computer science

Spaghetti sort

Spaghetti sort is a computer science topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Spaghetti sort rather than just read about it. In short: Spaghetti sort is a linear-time, analog algorithm for sorting a sequence of items, introduced by A. K.

Key takeaways

Spaghetti sort belongs to computer science; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect Spaghetti sort to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of Spaghetti sort from memory before moving on to harder problems.

Reference excerpt

Spaghetti sort is a linear-time, analog algorithm for sorting a sequence of items, introduced by A. K. Dewdney in his Scientific American column. This algorithm sorts a sequence of items requiring O(n) stack space in a stable manner. It requires a parallel processor, which is assumed to be able to find the maximum of a sequence of items in O(1) time.

Algorithm For simplicity, assume we are sorting a list of natural numbers. The sorting method is illustrated using uncooked rods of spaghetti:

For each number x in the list, obtain a rod of length x. (One practical way of choosing the unit is to let the largest number m in the list correspond to one full rod of spaghetti. In this case, the full rod equals m spaghetti units. To get a rod of length x, break a rod in two so that one piece is of length x units; discard the other piece.) Once you have all your spaghetti rods, take them loosely in your fist and lower them to the table, so that they all stand upright, resting on the table surface. Now, for each rod, lower your other hand from above until it meets with a rod—this one is clearly the longest. Remove this rod and insert it into the front of the (initially empty) output list (or equivalently, place it in the last unused slot of the output array). Repeat until all rods have been removed.

Analysis Preparing the n rods of spaghetti takes linear time. Lowering the rods on the table takes constant time, O(1). This is possible because the hand, the spaghetti rods and the table work as a fully parallel computing device. There are then n rods to remove so, assuming each contact-and-removal operation takes constant time, the worst-case time complexity of the algorithm is O(n).

References

External links A. K. Dewdney's homepage Implementations of a model of physical sorting, Boole Centre for Research in Informatics Classical/Quantum Computing, IFF-Institute Archived 2011-07-19 at the Wayback Machine

Illustrations

Worked examples

Example 1 — a first encounter with Spaghetti sort

Start with the simplest possible case. Write down what Spaghetti sort claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In computer science, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Spaghetti sort before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Spaghetti sort ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Spaghetti sort

In research: Spaghetti sort appears in computer science research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses Spaghetti sort in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: Spaghetti sort is common in secondary-school and first-year university syllabi. It links to neighbouring topics Metaphors referring to spaghetti, Sorting algorithms, so understanding it makes those chapters shorter.
In everyday life: Look for Spaghetti sort outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

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How to study Spaghetti sort in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Spaghetti sort means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain Spaghetti sort out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Spaghetti sort in simple terms?

Spaghetti sort is a linear-time, analog algorithm for sorting a sequence of items, introduced by A. K.

Why does Spaghetti sort matter?

Because it connects several computer science ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Spaghetti sort?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Spaghetti sort.