1.0022 Given sorted lists of 173, 3200, and 5600 names, what is the maximum number of comparisons will it take to find an name using a binary search? The average number of comparisons?

Using a binary search, the maximum number of searches is: (the ceiling of) log₂ n. Therefore:

For 173 elements: (ceiling of) log₂ 173 = (ceiling of) 7.43 = 8

For 3200 elements: (ceiling of) log₂ 3200 = (ceiling of) 11.64 = 12

For 5600 elements: (ceiling of) log₂ 5600 = (ceiling of) 12.45 = 13

The Average number of searches is (log₂ n) – 1. Therefore:

For 173 elements: (log₂ 173) – 1 = 7.43 – 1 = 6.43

For 3200 elements: (log₂ 3200) – 1 = 11.64 – 1 = 10.43

For 5600 elements: (log₂ 5600) – 1 = 12.45 – 1 = 11.45