Linked Structures

Insert at Head

Insert a new first node by pointing it at the old head and then moving the head pointer.

Algorithm

Basic Implementation

basic.sql 
.mode list
.headers off
CREATE TABLE node(idx INTEGER PRIMARY KEY, val INTEGER, next_idx INTEGER);
INSERT INTO node(idx, val, next_idx) VALUES (2, 20, 3), (3, 30, NULL);
INSERT INTO node(idx, val, next_idx) VALUES (1, 10, 2);
WITH RECURSIVE walk(idx, line) AS (
  SELECT 1, CAST(val AS TEXT) || ' -> ' FROM node WHERE idx = 1
  UNION ALL
  SELECT node.idx, walk.line || CAST(node.val AS TEXT) || ' -> '
  FROM walk JOIN node ON node.idx = (SELECT next_idx FROM node WHERE idx = walk.idx)
)
SELECT line || 'null' FROM walk
ORDER BY LENGTH(line) DESC LIMIT 1;

Head insertion changes only two references: the new node points at the old head, then head moves to the new node.

Step 1 - Old first node

Before insertion, head points at node(20).

Original chain before inserting 10 at the head.headnode(20)node(30)null

Step 2 - New node links to old head

Set new.next to the old first node before moving head.

node(10) is allocated and points at the old head node(20).headnode(10)newnode(20)old headnode(30)null

Step 3 - Head moves to the new node

The final chain has 10 first: 10 -> 20 -> 30 -> null.

After insertion, head points at node(10).headnode(10)node(20)node(30)null

Complexity

  • Time: O(1)
  • Space: O(1)

Implementation notes

  • Keep the explicit node and pointer/reference operations; array shortcuts hide the linked-list state this lesson is meant to replay.
  • The final output prints the chain in a deterministic a -> b -> null form for cross-language comparison.
old head The previous first node becomes the second node.
constant-time insert Only the new node and head pointer change.