Binary trees greatly reduce the number of comparison operations by creating branches from the collection, just like a binary tree would. This creates a tree on-the-fly, resulting in superior search performance. The significance is predictability, which allows us to build the tree and provides the options for what branch the algorithm can expect the result in.
A binary search, just like a jump search, requires the incoming slice to be ordered for it to work. Then the algorithm splits the array in half and chooses the side that will most likely contain the item. Once there are two collections, the behavior is very similar to that of a binary tree walk, as follows:
Again, given that the sorting effort trumps the algorithm's runtime complexity, it's that of the sorting algorithm that will be considered the outcome: O(n log n). However, we should also be interested in the real performance, if the collection is already sorted; it's significantly lower! First...
