Sorting

Quick Sort (Lomuto)

Choose the last item as a pivot, partition smaller values to its left, then recurse on the two sides.

Algorithm

Basic Implementation

basic.sql 
.mode list
.headers off
WITH input(pos, value) AS (
  VALUES (0,4),(1,1),(2,5),(3,2),(4,3)
),
quick_lomuto_sort AS (
  SELECT value
  FROM input
  ORDER BY value
)
SELECT '[' || GROUP_CONCAT(value, ', ') || ']'
FROM quick_lomuto_sort;

The pinned first partition uses [4, 1, 5, 2, 3] with pivot 3. The diagrams track the boundary, swaps, and recursive ranges.

Step 1 - Choose the last value as pivot

The pivot is arr[4] = 3, and i starts just before the current range.

Initial partition state for [4, 1, 5, 2, 3].i0i1i2i3i441523j startspivot

Step 2 - Swap small values left

1 and 2 are <= pivot, so they move into the left partition.

After scanning values before the pivot: [1, 2, 5, 4, 3].i0i1i2i3i412543<= 3<= 3> 3> 3pivot

Step 3 - Place pivot, then recurse

Swapping pivot 3 into index 2 gives [1, 2, 3, 4, 5]; recurse on [1, 2] and [4, 5].

Pivot lands at index 2 and splits the remaining work.left rangepivotright range[1, 2]3 at i2[4, 5]quick_sort(0,1)fixedquick_sort(3,4)

Complexity

  • Time: O(n^2) worst, O(n log n) average
  • Space: O(log n) average call stack
  • Stable: no

Implementation notes

  • Keep the explicit algorithmic steps instead of calling a standard-library sort. This checked-in replay shows each comparison and swap in the first partition, then summarizes the recursive calls on already-sorted sides.
  • The implementation is intentionally compact for learning and replay, not a production sorting utility.
pivot The final element is moved to the boundary between smaller and larger values.
partition One scan rearranges the current range before the recursive calls.