Learning objective
Comparing algorithms: Understand that algorithms can be compared by expressing their complexity as a function relative to the size of the problem. Understand that the size of the problem is the key issue. Understand that some algorithms are more efficient: • time-wise than other algorithms • space-wise than other algorithms. Efficiently implementing automated abstractions means designing data models and algorithms to run quickly while taking up the minimal amount of resources such as memory.
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Classification of algorithms
Subtopic
Comparing algorithms
Aqa A Level Computer ScienceTheory of computation
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Quick explanation
Comparing algorithms: Understand that algorithms can be compared by expressing their complexity as a function relative to the size of the problem. Understand that the size of the problem is the key issue. Understand that some algorithms are more efficient: • time-wise than other algorithms • space-wise than other algorithms. Efficiently implementing automated abstractions means designing data models and algorithms to run quickly while taking up the minimal amount of resources such as memory
- This point belongs to Classification of algorithms, especially Comparing algorithms.
- You need to be able to comparing algorithms: Understand that algorithms can be compared by expressing their complexity as a function relative to the size of the problem. Understand that the size of the problem is the key issue. Understand that some algorithms are more efficient: • time-wise than other algorithms • space-wise than other algorithms. Efficiently implementing automated abstractions means designing data models and algorithms to run quickly while taking up the minimal amount of resources such as memory.
- Use the linked flashcards and practice questions to check recall, then practise applying the idea in an exam-style answer.
Why it matters
This objective helps connect Comparing algorithms to exam-style questions, flashcards, and revision notes for Classification of algorithms.
Quick student answer
When comparing the time efficiency of two algorithms, which factor is most important to consider?
Direct answer
The size of the problem being solved
Key terms
- Problem size: The amount of data or work that an algorithm must handle, used as the basis for comparing how its requirements change.
- Space efficiency: The extent to which an algorithm minimises the memory and other storage resources needed to operate.
Common trap
Assuming fewer lines means greater efficiency: Compare how the algorithm's time and space requirements change relative to the problem size. Code length alone does not establish efficiency.
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Related learning objectives
- Maths for understanding Big-0 notation: Be familiar with the mathematical concept of a function as a mapping from one set of values, the domain, to another set of values, drawn from the co-domain, for example ℕ → ℕ. 60 Be familiar with the concept of: • a linear function, for example y = 2x • a polynomial function, for example y = 2x 2 • an exponential function, for example y = 2x • a logarithmic function, for example y = log10 x. Be familiar with the notion of permutation of a set of objects or values, for example, the letters of a word and that the number of permutations of n distinct objects is n factorial (n!). n! is the product of all positive integers less than or equal to n.
Maths for understanding Big-0 notation
- Order of complexity: Be familiar with Big-O notation to express time complexity and be able to apply it to cases where the running time requirements of the algorithm grow in: • constant time • logarithmic time • linear time • polynomial time • exponential time. Be able to derive the time complexity of an algorithm.
Order of complexity
- Limits of computation: Be aware that algorithmic complexity and hardware impose limits on what can be computed.
Limits of computation
- Classification of algorithmic problems: Know that algorithms may be classified as being either: • tractable - problems that have a polynomial (or less) time solution are called tractable problems. • intractable - problems that have no polynomial (or less) time solution are called intractable problems. Heuristic methods are often used when tackling intractable problems.
Classification of algorithmic problems
- Computable and non-computable problems: Be aware that some problems cannot be solved algorithmically.
Computable and non-computable problems