Which of the Following Statements About the Binary Search of an Array

Multiple Choice

Which of the following statements about the binary search of an array in ascending order is false?

A) In the worst-case scenario, searching a sorted array of 1023 elements takes only 10 comparisons when using a xe "binary search:algorithm"bxe "efficiency of:binary search"inary search. The number 1023 (which is 2¹⁰ - 1) is divided by 2 only 10 times to get the value 0, which indicates that there are no more elements to test.
B) Dividing by 2 is equivalent to one comparison in the binary search algorithm. Thus, an array of 1,048,575 (2²⁰ - 1) elements takes a maximum of 20 comparisons to find the key, and an array of about one billion elements takes a maximum of 30 comparisons to find the key. This is a tremendous performance improvement over the xe "linear search algorithm"linear search.
C) For a one-billion-element array, the increase in performance of a binary search over a linear search is a difference between an average of five million comparisons for the linear search and a maximum of only 30 comparisons for the binary search!
D) The binary search's big O is xe "Big O notation"O(log n) , which also is known as logarithmic run time and pronounced as "order log n." Of course, this assumes the array is sorted, though, which could take substantial time.