science

Sorted array

Sorted array is a 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 Sorted array rather than just read about it. In short: A sorted array is an array data structure in which each element is sorted in numerical, alphabetical, or some other order, and placed at equally spaced addresses in computer memory. It is typically used in computer science to implement static lookup tables to hold multiple values which have the same data type.

Key takeaways

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

Reference excerpt

A sorted array is an array data structure in which each element is sorted in numerical, alphabetical, or some other order, and placed at equally spaced addresses in computer memory. It is typically used in computer science to implement static lookup tables to hold multiple values which have the same data type. Sorting an array is useful in organising data in ordered form and recovering them rapidly.

Overview Sorted arrays are the most space-efficient data structure with the best locality of reference for sequentially stored data. Elements within a sorted array are found using a binary search, in O(log n); thus sorted arrays are suited for cases when one needs to be able to look up elements quickly, e.g. as a set or multiset data structure. This complexity for lookups is the same as for self-balancing binary search trees. In some data structures, an array of structures is used. In such cases, the same sorting methods can be used to sort the structures according to some key as a structure element; for example, sorting records of students according to roll numbers or names or grades. If one is using a sorted dynamic array, then it is possible to insert and delete elements. The insertion and deletion of elements in a sorted array executes at O(n), due to the need to shift all the elements following the element to be inserted or deleted; in comparison a self-balancing binary search tree inserts and deletes at O(log n). In the case where elements are deleted or inserted at the end, a sorted dynamic array can do this in amortized O(1) time while a self-balancing binary search tree always operates at O(log n). Elements in a sorted array can be looked up by their index (random access) at O(1) time, an operation taking O(log n) or O(n) time for more complex data structures.

History John von Neumann wrote the first array sorting program (merge sort) in 1945, when the first stored-program computer was still being built.

See also Sorting algorithm Binary search algorithm Heap (data structure) Search data structure

References

Worked examples

Example 1 — a first encounter with Sorted array

Start with the simplest possible case. Write down what Sorted array claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In 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 Sorted array 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 Sorted array 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 Sorted array

In research: Sorted array appears in 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 Sorted array 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: Sorted array is common in secondary-school and first-year university syllabi. It links to neighbouring topics Arrays, so understanding it makes those chapters shorter.
In everyday life: Look for Sorted array 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 Sorted array in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Sorted array 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 Sorted array out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Sorted array in simple terms?

Why does Sorted array matter?

Because it connects several 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 Sorted array?

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 Sorted array.