Why does sorting a list make binary search faster?

Sorting a list makes binary search faster because it establishes a predictable, ordered structure that allows the algorithm to eliminate large portions of the data during each step of the search.1

In an unsorted list, an algorithm must typically check each element individually to find a match, which is inefficient. However, when a list is sorted—such as in alphabetical or numerical order—binary search can compare the target value to the middle element of the current range. Because the list is ordered, the algorithm can determine whether the target must be in the first half or the second half of the remaining data, effectively cutting the search space in half with every iteration. This process is analogous to searching for a name in a telephone book; knowing the entries are alphabetized allows you to quickly narrow your search to a specific section rather than scanning every page.1