Recursive CTE for hierarchical data in PostgreSQL - 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 recursive query.

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

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

Identify Repeating Operations

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

How Execution Grows With Input

Each recursion step adds employees reporting to the previous level.

Input Size (n)	Approx. Operations
10	About 10 joins to find all employees.
100	About 100 joins as it explores each employee once.
1000	About 1000 joins, one per employee in the hierarchy.

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

Final Time Complexity

Time Complexity: O(n)

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

Common Mistake

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

[OK] Correct: The query visits each employee once, so work grows linearly, not exponentially.

Interview Connect

Understanding recursive queries helps you handle real-world data like org charts or file systems efficiently.

Self-Check

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

Practice

1. What is the main purpose of using a WITH RECURSIVE clause in PostgreSQL when working with hierarchical data?

easy

A. To repeatedly query related rows and build a hierarchy step-by-step

B. To create temporary tables for faster queries

C. To join two unrelated tables efficiently

D. To update multiple rows in a single statement

Solution

1. Step 1: Understand the purpose of recursive CTEs

   Recursive CTEs allow querying hierarchical data by starting with a base case and repeatedly adding related rows.

2. Step 2: Compare options with this purpose

   Only To repeatedly query related rows and build a hierarchy step-by-step describes this step-by-step building of hierarchy, while others describe unrelated SQL features.

3. Final Answer:

   To repeatedly query related rows and build a hierarchy step-by-step -> Option A

4. Quick Check:

   Recursive CTE = step-by-step hierarchy building [OK]

Hint: Recursive CTEs build hierarchies by repeating queries [OK]

Common Mistakes:

• Confusing recursive CTE with temporary tables
• Thinking recursive CTEs update data
• Assuming recursive CTEs join unrelated tables

2. Which of the following is the correct basic syntax to start a recursive CTE named tree in PostgreSQL?

easy

A. RECURSIVE WITH tree AS (SELECT ... UNION ALL SELECT ...)

B. WITH RECURSIVE tree AS (SELECT ... UNION ALL SELECT ...)

C. WITH tree RECURSIVE AS (SELECT ... UNION ALL SELECT ...)

D. WITH tree AS RECURSIVE (SELECT ... UNION ALL SELECT ...)

Solution

1. Step 1: Recall correct recursive CTE syntax

   The correct syntax starts with WITH RECURSIVE cte_name AS ( ... ).

2. Step 2: Match options to syntax

   Only WITH RECURSIVE tree AS (SELECT ... UNION ALL SELECT ...) matches this exact syntax; others misplace the keyword RECURSIVE.

3. Final Answer:

   WITH RECURSIVE tree AS (SELECT ... UNION ALL SELECT ...) -> Option B

4. Quick Check:

   WITH RECURSIVE before CTE name [OK]

Hint: Start with 'WITH RECURSIVE cte_name AS' [OK]

Common Mistakes:

• Placing RECURSIVE after CTE name
• Using RECURSIVE inside parentheses
• Omitting RECURSIVE keyword

3. Given the table employees(id, name, manager_id) with data:
1, 'Alice', NULL
2, 'Bob', 1
3, 'Carol', 2
What will the following query return?

WITH RECURSIVE emp_tree AS (SELECT id, name, manager_id FROM employees WHERE id = 1 UNION ALL SELECT e.id, e.name, e.manager_id FROM employees e JOIN emp_tree et ON e.manager_id = et.id) SELECT name FROM emp_tree ORDER BY id;

medium

A. Alice only

B. Carol only

C. Bob, Carol only

D. Alice, Bob, Carol

Solution

1. Step 1: Understand base case and recursion

   The base case selects employee with id=1 (Alice). The recursive part adds employees whose manager_id matches ids in emp_tree.

2. Step 2: Trace recursion

   First iteration adds Bob (manager_id=1), second adds Carol (manager_id=2). So all three are included.

3. Final Answer:

   Alice, Bob, Carol -> Option D

4. Quick Check:

   Recursive CTE collects all subordinates [OK]

Hint: Recursive CTE collects all descendants starting from base [OK]

Common Mistakes:

• Ignoring base case rows
• Confusing manager_id direction
• Assuming only direct reports are included

4. Consider this recursive CTE:

WITH RECURSIVE cte AS (SELECT id, parent_id FROM items WHERE parent_id IS NULL UNION ALL SELECT i.id, i.parent_id FROM items i JOIN cte ON i.parent_id = cte.id) SELECT * FROM cte;

It returns no rows. What is the most likely cause?

medium

A. The base case SELECT returns no rows because no parent_id is NULL

B. The JOIN condition is reversed and should be cte.parent_id = i.id

C. The recursive part uses UNION instead of UNION ALL

D. The CTE is missing an ORDER BY clause

Solution

1. Step 1: Check base case condition

   The base case selects rows where parent_id IS NULL. If none exist, base returns zero rows.

2. Step 2: Understand recursion depends on base

   Without base rows, recursion never starts, so no rows returned.

3. Final Answer:

   The base case SELECT returns no rows because no parent_id is NULL -> Option A

4. Quick Check:

   Base case must return rows to start recursion [OK]

Hint: Check base case returns rows before recursion [OK]

Common Mistakes:

• Assuming JOIN condition is wrong without checking data
• Thinking UNION vs UNION ALL causes no rows
• Believing ORDER BY affects recursion output

5. You have a table folders(id, name, parent_id) representing nested folders. Write a recursive CTE query to list all folders with their full path from the root, separated by '/'. Which query correctly achieves this?

hard

A. WITH RECURSIVE folder_paths AS (SELECT id, name, parent_id, name AS path FROM folders WHERE parent_id IS NOT NULL UNION ALL SELECT f.id, f.name, f.parent_id, fp.path || '/' || f.name FROM folders f JOIN folder_paths fp ON f.parent_id = fp.id) SELECT id, path FROM folder_paths ORDER BY path;

B. WITH RECURSIVE folder_paths AS (SELECT id, name, parent_id, '/' || name AS path FROM folders WHERE parent_id IS NULL UNION ALL SELECT f.id, f.name, f.parent_id, '/' || fp.path || '/' || f.name FROM folders f JOIN folder_paths fp ON f.parent_id = fp.id) SELECT id, path FROM folder_paths ORDER BY path;

C. WITH RECURSIVE folder_paths AS (SELECT id, name, parent_id, name AS path FROM folders WHERE parent_id IS NULL UNION ALL SELECT f.id, f.name, f.parent_id, fp.path || '/' || f.name FROM folders f JOIN folder_paths fp ON f.parent_id = fp.id) SELECT id, path FROM folder_paths ORDER BY path;

D. WITH RECURSIVE folder_paths AS (SELECT id, name, parent_id, name AS path FROM folders WHERE parent_id IS NULL UNION ALL SELECT f.id, f.name, f.parent_id, fp.path + '/' + f.name FROM folders f JOIN folder_paths fp ON f.parent_id = fp.id) SELECT id, path FROM folder_paths ORDER BY path;

Solution

1. Step 1: Identify correct base case and path initialization

   The base case must select root folders (parent_id IS NULL) and set path to just the folder name without leading '/'. The recursive part builds path as parent_path || '/' || name.

2. Step 2: Compare options with correct logic

   The correct query uses parent_id IS NULL for base, name AS path, and fp.path || '/' || f.name for recursion (PostgreSQL string concat). Distractors fail by using invalid + concat, adding extra '/' (causing '//'), or starting from non-roots (parent_id IS NOT NULL).

3. Final Answer:

   WITH RECURSIVE folder_paths AS (SELECT id, name, parent_id, name AS path FROM folders WHERE parent_id IS NULL UNION ALL SELECT f.id, f.name, f.parent_id, fp.path || '/' || f.name FROM folders f JOIN folder_paths fp ON f.parent_id = fp.id) SELECT id, path FROM folder_paths ORDER BY path; -> Option C

4. Quick Check:

   Use base root rows + '||' concat for paths [OK]

Hint: Use '||' for string concat and start from root folders [OK]

Common Mistakes:

• Using '+' instead of '||' for string concatenation
• Starting recursion from non-root folders
• Adding extra '/' at path start