1.2c Bubble Sort — Edexcel 1CP2

What is Bubble Sort?

Bubble sort is a simple sorting algorithm that works by repeatedly comparing adjacent pairs of elements and swapping them if they are in the wrong order. After each pass through the list, the largest unsorted element "bubbles up" to its correct position at the end.

How Bubble Sort Works — Step by Step

Start at the first element of the list
Compare the first and second elements; if the first is larger, swap them
Move to the next pair (second and third) and repeat
Continue until the end of the list — this completes one pass
Repeat the whole process for the remaining unsorted portion
Stop when a complete pass makes no swaps — the list is sorted

Worked Example

Sort [5, 3, 8, 1, 2] using bubble sort:

Pass	List state	Swaps made
Pass 1	[3, 5, 1, 2, 8]	3: (5,3), (5,8 no), (8,1), (8,2) → 8 in place
Pass 2	[3, 1, 2, 5, 8]	2: (3,5 no), (5,1), (5,2) → 5 in place
Pass 3	[1, 2, 3, 5, 8]	2: (3,1), (3,2) → 3 in place
Pass 4	[1, 2, 3, 5, 8]	0 swaps → STOP (list sorted)

Efficiency

Best case: The list is already sorted. One pass with 0 swaps is needed → n-1 comparisons total.

Worst case: The list is in reverse order. n passes each comparing n elements → roughly n² comparisons total.

Bubble sort is considered inefficient for large lists because its worst-case performance is quadratic. For small lists, it is easy to understand and implement.

Exam tip: In an Edexcel exam, you may be asked to trace through one or two passes of bubble sort on a given list. Make sure to show the state of the list after each comparison where a swap occurs, and state how many swaps were made in each pass.

Optimisation

Bubble sort can be optimised by keeping track of whether any swap occurred in a pass. If no swaps happened, the list is already sorted and the algorithm can stop early. This is the optimised/early exit bubble sort.

⚠️ Common Mistakes

Stopping after a fixed number of passes rather than checking for zero swaps
Forgetting that after each pass, the last n items are already in place and don't need to be compared again
Showing the wrong state after a swap — always update the list immediately
Confusing bubble sort with selection or insertion sort in an exam

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Key points covered

Bubble sort step-by-step trace on a worked example
What a pass is and what happens at the end of each pass
Optimised bubble sort with early exit
Best case and worst case scenarios
Exam technique: showing passes in a trace table

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Worksheet — 1.2c Bubble Sort

8 Edexcel-style questions · instantly marked

Q1State what happens when two adjacent elements are compared and found to be in the wrong order in bubble sort.[1]

✅ Mark scheme

They are swapped. [1]

Q2Describe what a "pass" means in the context of bubble sort.[1]

✅ Mark scheme

One complete iteration through the list, comparing each adjacent pair. [1]

Q3Show the state of the list [4, 1, 6, 3, 2] after the first complete pass of bubble sort. Clearly show each swap.[3]

✅ Mark scheme

Compare 4,1 → swap → [1,4,6,3,2] [1]
Compare 4,6 → no swap
Compare 6,3 → swap → [1,4,3,6,2] [1]
Compare 6,2 → swap → [1,4,3,2,6] [1]
End of pass 1: [1,4,3,2,6] — 6 is now in its final position

Q4State the condition that causes bubble sort to stop early (optimised version).[1]

✅ Mark scheme

When a complete pass is made with zero swaps / no swaps occur during a pass. [1]

Q5After each pass of bubble sort, what is guaranteed about the end of the list?[1]

✅ Mark scheme

The largest unsorted element has moved to its correct final position at the end. [1]

Q6A list already sorted in ascending order is given to bubble sort. How many passes will the optimised version need? Explain your answer.[2]

✅ Mark scheme

One pass [1] — the algorithm makes a single pass, finds no swaps, and stops immediately as the list is already sorted [1].

Q7Explain why bubble sort is considered inefficient for large lists.[2]

✅ Mark scheme

In the worst case, bubble sort requires approximately n² comparisons for n items [1]; as the list grows, the number of comparisons grows quadratically, making it very slow for large datasets [1].

Q8Trace all passes of bubble sort on the list [9, 3, 7, 1]. Show the list after each pass and count the number of swaps per pass.[4]

✅ Mark scheme

Pass 1: compare(9,3)→swap, compare(9,7)→swap, compare(9,1)→swap → [3,7,1,9], 3 swaps [1]
Pass 2: compare(3,7)→no, compare(7,1)→swap → [3,1,7,9], 1 swap [1]
Pass 3: compare(3,1)→swap → [1,3,7,9], 1 swap [1]
Pass 4: no swaps → stop [1] — sorted: [1,3,7,9]

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What is Bubble Sort?

How Bubble Sort Works — Step by Step

Worked Example

Efficiency

Optimisation

Key points covered

Worksheet — 1.2c Bubble Sort

Mini Test — 1.2c Bubble Sort

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