Final answer:
A problem is likely to have a log N runtime if it uses an algorithm that divides the problem in half at every step, such as binary search or operations with a balanced binary search tree. Logarithmic complexity is efficient, particularly for large datasets, as the operations grow slowly relative to the dataset size.
Step-by-step explanation:
When you encounter a log N runtime, it typically involves an algorithm that divides the problem in half with each step. This is common in algorithms like binary search or in data structures like binary trees. For instance, in a binary search where you are looking for a specific value within a sorted list, you can discard half of the list in each step based on whether the value you are looking for is greater or less than the item in the middle of the list.
Another example is a balanced binary search tree (BST), where operations such as insertion, deletion, and lookup can all be done in O(log N) time because they only need to traverse the height of the tree, which is proportional to the logarithm of the number of elements in the tree.
Therefore, logarithmic complexity indicates that an algorithm is very efficient, especially for large datasets, because the number of operations needed grows very slowly compared to the size of the input data set.