Community resourceWorksheet
OCR H446 2.3.1 Best, average and worst cases
Part 4 of 16 · H446 2.3.1 · Algorithms
Input size is not the whole story: arrangement and target position change the work done, which is the distinction H446 2.3.1 draws between best, average and worst cases. The worksheet insists that every case claim carries its assumptions, and keeps cases apart from the growth classes students meet alongside them.
Students will:
- define best, average and worst by describing the input condition that produces each
- identify the arrangements that give insertion sort its least and most shifting work
- state the algorithm version, size, arrangement and counted operation behind any claim
- critique a statement that mixes a case up with a complexity class
- construct concrete inputs for a stopping condition and draw growth conclusions from them
Inside: 6 explanation cells, 1 multiple-choice question, 1 fill-in-the-blanks cell and 3 written answers. 21 marks, about 20 to 30 minutes.
Series: H446 2.3.1 · Algorithms, part 4 of 16.
Shared by Coding PathwayVerified teacher
- 11 cells
- About 30 minutes
- CC BY-SA 4.0
- Shared 31 Aug 2026
- Updated 3 Sept 2026
Preview
The whole resource, exactly as a class sees it. Answers and marking are held back.
Best, average and worst cases
Input size alone does not determine every run. Arrangement and target position can change the work.
By the end, you will be able to
- define best, average and worst under stated assumptions;
- identify cases for searches and sorts;
- distinguish a case from Big O notation;
- communicate average-case assumptions honestly.
Reactivate: n is the number of data items.
Worked search cases
Linear search best case: target is first, one comparison, O(1). Worst case: target is last or absent, n comparisons, O(n). An average statement assumes a target distribution; it is not automatically n/2 without explaining equally likely positions and successful search.
Binary search best: middle matches, O(1). Worst/typical repeated halving: O(log n), provided data is sorted.
Which is a valid worst case for linear search?
- ATarget is first
- BList is sorted
- Cn equals one
- DTarget is absent after all n items are checked
Describe best and worst input arrangements for insertion sort and link each to the amount of shifting/comparison work.
Use already sorted and reverse sorted.
Students type their answer here.
Guided discipline
Always state: algorithm/version, input size, arrangement/target condition, operation counted, and any probability assumption. Best, average and worst describe classes of inputs; O notation describes growth.
Critique: 'Binary search is always O(log n), and the average case of linear search is exactly n/2.'
Correct both overclaims.
Students type their answer here.
Independent transfer
For an algorithm that stops when it sees a negative value or after n values, construct best, plausible average and worst inputs. Then give growth for best and worst.
Give concrete inputs, assumptions and complexity conclusions.
State where the first negative appears.
Students type their answer here.
Closed-book checkpoint
Complete each sentence from memory. There is no answer bank and correctness is held for teacher review.
Review your understanding
Before submitting, check that you can explain the central distinction in your own words, expose the intermediate state that supports your answer and apply the method in an unfamiliar context.