computer science

Index mapping

Index mapping 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 Index mapping rather than just read about it. In short: Index mapping (or direct addressing, or a trivial hash function) in computer science describes using an array, in which each position corresponds to a key in the universe of possible values. The technique is most effective when the universe of keys is reasonably small, such that allocating an array with one position for every possible key is affordable.

Key takeaways

Index mapping 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 Index mapping to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of Index mapping from memory before moving on to harder problems.

Reference excerpt

Index mapping (or direct addressing, or a trivial hash function) in computer science describes using an array, in which each position corresponds to a key in the universe of possible values. The technique is most effective when the universe of keys is reasonably small, such that allocating an array with one position for every possible key is affordable. Its effectiveness comes from the fact that an arbitrary position in an array can be examined in constant time.

Applicable arrays There are many practical examples of data whose valid values are restricted within a small range. A trivial hash function is a suitable choice when such data needs to act as a lookup key. Some examples include:

month in the year (1–12) day in the month (1–31) day of the week (1–7) human age (0–130) – e.g. lifecover actuary tables, fixed-term mortgage ASCII characters (0–127), encompassing common mathematical operator symbols, digits, punctuation marks, and English language alphabet

Examples Using a trivial hash function, in a non-iterative table lookup, can eliminate conditional testing and branching completely, reducing the instruction path length of a computer program.

Avoid branching Roger Sayle gives an example of eliminating a multiway branch caused by a switch statement:

Which can be replaced with a table lookup:

References

Worked examples

Example 1 — a first encounter with Index mapping

Start with the simplest possible case. Write down what Index mapping 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 Index mapping 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 Index mapping 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 Index mapping

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

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

Frequently asked questions

What is Index mapping in simple terms?

Why does Index mapping 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 Index mapping?

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 Index mapping.