Question

The average number of comparisons needed to find a target value in an n-element list using a sequential search is slightly higher than n/2. Now, we'll find an exact expression for this average.

A. Suppose the list has an odd number of items (say 15). At what position is the middle item? Using a sequential search, how many comparisons are required to find the middle item? Repeat this exercise with a few more odd numbers until you can answer the following: If there are n items in the list, and n is an odd number, write an expression for the number of comparisons required to find the middle item.

Answer 1

The position of the middle item in an odd number of items can be found by taking the floor division of n by 2. To find the number of comparisons required to find the middle item in a sequential search, we need to compare each item in the list until we find the middle item. The expression for the number of comparisons required to find the middle item in an odd number of items is floor(n/2).

Step-by-step explanation:

The position of the middle item in an odd number of items can be found by taking the floor division of n by 2. For example, if there are 15 items, the middle item is at position floor(15/2) = 7. To find the number of comparisons required to find the middle item in a sequential search, we need to compare each item in the list until we find the middle item. Since the middle item is at position floor(n/2), we need to make floor(n/2) comparisons to find it.

Therefore, the expression for the number of comparisons required to find the middle item in an odd number of items is floor(n/2).