of T is whether the search key k is less
than, equal to, or greater than the key stored at node v, denoted with key(v). If the
answer is "smaller," then the search continues in the left subtree. If the answer is
"equal," then the search terminates successfully. If the answer is "greater," then the
search continues in the right subtree. Finally, if we reach an external node, then the
search terminates unsuccessfully. (See Figure 10.1.)
Figure 10.1: (a) A binary search tree T representing a
dictionary D with integer keys; (b) nodes of T visited
when executing operations find(76) (successful) and
find(25) (unsuccessful) on D. For simplicity, we show
keys but entry values.
We describe this approach in detail in Code Fragment 10.1. Given a search key k
and a node v of T, this method, TreeSearch, returns a node (position) w of the
subtree T(v) of T rooted at v, such that one of the following occurs:
• w is an internal node and w's entry has key equal to k.
• w is an external node representing k's proper place in an inorder traversal
of T(v), but k is not a key contained in T(v).
Thus, method find(k) can be performed by calling TreeSearch(k, T.root()).
Let w be the node of T returned by this call. If w is an internal node, then we return
w's entry; otherwise, we return null.
Code Fragment 10.1:
search tree.
Recursive search in a binary
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