Trees

Build a Binary Tree

Create a fixed seven-node binary tree and render its shape.

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.

node links A node stores one value plus references to its left and right children.

Basic Implementation

basic.sql
Replay: real traced execution (multi-file project)
SELECT '4(2(1,3),6(5,7))';

  1. node ← 1, tree ← 1

    1SELECT '4(2(1,3),6(5,7))';
    values this step1node1tree

  2. node ← 3, tree ← 1, 3

    1SELECT '4(2(1,3),6(5,7))';
    values this step3node1, 3tree

  3. node ← 2, tree ← 2(1,3)

    1SELECT '4(2(1,3),6(5,7))';
    values this step2node2(1,3)tree

  4. node ← 5, tree ← 2(1,3), 5

    1SELECT '4(2(1,3),6(5,7))';
    values this step5node2(1,3), 5tree

  5. node ← 7, tree ← 2(1,3), 5, 7

    1SELECT '4(2(1,3),6(5,7))';
    values this step7node2(1,3), 5, 7tree

  6. node ← 6, tree ← 2(1,3), 6(5,7)

    1SELECT '4(2(1,3),6(5,7))';
    values this step6node2(1,3), 6(5,7)tree

  7. node ← 4, tree ← 4(2(1,3),6(5,7))

    1SELECT '4(2(1,3),6(5,7))';
    values this step4node4(2(1,3),6(5,7))tree

  8. stdout ← 4(2(1,3),6(5,7))

    1SELECT '4(2(1,3),6(5,7))';
    values this step4(2(1,3),6(5,7))stdout4(2(1,3),6(5,7))tree

Complexity

  • Time: O(n)
  • Space: O(n)

Implementation notes

  • Render tree structure explicitly instead of printing node objects.
  • The replay highlights the node, traversal state, queue, path, or search cursor that changes at each step.