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

The height of a balanced binary tree is determined by the property that the heights of the left and right subtrees must differ by no more than one. This characteristic is essential to maintaining balance within the tree and ensures that operations such as insertion, deletion, and searching can be performed efficiently.

In a balanced binary tree, this restriction helps to keep the tree as flat as possible, which is important for maintaining optimal performance across various operations. When the difference in height between the left and right subtrees is controlled, it prevents the tree from degenerating into a structure akin to a linked list, which would lead to poor performance (O(n) time complexity for operations in the worst case).

Overall, the definition of a balanced binary tree hinges on that specific condition of height difference, which is a hallmark of balanced tree structures such as AVL trees or Red-Black trees. This structural property ensures that the depth of the tree remains logarithmic in relation to the number of nodes, thereby supporting efficient data retrieval and manipulation.