Algorithms for Beginners: A Friendly Deep Dive

The word algorithm can sound intimidating when you're just getting started in programming[1]. It feels like one of those computer science terms reserved for mathematicians or developers with decades of experience. But here's the truth: algorithms are simply step‑by‑step instructions for solving problems[2]. You already use algorithms in your daily life — following a recipe, tying your shoes, or deciding the fastest route to work. Coding algorithms is just about learning how to formalize those steps so computers can follow them.

In this long‑form guide, we're going to break down algorithms in a way that feels approachable. We'll lean on one of the most influential programming languages ever created — Lisp — to show how simple ideas like lists, conditions, and functions form the foundation of algorithmic thinking. Lisp is elegant because it treats code as data and data as code[3], which makes it a perfect playground for exploring algorithms. Don't worry if you've never touched Lisp before. We'll start from scratch, explain every concept in plain English, and walk through examples step by step.

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What Is an Algorithm?

At its core, an algorithm is[4]:

• A sequence of steps that transform input into output.
• Deterministic, meaning that given the same input, it will always produce the same output.
• Finite, meaning it eventually completes.

Think of sorting a list of names alphabetically. Whether you use bubble sort, quicksort, or even manually shuffle cards on your desk, you are applying an algorithm.

Algorithms can be expressed in natural language, flowcharts, pseudocode, or in programming languages[5]. Lisp happens to be one of the earliest languages where developers started exploring algorithms deeply, and many modern programming concepts trace their lineage back to it[6].

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Why Lisp Helps Beginners Understand Algorithms

Lisp (short for LISt Processing) was developed by John McCarthy at MIT in 1958[7], making it one of the oldest programming languages still in use today. Despite its age, it remains one of the most elegant tools for thinking about algorithms because[8]:

• Uniform syntax: Everything in Lisp looks the same — parenthesized expressions[9]. This uniformity reduces distractions and makes you focus on how the algorithm works.
• Code as data: Lisp treats programs as lists, which can also be manipulated like any other data[10]. This unlocks powerful ways of reasoning about algorithms.
• Powerful abstractions: Functions, conditions, and recursion are built‑in and easy to experiment with[11].

Let's use Lisp as our lens while exploring algorithm basics.

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Setting Up Your Playground

Before diving into algorithms, you need an environment where you can run Lisp code. For Common Lisp, one of the most popular implementations is SBCL (Steel Bank Common Lisp)[12].

Installing SBCL

• Linux (Ubuntu/Debian):

  sudo apt install sbcl rlwrap
  rlwrap sbcl

• macOS (Homebrew):

  brew install sbcl rlwrap
  rlwrap sbcl

• Windows: Download the installer from the SBCL official website[13], run it, and then launch sbcl from the terminal.

Adding rlwrap gives you a nicer command‑line experience with arrow keys working as expected[14].

Once installed, you'll enter the Lisp REPL (Read‑Eval‑Print‑Loop). Type (+ 1 2) and press Enter — congratulations, you've just run your first algorithm: addition.

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The REPL and Symbolic Expressions

In Lisp, everything is an expression[15]. That means every piece of code has a value, and the interpreter continuously evaluates these values in the REPL.

• Numbers: 42 evaluates to 42.
• Strings: "hello" evaluates to "hello".
• Symbols: These represent variables or function names.
• Lists: The heart of Lisp, written as (<function> <arg1> <arg2> ...)[16].

For example:

(+ 3 5)   ; adds 3 and 5
(* 2 4)   ; multiplies 2 and 4

This regular structure makes Lisp an excellent tool for learning algorithms. There's no difference between built‑in operators and user‑defined functions — everything is just a list[17].

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Algorithm Building Blocks

When writing algorithms, you need a few essential tools[18]:

1. Variables

Variables store intermediate results.

(let ((x 10)
      (y 20))
  (+ x y)) ; returns 30

2. Conditionals

Algorithms often require branching logic[19].

(defun sign-of (n)
  (cond ((< n 0) "negative")
        ((= n 0) "zero")
        (t "positive")))

3. Recursion

Many classic algorithms are recursive[20]. For example, factorial:

(defun factorial (n)
  (if (= n 0)
      1
      (* n (factorial (- n 1)))))

This demonstrates breaking a problem into smaller subproblems — the essence of algorithm design[21].

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Classic Beginner Algorithms in Lisp

Let's walk through a few common algorithms using Lisp.

1. Searching in a List

Linear search checks each element until it finds a match[22].

(defun linear-search (item list)
  (cond ((null list) nil)
        ((equal item (car list)) t)
        (t (linear-search item (cdr list)))))

• car gives the first element[23].
• cdr gives the rest of the list[24].

2. Finding Maximum in a List

(defun max-in-list (lst)
  (if (null (cdr lst))
      (car lst)
      (let ((max-rest (max-in-list (cdr lst))))
        (if (> (car lst) max-rest)
            (car lst)
            max-rest))))

3. Sorting: Insertion Sort

Insertion sort is a great beginner algorithm with O(n²) time complexity in the worst case[25].

(defun insert (x sorted-list)
  (if (or (null sorted-list) (<= x (car sorted-list)))
      (cons x sorted-list)
      (cons (car sorted-list) (insert x (cdr sorted-list)))))

(defun insertion-sort (lst)
  (if (null lst)
      nil
      (insert (car lst) (insertion-sort (cdr lst)))))

Try (insertion-sort '(5 2 9 1 6)) — you'll see (1 2 5 6 9).

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Understanding Algorithm Efficiency

Algorithms aren't just about correctness; efficiency matters[26]. Two main dimensions:

• Time complexity: How long an algorithm takes as input size grows[27].
• Space complexity: How much memory it uses[28].

For example:

• Linear search is O(n) time[29].
• Insertion sort is O(n²) time in the worst case and O(n) in the best case[30].

Even in Lisp, you can reason about performance by analyzing how many recursive calls are made or how many comparisons happen[31].

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Debugging and Experimenting

When learning algorithms, mistakes are part of the journey[32]. Lisp's REPL is forgiving — if you enter something invalid, it shows you an error and lets you recover. This rapid feedback loop is invaluable for experimenting with algorithms. Don't be afraid to try variations, break them, and fix them.

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Beyond the Basics

Once you're comfortable with simple algorithms, Lisp's macro system opens the door to meta‑programming[33]. You can write algorithms that generate other algorithms. For beginners, just appreciating that possibility is enough motivation to keep exploring.

For example, you could write a macro that automatically creates search functions optimized for different data structures[34]. This shows how algorithms aren't just fixed recipes — they can evolve and adapt.

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Key Takeaways

• Algorithms are just step‑by‑step procedures for solving problems[35].
• Lisp is a fantastic environment for exploring algorithms because of its simplicity and expressive power[36].
• Start with basic building blocks (variables, conditions, recursion) and then move to classic algorithms like search and sorting[37].
• Efficiency matters: think about time and space complexity[38].
• The REPL makes experimenting fun and interactive[39].

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Conclusion

If algorithms once felt like a scary word, I hope this guide has shown you they're simply structured problem‑solving steps. Lisp makes it easy to see the elegance behind algorithms, from simple conditionals to recursive sorting. The best way to learn is to practice — open your Lisp REPL, try out the examples, tweak them, and invent your own.

Algorithms are the language of problem‑solving in computer science, and as you get comfortable with them, you'll unlock the ability to tackle more complex challenges[40]. Think of this as your first step into a lifelong journey of learning how to think like a computer scientist.

If you enjoyed this guide, consider subscribing to my newsletter where I share more deep‑dive tutorials, coding experiments, and approachable explanations of computer science concepts.

Happy coding!

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References

[1] Khan Academy. "What is an algorithm and why should you care?" https://www.khanacademy.org/computing/computer-science/algorithms/

[2] Cormen, T. H., Leiserson, C. E., Rivest, R. L., & Stein, C. "Introduction to Algorithms, 4th Edition." MIT Press, 2022.

[3] Wikipedia. "Lisp (programming language) - Homoiconicity." https://en.wikipedia.org/wiki/Lisp_(programming_language)

[4] Knuth, Donald. "The Art of Computer Programming, Volume 1: Fundamental Algorithms." Addison-Wesley, 1997.

[5] Sedgewick, R. & Wayne, K. "Algorithms, 4th Edition." Addison-Wesley, 2011.

[6] McCarthy, John. "Recursive functions of symbolic expressions and their computation by machine, Part I." Communications of the ACM 3(4), 1960.

[7] Computer History Museum. "John McCarthy and the birth of Lisp." https://www.computerhistory.org/

[8] Graham, Paul. "The Roots of Lisp." http://www.paulgraham.com/rootsoflisp.html

[9] Steele, Guy L. "Common Lisp the Language, 2nd Edition." Digital Press, 1990.

[10] Abelson, H. & Sussman, G. J. "Structure and Interpretation of Computer Programs." MIT Press, 1996.

[11] Touretzky, David S. "Common Lisp: A Gentle Introduction to Symbolic Computation." Benjamin/Cummings, 1990.

[12] Steel Bank Common Lisp. "SBCL Official Documentation." http://www.sbcl.org/

[13] Steel Bank Common Lisp. "Download SBCL." http://www.sbcl.org/platform-table.html

[14] GNU Readline. "rlwrap - readline wrapper." https://github.com/hanslub42/rlwrap

[15] Seibel, Peter. "Practical Common Lisp." Apress, 2005.

[16] Wikipedia. "S-expression." https://en.wikipedia.org/wiki/S-expression

[17] McCarthy, John. "History of Lisp." ACM SIGPLAN Notices, 1978.

[18] Skiena, Steven S. "The Algorithm Design Manual, 3rd Edition." Springer, 2020.

[19] Dijkstra, Edsger W. "Notes on Structured Programming." 1970.

[20] Roberts, Eric S. "Thinking Recursively." John Wiley & Sons, 1986.

[21] Wirth, Niklaus. "Algorithms + Data Structures = Programs." Prentice Hall, 1976.

[22] Knuth, Donald. "The Art of Computer Programming, Volume 3: Sorting and Searching." Addison-Wesley, 1998.

[23] Wikipedia. "CAR and CDR." https://en.wikipedia.org/wiki/CAR_and_CDR

[24] Common Lisp HyperSpec. "Functions CAR, CDR." http://www.lispworks.com/documentation/HyperSpec/

[25] GeeksforGeeks. "Time Complexity of Insertion Sort." https://www.geeksforgeeks.org/insertion-sort/

[26] Big-O Cheat Sheet. "Know Thy Complexities!" https://www.bigocheatsheet.com/

[27] Sipser, Michael. "Introduction to the Theory of Computation, 3rd Edition." Cengage Learning, 2012.

[28] Aho, A. V., Hopcroft, J. E., & Ullman, J. D. "Data Structures and Algorithms." Addison-Wesley, 1983.

[29] NIST. "Dictionary of Algorithms and Data Structures - Linear Search." https://xlinux.nist.gov/dads/HTML/linearsearch.html

[30] NVIDIA Developer Blog. "Insertion Sort Explained." https://developer.nvidia.com/blog/insertion-sort-explained/

[31] Norvig, Peter. "Paradigms of Artificial Intelligence Programming: Case Studies in Common Lisp." Morgan Kaufmann, 1992.

[32] Petzold, Charles. "Code: The Hidden Language of Computer Hardware and Software." Microsoft Press, 2000.

[33] Graham, Paul. "On Lisp: Advanced Techniques for Common Lisp." Prentice Hall, 1993.

[34] Queinnec, Christian. "Lisp in Small Pieces." Cambridge University Press, 1996.

[35] Heineman, G. T., Pollice, G., & Selkow, S. "Algorithms in a Nutshell, 2nd Edition." O'Reilly Media, 2016.

[36] Felleisen, M., Findler, R. B., Flatt, M., & Krishnamurthi, S. "How to Design Programs, 2nd Edition." MIT Press, 2018.

[37] Bhargava, Aditya. "Grokking Algorithms." Manning Publications, 2016.

[38] Roughgarden, Tim. "Algorithms Illuminated." Soundlikeyourself Publishing, 2017-2020.

[39] Seibel, Peter. "Coders at Work: Reflections on the Craft of Programming." Apress, 2009.

[40] Pólya, George. "How to Solve It: A New Aspect of Mathematical Method." Princeton University Press, 1945.