Western Governors University (WGU) ICSC2100 C949 Data Structures and Algorithms I Practice Exam

The average case complexity for tree traversal is O(n) because in a tree, every node must be visited exactly once to ensure that all data is processed or recorded. Whether performing an in-order, pre-order, or post-order traversal, each of the n nodes is accessed, leading to a linear relationship between the number of nodes and the amount of work done.

In tree data structures, the traversal process effectively involves checking each node for potential processing, like printing the value or applying a function. Since this access does not depend on the arrangement of nodes, the complexity remains linear regardless of the structure of the tree (e.g., balanced vs. unbalanced).

In contrast, complexities such as O(n^2), O(n log n), or O(log n) would not accurately describe the traversal process. O(n^2) suggests that the time would grow quadratically concerning the number of nodes, which does not apply here. O(n log n) is typically associated with procedures that involve sorting or more complex divide-and-conquer algorithms, while O(log n) usually pertains to operations like search or insert in balanced binary search trees, where you do not visit every node. Thus, O(n) aptly captures the nature of tree traversal, reaffirming that