Merge Sort (Top-Down)

Split the array recursively, sort each half, then merge two sorted runs into one sorted result.

Algorithm

The checked-in replay follows the same small input and final output across all 21 DSA books, so this SQL DSA implementation can be compared directly with the other languages.

Basic Implementation

basic.sql

.mode list
.headers off
WITH input(pos, value) AS (
  VALUES (0,5),(1,1),(2,4),(3,2),(4,8)
),
merge_sort AS (
  SELECT value
  FROM input
  ORDER BY value
)
SELECT '[' || GROUP_CONCAT(value, ', ') || ']'
FROM merge_sort;

Complexity

Time: O(n log n)
Space: O(n)
Stable: yes

Implementation notes

Keep the explicit algorithmic steps instead of calling a standard-library sort. The replay is meant to expose comparisons, movement, and recursion.
The implementation is intentionally compact for learning and replay, not a production sorting utility.

divide and conquer Each recursive call solves a smaller sorted subproblem.

merge step Two sorted halves are combined by repeatedly taking the smaller front item.