Algorithms

Key Concepts

Natural Language	Spoken and written communication developed and evolved over time, and used by humans
Ambiguity	Imprecise nature of a construct. For Natural Language, how individuals interpret the meaning or intent of a word or phrase
Algorithm	In the context of Computer Science, describe the solution to a Problem in a form that minimizes the Ambiguity of Natural Language

Introduction

Computers function on sets of ordered steps, organized in an efficient and effective sequence to reach some solution. Changing the order would likely result with a different solution.

These groups of steps make up an Algorithm that completes a Cycle.

Everyday College Course Example

Algorithm Example

They typical college class flow can be described as the following Algorithm:

1. Instructor lectures on new material.
2. Students complete quiz to see they understand.
3. Instructor provide feedback on commonly missed questions.
4. Students complete assignment to put their understanding to the test.
5. Instructor provides feedback on assignment to ensure students understanding.

This cycle repeats for each new chapter or topic.

Algorithms can be written at different levels of detail (Abstraction Levels) depending on the audience or purpose of the Algorithm.

Algorithms

An Algorithm is a common term associated with technology today. An example of an Algorithm is using a specific type of software that takes in historic viewing data, applies statistical analysis to that data, and then turns out recommendations for the next movie or series to binge.

In general, algorithms are a sequence of steps that solve a problem with a reliable result. So the above movie recommendation algorithm solves the problem of location streaming media you might like, based on previous viewing history.

Algorithms in Computer Organization

We will use Algorithms to understand how common analog procedures are executed in the digital world. If we were to add two multi-digit numbers, we can likely complete the task without much step-by-step thought. However, if we were to explain it in using digital logic and assembly language, we would need to think of how to use simple math operations as part of an Algorithm.

Quick Thought Experiment

Think about how you would teach a first grade student how to add two multi-digit numbers:

First, think of the steps to add 1234 and 4321 (note, there are no carries).

Next, think of the steps to add 1234 and 9999 (note, there are carries).

Finally, think of the steps to describe how to add any set of two multi-digit numbers (there may or may not be carries).

In addition, we will also create algorithms that describe at a higher level of abstraction, what our assembly program will do. Sketching out or prototyping code before writing it will help:

• Identify the high-level section of code needed to solve the problem
• Create a program without an actual programming language in mind
  • You are free to design the algorithm without language constraints
  • The algorithm may help decide the best language to use for the final program
  • Other software engineers can understand the algorithm, even if they don't know the final programming language
• Help with coding the actual program, as you can implement parts of the algorithm, test the part, and repeat

Creating an Algorithm

To create an algorithm, we typically start with the problem or Problem Statement. A problem statement will capture an issue that, hopefully, can be solved by computer and some clever code. It will be written in the author's native language

Natural Language

Spoken, written, and signed communication that evolved along with humans. The natural languages we use today exist by common use and repetition, without formal planning or design.

Natural Language

This means it will likely include Ambiguity that is understandable to most people that are fluent in the native language.

Ambiguity

Words, phrases, and other communication elements that are not strictly defined. Information having ambiguity has some level of vagueness, and can be interpreted differently by each consumer.

Ambiguity

However, software engineers must remove all ambiguity somewhere between the problem statement and the final program, as computers do not handle any ambiguity. In addition, any Natural language terms must be converted to generally-understood words/phrases.

We are going to removal all ambiguity and natural language when converting the problem statement to an algorithm.

TIP

Learn how trivial bit of ambiguity caused the Mars Climate Orbiter that burned up in Mars' atmosphere Mars Climate Orbiter 1998

An Algorithm to Create Algorithms

1. Understand the Problem Statement
   • This may require research or asking questions of the author
   • Note the Ambiguities in the Problem Statement. Clarify the intended meaning, even if fairly certain you understand (if you think this is unnecessary, please review the Mars Climate Orbiter article)
2. Declare any given situations
   • Elements that are already available
   • Options/capabilities that already exist
3. Write a sequence of steps that would solve the problem
   • Write english words that describe each step
   • Do not give in to the temptation of writing steps the look like code
   • In most cases each step will include a primary noun and verb/action
   • Each step is a single action that stands on its own

Example Algorithm

Algorithm to Make a Bagel

Given

1. Toaster is working
2. User knows how to use a knife safely
3. User understands basic kitchen sanitary practices

Algorithm

1. Open bagel container
2. Remove 1 bagel
3. Place bagel on cutting board
4. Use bread knife to slice bagel into to section along its circular axis
5. Place bagel halves in separate toaster slots
6. Set toaster to medium darkness setting
7. Press toaster slide handle down until it locks
8. Verify heating elements emit heat
9. Remove cream cheese container from refrigerator
10. Obtain butter knife
11. Remove lid from cream cheese tub
12. Wait for toaster to complete cycle
13. Use hand protection to extract each bagel half from toaster and place on flat surface
14. Swipe knife across surface of cream cheese, gathering approximately 1 ounce on the knife
15. Spread gathered cream cheese into toasted surface of 1 bagel half
16. Swipe knife across surface of cream cheese, gathering approximately 1 ounce on the knife
17. Spread gathered cream cheese into toasted surface of other bagel half
18. Return cream cheese tub to refrigerator
19. Place bagel haves on plate
20. Serve bagel halves

Conclusion

A general algorithm describes a procedure without using ambiguous terminology. It orders steps to successfully complete a procedure consistently.

In Computer Science and algorithm is a high-level description of a solution that will be written in a programming language. The nouns used in this type of algorithm are likely names of data or functions. The verbs are commands or instructions that modify the data or execute functions