Question

An algorithm is approximately the same thing as a recipe, but some kinds of steps that would be allowed in a recipe are not allowed in an algorithm. Which steps in the following recipe would be allowed in an algorithm? Place 2 teaspoons of sugar in mixing bowl. Add 1 egg to mixing bowl. Add 1 cup of milk to mixing bowl. Add 1 ounce of rum, if you are not driving. Add vanilla extract to taste. Beat until smooth. Pour into a pretty glass. Sprinkle with nutmeg.

Short answer

Answer: Steps 1, 2, 3, and 8 are allowed in an algorithm because they have clear instructions and specific actions. However, step 8 would be improved by providing a specific quantity of nutmeg. Steps 4, 5, 6, and 7 are not allowed in an algorithm due to conditional statements, ambiguous instructions, and subjective criteria that do not meet the requirements for an algorithm step.

Step-by-step solution

Place 2 teaspoons of sugar in mixing bowl.

This step is allowed in an algorithm because it has clear instructions with specific measurements.

Add 1 egg to mixing bowl.

This step is allowed in an algorithm because it clearly states what to add to the mixing bowl.

Add 1 cup of milk to mixing bowl.

This step is allowed in an algorithm because it has a specific quantity and clear instructions.

Add 1 ounce of rum, if you are not driving.

This step is not allowed in an algorithm because it contains a conditional statement ("if you are not driving") that depends on individual circumstances, which an algorithm cannot account for.

Add vanilla extract to taste.

This step is not allowed in an algorithm because "to taste" is ambiguous and does not provide a specific quantity.

Beat until smooth.

This step is not allowed in an algorithm because "until smooth" is subjective and cannot be measured or determined in a clear, unambiguous manner.

Pour into a pretty glass.

This step is not allowed in an algorithm because "pretty glass" is subjective and does not provide clear, unambiguous instructions.

Sprinkle with nutmeg.

This step is allowed in an algorithm, although it doesn't specify the amount of nutmeg, this action does not impact the overall outcome. However, it is preferable to provide a specific quantity to make the step more algorithmic.

Key concepts

Conditional Statements

Conditional statements are a key part of many algorithms, and can be seen as the logic gates that direct the flow of actions based on certain conditions being met. In the recipe mentioned, the statement "if you are not driving" acts as a condition. However, when creating algorithms, especially in computing, conditional statements should be precise and based on quantifiable criteria to minimize ambiguity.
For example, in programming, a conditional statement might look like: "if (temperature > 100) then proceed to cooling".
These conditions rely on measurable data, contrary to the subjective condition of someone driving or not. Only clear, objective conditions can be effectively used in algorithms to ensure consistent outcomes.

Clear Instructions

Clear instructions are essential in algorithms to ensure that every step is carried out without confusion or error. In the given recipe, instructions like "add 1 egg to mixing bowl" embody clarity. They define what action needs to be taken and with what item, leaving no room for misinterpretation.
Clear instructions in algorithms not only tell you what to do, but also often include the tools or methods to use. For example, "stir mixture using a wooden spoon" provides additional clarity and eliminates ambiguity.

• Specify the exact actions needed.
• Identify the materials or tools to be used.
• Avoid vagueness such as "until done" or "to taste".

This makes algorithms reliable and consistent, as each step has an exact method to follow.

Specific Measurements

Specific measurements are critical in algorithms to maintain consistency and precision. Measurements like "2 teaspoons of sugar" in the recipe reflect this precision. Such specifics are vital in ensuring the desired outcome, as they eliminate guesswork.
In computing, this could refer to allocating a certain amount of memory, or specifying pixel dimensions in a graphic design application. Precise numbers and measurements are fundamental for the predictable execution of an algorithm.

• Use exact figures – be it grams, bytes, or units – instead of vague terms.
• Ensure compatibility with the rest of the algorithm (e.g., don't mix metric and imperial measures unless converted).
• Facilitate troubleshooting and optimization.

These practices ensure that algorithms behave consistently and achieve the intended results.

Subjectivity in Algorithms

Subjectivity in algorithms brings an element of unpredictability that can be problematic. Phrases from the recipe like "to taste" or "in a pretty glass" introduce elements that are open to individual interpretation. In algorithm design, such subjectivity leads to inconsistent outcomes and confusion.
Algorithms thrive on objectivity, where every outcome should result predictably from a given set of inputs. Subjective measures make it difficult to replicate results or debug issues effectively.
To remove subjectivity:

• Define clear, objective criteria for each action.
• Avoid opinions or personal preferences.
• Ensure all variables are quantifiable and standardized.

In educational or computing settings, reducing subjectivity in algorithms enhances reliability and accurately achieves the desired goals.