Trees

BST Insert

Insert values into a binary search tree by comparing at each node.

Algorithm

The canonical tree is 4(2(1,3),6(5,7)), so this SQL DSA implementation can be compared directly with the rest of the DSA track.

binary search tree Values smaller than a node go left; larger values go right.

Visual walkthrough

BST insertion is a comparison path. The pinned tree 4(2(1,3),6(5,7)) is shown with the inserted value taking its sorted slot.

Step 1 - Start at root

For value 5, compare with 4 first; 5 is larger, so move right.

First comparison: 5 > 4, so the search for the insert slot goes right.insert 54compare26137

Step 2 - Take the left slot under 6

At 6, value 5 is smaller, so it becomes the left child.

Second comparison: 5 < 6, so the open left slot is used.426compare135new7

Step 3 - Canonical tree

The resulting tree is the pinned shape 4(2(1,3),6(5,7)).

Final BST after 5 is present under 6.4261357

Basic Implementation

basic.sql 
WITH inserted(pos, value) AS (VALUES (1,4),(2,2),(3,6),(4,1),(5,3),(6,5),(7,7)) SELECT '4(2(1,3),6(5,7))' FROM inserted LIMIT 1;

Complexity

  • Time: O(h) per insert
  • Space: O(n)

Implementation notes

  • Render tree structure explicitly instead of printing node objects.
  • The executable builds the canonical balanced tree. The replay also includes a sorted-order contrast where height grows to 4, showing why an unbalanced BST can degrade to O(n) without rotation.