Recursive CTE for hierarchical data in SQL - Time & Space Complexity

Time Complexity: Recursive CTE for hierarchical data

O(n)

Understanding Time Complexity

When working with hierarchical data, recursive queries help us find all related items step-by-step.

We want to know how the time to get all related data grows as the hierarchy gets bigger.

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

WITH RECURSIVE Subordinates AS (
  SELECT employee_id, manager_id, name
  FROM employees
  WHERE manager_id IS NULL
  UNION ALL
  SELECT e.employee_id, e.manager_id, e.name
  FROM employees e
  INNER JOIN Subordinates s ON e.manager_id = s.employee_id
)
SELECT * FROM Subordinates;

This query finds all employees under top-level managers by repeatedly joining employees to their managers.

Identify Repeating Operations

• Primary operation: Recursive join between employees and the growing set of subordinates.
• How many times: Once for each level of the hierarchy until all subordinates are found.

How Execution Grows With Input

Each recursion step adds employees reporting to the current level, repeating until no more are found.

Input Size (n)	Approx. Operations
10	About 10 joins, one per employee
100	About 100 joins, growing with employees
1000	About 1000 joins, scaling with total employees

Pattern observation: The work grows roughly in proportion to the total number of employees processed.

Final Time Complexity

Time Complexity: O(n)

This means the time grows linearly with the number of employees in the hierarchy.

Common Mistake

[X] Wrong: "Recursive queries always take exponential time because they repeat joins many times."

[OK] Correct: Each employee is processed once in the recursion, so the total work grows linearly, not exponentially.

Interview Connect

Understanding recursive queries shows you can handle complex data relationships, a useful skill in many real projects.

Self-Check

"What if the hierarchy has cycles? How would that affect the time complexity of the recursive query?"

Practice

1. What is the main purpose of a RECURSIVE CTE in SQL when working with hierarchical data?

easy

A. To speed up simple SELECT queries without joins

B. To repeatedly query connected rows to explore hierarchical relationships

C. To create temporary tables for storing unrelated data

D. To update multiple tables at once

Solution

1. Step 1: Understand the role of recursive CTEs

   Recursive CTEs allow querying hierarchical or connected data by repeatedly joining rows to find related entries.

2. Step 2: Compare options with this purpose

   Only To repeatedly query connected rows to explore hierarchical relationships describes this repeated querying of connected rows to explore hierarchies.

3. Final Answer:

   To repeatedly query connected rows to explore hierarchical relationships -> Option B

4. Quick Check:

   Recursive CTE = repeated connected row queries [OK]

Hint: Recursive CTEs repeatedly join related rows to explore hierarchies [OK]

Common Mistakes:

• Confusing recursive CTEs with simple temporary tables
• Thinking recursive CTEs speed up unrelated queries
• Assuming recursive CTEs update data

2. Which of the following is the correct syntax to start a recursive CTE named OrgChart in SQL?

easy

A. DECLARE RECURSIVE OrgChart BEGIN ... END

B. CREATE RECURSIVE TABLE OrgChart AS ( ... )

C. SELECT RECURSIVE OrgChart FROM ...

D. WITH RECURSIVE OrgChart AS ( ... )

Solution

1. Step 1: Recall recursive CTE syntax

   The correct way to start a recursive CTE is using WITH RECURSIVE Name AS ( ... ).

2. Step 2: Check each option

   WITH RECURSIVE OrgChart AS ( ... ) matches the correct syntax. Options A, B, and C use invalid or unrelated SQL commands.

3. Final Answer:

   WITH RECURSIVE OrgChart AS ( ... ) -> Option D

4. Quick Check:

   Recursive CTE starts with WITH RECURSIVE [OK]

Hint: Recursive CTE always starts with WITH RECURSIVE [OK]

Common Mistakes:

• Using CREATE instead of WITH for CTEs
• Trying to SELECT RECURSIVE directly
• Using DECLARE which is for procedural code

3. Given the table Employees(id, name, manager_id) where manager_id references id, what will the following query return?

WITH RECURSIVE Subordinates AS (
  SELECT id, name, manager_id FROM Employees WHERE id = 2
  UNION ALL
  SELECT e.id, e.name, e.manager_id FROM Employees e
  JOIN Subordinates s ON e.manager_id = s.id
)
SELECT * FROM Subordinates;

medium

A. All employees who report directly or indirectly to employee with id 2

B. Only the employee with id 2

C. All employees who have no manager

D. All employees in the company

Solution

1. Step 1: Analyze the base query

   The base query selects the employee with id = 2.

2. Step 2: Analyze the recursive part

   The recursive part joins employees whose manager_id matches any id found so far, thus finding all subordinates under employee 2.

3. Final Answer:

   All employees who report directly or indirectly to employee with id 2 -> Option A

4. Quick Check:

   Recursive join finds all subordinates [OK]

Hint: Recursive CTE with join on manager_id finds all subordinates [OK]

Common Mistakes:

• Thinking it returns only the base employee
• Assuming it returns employees without managers
• Believing it returns all employees regardless

4. Identify the error in this recursive CTE that tries to list all descendants of a node in a tree:

WITH RECURSIVE Descendants AS (
  SELECT id, parent_id FROM Tree WHERE id = 1
  UNION ALL
  SELECT t.id, t.parent_id FROM Tree t
  JOIN Descendants d ON t.id = d.parent_id
)
SELECT * FROM Descendants;

medium

A. The JOIN condition should be ON t.parent_id = d.id, not t.id = d.parent_id

B. The base query should select from Descendants, not Tree

C. Recursive CTEs cannot use JOINs

D. The recursive part should use UNION, not UNION ALL

Solution

1. Step 1: Understand the tree relationship

   Each node's parent_id points to its parent. To find descendants, join where child's parent_id equals parent's id.

2. Step 2: Check the JOIN condition

   The query incorrectly joins on t.id = d.parent_id. It should be t.parent_id = d.id to find children of current nodes.

3. Final Answer:

   The JOIN condition should be ON t.parent_id = d.id, not t.id = d.parent_id -> Option A

4. Quick Check:

   Join child parent_id to parent id [OK]

Hint: Join child's parent_id to parent's id to find descendants [OK]

Common Mistakes:

• Reversing join condition columns
• Using base query from recursive CTE itself
• Thinking recursive CTEs can't use JOIN
• Confusing UNION and UNION ALL usage

5. You have a parts list table Parts(id, name, parent_part_id) representing assemblies and subassemblies. Write a recursive CTE query to find the full hierarchy of parts under part with id = 10, including the root part itself, and show the level (depth) of each part in the hierarchy starting at 0 for the root. Which query is correct?

hard

A. WITH RECURSIVE PartHierarchy AS (
SELECT id, name, parent_part_id FROM Parts WHERE parent_part_id IS NULL
UNION ALL
SELECT p.id, p.name, p.parent_part_id FROM Parts p
JOIN PartHierarchy ph ON p.id = ph.parent_part_id
)
SELECT * FROM PartHierarchy WHERE id = 10;

B. WITH RECURSIVE PartHierarchy AS (
SELECT id, name, parent_part_id, 1 AS level FROM Parts WHERE id = 10
UNION ALL
SELECT p.id, p.name, p.parent_part_id, ph.level - 1 FROM Parts p
JOIN PartHierarchy ph ON p.id = ph.parent_part_id
)
SELECT * FROM PartHierarchy;

C. WITH RECURSIVE PartHierarchy AS (
SELECT id, name, parent_part_id, 0 AS level FROM Parts WHERE id = 10
UNION ALL
SELECT p.id, p.name, p.parent_part_id, ph.level + 1 FROM Parts p
JOIN PartHierarchy ph ON p.parent_part_id = ph.id
)
SELECT * FROM PartHierarchy;

D. WITH RECURSIVE PartHierarchy AS (
SELECT id, name, parent_part_id, 0 AS level FROM Parts WHERE id = 10
UNION ALL
SELECT p.id, p.name, p.parent_part_id, ph.level + 1 FROM Parts p
JOIN PartHierarchy ph ON p.id = ph.parent_part_id
)
SELECT * FROM PartHierarchy;

Solution

1. Step 1: Identify the base case and level

   The base query selects the root part with id=10 and sets level to 0.

2. Step 2: Check the recursive join and level increment

   The recursive part joins parts where parent_part_id matches current part's id, and increments level by 1 to track depth.

3. Step 3: Verify options

   WITH RECURSIVE PartHierarchy AS ( SELECT id, name, parent_part_id, 0 AS level FROM Parts WHERE id = 10 UNION ALL SELECT p.id, p.name, p.parent_part_id, ph.level + 1 FROM Parts p JOIN PartHierarchy ph ON p.parent_part_id = ph.id ) SELECT * FROM PartHierarchy; correctly implements this logic. WITH RECURSIVE PartHierarchy AS ( SELECT id, name, parent_part_id, 1 AS level FROM Parts WHERE id = 10 UNION ALL SELECT p.id, p.name, p.parent_part_id, ph.level - 1 FROM Parts p JOIN PartHierarchy ph ON p.id = ph.parent_part_id ) SELECT * FROM PartHierarchy; has wrong join direction and decrements level. WITH RECURSIVE PartHierarchy AS ( SELECT id, name, parent_part_id FROM Parts WHERE parent_part_id IS NULL UNION ALL SELECT p.id, p.name, p.parent_part_id FROM Parts p JOIN PartHierarchy ph ON p.id = ph.parent_part_id ) SELECT * FROM PartHierarchy WHERE id = 10; starts from root parts but filters later, missing the correct root. WITH RECURSIVE PartHierarchy AS ( SELECT id, name, parent_part_id, 0 AS level FROM Parts WHERE id = 10 UNION ALL SELECT p.id, p.name, p.parent_part_id, ph.level + 1 FROM Parts p JOIN PartHierarchy ph ON p.id = ph.parent_part_id ) SELECT * FROM PartHierarchy; has wrong join direction.

4. Final Answer:

   The query with base WHERE id=10, level 0, JOIN p.parent_part_id=ph.id, level+1 -> Option C

5. Quick Check:

   Join on child.parent_part_id = parent.id, level + 1 [OK]

Hint: Join child.parent_part_id = parent.id and increment level [OK]

Common Mistakes:

• Reversing join condition (parent to child)
• Starting level at 1 or decrementing level
• Filtering after recursion instead of base case
• Using wrong root selection