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

The removal complexity in a binary tree, particularly for a balanced binary search tree (BST), is O(log n). This is because, in a balanced binary search tree, the height of the tree is maintained logarithmic relative to the number of nodes, allowing for efficient searching, inserting, and deleting operations.

When you remove a node from a binary search tree, you first need to locate that node. This lookup process involves traversing the tree from the root to the desired node, taking O(log n) time in the case of a balanced tree. After finding the node, if it has zero or one child, it can be removed directly. If it has two children, a common approach is to find the successor or predecessor (the smallest node in the right subtree or the largest in the left subtree) to replace the node being removed, which also requires traversal but remains within O(log n) complexity.

In summary, for balanced binary trees, the overall removal process remains efficient due to the logarithmic height, thus maintaining a removal complexity of O(log n).