Preamble

Using simple English sentences $($in the style of the example algorithms presented in class$),$ write algorithms for each of the following problems. Be sure to describe your algorithms accurately and explicitly. Assume that the person who reads your instructions does not understand the problem.

Type your algorithms into a word processor with your name and student number at the top. Use good indentation and spacing for readability.

Finally, remember the basic computer design rules and do not write code in any programming language!

Problem Statement

The problems:

A$.$ Many jam recipes measure the amount of fruit and white sugar required in cups, for example. Other recipes use kilograms of fruit and white sugar, for example. Give an algorithm that will determine which recipe uses more white sugar. $($Note: Pay attention to what type of sugar your recipe uses!$)$

B$.$ Suppose you have a calculator with no square root button, but you really need to calculate $\sqrt[\phantom{2}]{x}.$ What do you do$?$ You guess! $($Carefully$,$ of course.$)$

For example, suppose you need to calculate $\sqrt[\phantom{2}]{27}.$ You would first guess that $1$ is your answer. Definitely not close enough because $1^2$ is not close to $27.$ A second better guess is $\frac{1+\frac{27}{1}}{2},$ which is $14.$ Still not close enough because ${14}^2$ is not close to $27.$ A third better guess is $\frac{14+\frac{27}{14}}{2}=7\mathrm{.}9642$dots, which is still not close enough, but is closer! Keep going until your guess is accurate enough.

If a particular guess, $n,$ is not close enough to being an accurate square root of a number $x,$ we can produce a new and better guess by calculating $\frac{n+\frac{x}{n}}{2}.$ For your algorithm, "accurate enough" means accurate to three decimal places.

C$.$ Write an algorithm to determine whether it is cheaper for your instructor to purchase a Translink monthly pass for the month of February or to use Stored Value instead. $($Assume your instructor arrives immediately before his first class at Langara and returns to New Westminster immediately after his last class each day.$)$ Think about how you would generalize your algorithm so it will work for other instructors and other schedules and situations, too.