Understand that more than one algorithm can be used to solve the same…

The idea

Many problems have several valid solutions. Searching a list for a value, for example, can be done with a linear search that checks items one by one, or with a binary search that repeatedly halves a sorted list. Both are correct algorithms because both find the value when it is present, but they differ in how much work they do. Efficiency concerns how the number of steps grows as the input size grows: a linear search may need to examine every item, while a binary search needs far fewer comparisons on a large sorted list. Choosing between algorithms therefore involves checking correctness first, then comparing the number of operations, the data requirements such as whether the list must be sorted, and the resources used.

What earns the marks

• Recognises that a single problem can be solved by more than one correct algorithm.
• Gives an example of two different algorithms for the same task, such as linear search and binary search.
• Explains that both algorithms must produce a correct result to count as solutions.
• Compares efficiency by the number of steps or comparisons needed as input size grows.
• Notes practical differences such as whether data must be sorted before a binary search can be used.

Common mistakes and how to put them right

• Assuming only one algorithm can be correct for a problem.

  Put it right: Accept that several algorithms may all give correct results.

• Treating a faster-running program as automatically more efficient without considering input size.

  Put it right: Compare how the number of steps grows with input size.

• Claiming a binary search works on any list.

  Put it right: State that the list must be sorted first.

Exam tips

• Name two concrete algorithms for the same task before comparing them.
• Compare efficiency in terms of number of comparisons or steps, not seconds of runtime.
• Mention any precondition, such as sorted data, that one algorithm requires.