Related questions with answers

Respond using verbal or written explanations. Is it possible to find a set's complement if a universal set is not given? Explain your answer.

The following is Euclid’s 2,300-year-old algorithm for finding the greatest common divisor of two positive integers I and J. Step Operation: 1. Get two positive integers as input; call the larger value I and the smaller value J. 2. Divide I by J, and call the remainder R. 3. If R is not 0, then reset I to the value of J, reset J to the value of R, and go back to Step 2. 4. Print out the answer, which is the value of J. 5. Stop. a. Go through this algorithm using the input values 20 and 32. After each step of the algorithm is completed, give the values of I, J, and R. Determine the final output of the algorithm. b. Does the algorithm work correctly when the two inputs are 0 and 32? Describe exactly what happens, and modify the algorithm so that it gives an appropriate error message.

Add or subtract as indicated. Write all answers in lowest terms. $\frac{p^{3}}{p^{2}-p q+q^{2}}+\frac{q^{3}}{p^{2}-p q+q^{2}}$

Question

Compare the two solutions to the shampooing algorithm shown. Which do you think is a better general-purpose solution? Why? (Hint: What if you wanted to wash your hair 1,000 times?)
$\begin{array} {ll} \text{Step} & \text{Operation}\\ \text{1} & \text{Wet your hair}\\ \text{2} & \text{Set the value of WashCount to 0}\\ \text{3} & \text{Repeat Steps 4 through 6 until the value of WashCount equals 2}\\ \text{4} & \text{Lather your hair}\\ \text{5} & \text{Rinse your hair} & \text{ }\\ \text{6} & \text{Add 1 to the value of WashCount}\\ \text{7} & \text{Stop, you have finished shampooing your hair}\\ \end{array}$ $\begin{array}{ll}{\text { Step }} & {\text { Operation }} \\ {1} & {\text { Wet your hair }} \\ {2} & {\text { Lather your hair }} \\ {3} & {\text { Rinse your hair }} \\ {4} & {\text { Lather your hair }} \\ {5} & {\text { Rinse your hair }} \\ {6} & {\text { Stop, your have finished shampooing your hair }}\end{array}$

Solution

Verified

Step 1

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The algorithm from Fig 1.3 contains an iterative operation (repeating a number of steps) and a value to keep track of how many times the loop should be performed.

The Fig 1.4 algorithm simply has steps which look exactly the same and take extra space while not providing enough new information. One would only have to read the 3 steps and count how many times the same steps are written which is what $WashCount$ is for in the second algorithm.

The first one is more efficient and elegant since it would look the same regardless of how many times the loop has to be performed. Only the value of $WashCount$ would change.