Algorithms Analysis Practice Test

Searching in a balanced binary tree has a time complexity of O(log n) because the structure of the tree allows for efficient traversal based on the properties of binary search trees.

In a balanced binary tree, each node has up to two children, and the tree is structured in such a way that for any given node, the left child's value is less than the parent's value, and the right child's value is greater. This allows the search process to eliminate half of the remaining nodes at each step.

When searching for a value, you start at the root of the tree and compare the target value to the value of the current node. Depending on the result of that comparison, you either proceed to the left child (if the target is smaller) or the right child (if the target is larger). This halves the number of nodes you need to consider at each level of the tree, resulting in a logarithmic time complexity as you move down each level.

The height of a balanced binary tree is approximately log(n) relative to the number of nodes (n) in the tree. Consequently, the time it takes to search through the tree grows logarithmically as the number of nodes increases, making O(log n) the correct answer for the time complexity