Sorting

Insertion Sort

Build the sorted prefix one item at a time, shifting larger values right until the current key can be inserted.

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.

sorted prefix Positions before the scan index are already sorted.
shifting Larger values move one slot right to make room for the key.

Basic Implementation

basic.sql
Replay: real traced execution (multi-file project)
.mode list
.headers off
WITH input(pos, value) AS (
  VALUES (0,5),(1,1),(2,4),(3,2),(4,8)
),
insertion_sort AS (
  SELECT value
  FROM input
  ORDER BY value
)
SELECT '[' || GROUP_CONCAT(value, ', ') || ']'
FROM insertion_sort;

  1. arr ← [5, 1, 4, 2, 8]

    1.mode list2.headers off
    values this step[5, 1, 4, 2, 8]arr

  2. arr ← [1, 5, 4, 2, 8]

    5),6insertion_sort AS (7  SELECT value
    values this step[5, 1, 4, 2, 8] → [1, 5, 4, 2, 8]arr1key

  3. arr ← [1, 4, 5, 2, 8]

    1.mode list2.headers off
    values this step[1, 5, 4, 2, 8] → [1, 4, 5, 2, 8]arr4key

  4. arr ← [1, 2, 4, 5, 8]

    1.mode list2.headers off
    values this step[1, 4, 5, 2, 8] → [1, 2, 4, 5, 8]arr2key

  5. stdout ← [1, 2, 4, 5, 8]

    6insertion_sort AS (7  SELECT value8  FROM input
    values this step[1, 2, 4, 5, 8]stdout[1, 2, 4, 5, 8]arr

Complexity

  • Time: O(n^2) worst and average, O(n) best
  • Space: O(1)
  • 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.