Decision Mathematics A Level Further Maths Worksheets, Questions and Revision

The list 25, 11, 33, 4, 18, 7 is to be sorted into ascending order using quick sort, choosing the first item of each sublist as the pivot. Carry out the full sort, showing the sublists produced at each stage.

1. First pivot = 25 (the first item). Comparing each remaining item (11, 33, 4, 18, 7) to 25: those less than 25 form the sublist [11, 4, 18, 7] in their original order, and those greater form the sublist [33]. This gives [11, 4, 18, 7] | 25 | [33].
2. The sublist [33] has one item, so it needs no further sorting. Apply quick sort to [11, 4, 18, 7]: pivot = 11. The remaining items 4, 18, 7 split into [4, 7] (less than 11) and [18] (greater than 11), giving [4, 7] | 11 | [18].
3. [18] has one item, so it is done. Apply quick sort to [4, 7]: pivot = 4. The remaining item 7 is greater than 4, so the less-than sublist is empty and the greater-than sublist is [7], giving 4 | [7].
4. Every sublist now has at most one item, so sorting is complete. Reading the sublists in order gives 4, 7, 11, 18, 25, 33.
5. Final answer: sorted list is 4, 7, 11, 18, 25, 33.