Chapter 9.3, Problem 44E

a.

To determine

To calculate the steps taken to find the item with a sequential search

Answer to Problem 44E

In a sequential search 1000000 steps is taken

Explanation of Solution

Given information:

The ordered list is of one million items long

Sequential search algorithm uses the order of n steps. Thus in ordered list of one million items sequential search takes up 1,000,000 steps.

  ${\log }_n=1000000$

Therefore, in a sequential search 1000000 steps is taken

b.

To determine

To calculate the steps taken to find the item with a binary search

Answer to Problem 44E

In a binary search 20 steps is taken

Explanation of Solution

Given information:

The ordered list is of one million items long.

Binary search algorithm uses the order of ${\log }_{2}n$ steps

  $\begin{array}{l}{\log }_2\left(1000000\right)={\log }_2\left({10}^6\right)\\ {\log }_2\left(1000000\right)=6{\log }_2\left(10\right)\\ {\log }_2\left(1000000\right)=19.93\approx 20\text{ steps}\end{array}$

Therefore, in a binary search 20 steps is taken