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

eplace
O(1)
root, parent
O(1)
children(v)
O(c v )
isInternal, isExternal, isRoot
O(1)
7.2 Tree Traversal Algorithms
In this section, we present algorithms for performing traversal computations on a tree
by accessing it through the tree ADT methods.
7.2.1 Depth and Height
Let v be a node of a tree T. The depth of v is the number of ancestors of v,
excluding v itself. For example, in the tree of Figure 7.2, the node storing
International has depth 2. Note that this definition implies that the depth of the root
of T is 0.
The depth of a node v can also be recursively defined as follows:
• If v is the root, then the depth of v is 0
• Otherwise, the depth of v is one plus the depth of the parent of v.
Based on this definition, we present a simple, recursive algorithm, depth, in Code
Fragment 7.2, for computing the depth of a node v in T. This method calls itself
recursively on the parent of v, and adds 1 to the value returned. A simple Java
implementation of this algorithm is shown in Code Fragment 7.3.
Code Fragment 7.2: Algorithm for computing the
depth of a node v in a tree T.
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