Logarithmic complexity
This is the time complexity for cases where the search space of input size decreases (most commonly gets halved) each iteration. These algorithms are considered highly efficient, as the ratio of the number of operations to the size of the input decreases and tends to zero when n increases. An algorithm that must access all elements of its input cannot take logarithmic time, as the time taken for reading an input of size n is of the order of n.
Examples are Binary Search and other Binary Tree related algorithms. This is why Binary Search Tree (BST) are an efficient data structure