Performance
With each test that fails to find a match at the probed position, the search is continued with one or other of the two sub-intervals, each at most half the size. More precisely, if the number of items, N, is odd then both sub-intervals will contain (N - 1)/2 elements, while if N is even then the two sub-intervals contain N/2 - 1 and N/2 elements.
If the original number of items is N then after the first iteration there will be at most N/2 items remaining, then at most N/4 items, at most N/8 items, and so on. In the worst case, when the value is not in the list, the algorithm must continue iterating until the span has been made empty; this will have taken at most ⌊log2(N) + 1⌋ iterations, where the ⌊ ⌋ notation denotes the floor function that rounds its argument down to an integer. This worst case analysis is tight: for any N there exists a query that takes exactly ⌊log2(N) + 1⌋ iterations. When compared to linear search, whose worst-case behaviour is N iterations, we see that binary search is substantially faster as N grows large. For example, to search a list of one million items takes as many as one million iterations with linear search, but never more than twenty iterations with binary search. However, a binary search can only be performed if the list is in sorted order.
Read more about this topic: Binary Search Algorithm
Famous quotes containing the word performance:
“What avails it that you are a Christian, if you are not purer than the heathen, if you deny yourself no more, if you are not more religious? I know of many systems of religion esteemed heathenish whose precepts fill the reader with shame, and provoke him to new endeavors, though it be to the performance of rites merely.”
—Henry David Thoreau (1817–1862)
“The child to be concerned about is the one who is actively unhappy, [in school].... In the long run, a child’s emotional development has a far greater impact on his life than his school performance or the curriculum’s richness, so it is wise to do everything possible to change a situation in which a child is suffering excessively.”
—Dorothy H. Cohen (20th century)
“The audience is the most revered member of the theater. Without an audience there is no theater. Every technique learned by the actor, every curtain, every flat on the stage, every careful analysis by the director, every coordinated scene, is for the enjoyment of the audience. They are our guests, our evaluators, and the last spoke in the wheel which can then begin to roll. They make the performance meaningful.”
—Viola Spolin (b. 1911)