Recursive CTE for graph traversal in PostgreSQL - Practice Problems & Coding Challenges

Challenge - 5 Problems

❓ query_result

intermediate

Find all reachable nodes from node 1

Given the table edges with columns source and target, what is the output of this recursive CTE query that finds all nodes reachable from node 1?

PostgreSQL

WITH RECURSIVE reachable AS (
  SELECT source, target FROM edges WHERE source = 1
  UNION
  SELECT e.source, e.target FROM edges e
  INNER JOIN reachable r ON e.source = r.target
)
SELECT DISTINCT target FROM reachable ORDER BY target;

A [2, 3]

B [1, 2, 3, 4]

C [2, 3, 4]

D [3, 4]

💡 Hint

Think about how the recursive part expands the reachable nodes starting from source 1.

The base case selects edges starting at node 1. The recursive part joins on the target to find further reachable nodes. The distinct targets collected are nodes 2, 3, and 4.

📝 Syntax

intermediate

Identify the syntax error in recursive CTE

Which option contains a syntax error in this recursive CTE that tries to find all nodes reachable from node 1?

PostgreSQL

WITH RECURSIVE reachable AS (
  SELECT source, target FROM edges WHERE source = 1
  UNION
  SELECT e.source, e.target FROM edges e
  JOIN reachable r ON e.source = r.target
)
SELECT DISTINCT target FROM reachable ORDER BY target;

A No syntax error; query is valid

B Missing keyword RECURSIVE after WITH

C Using JOIN instead of INNER JOIN causes syntax error

D Missing alias for recursive CTE

💡 Hint

Check if JOIN without INNER is valid in PostgreSQL.

In PostgreSQL, JOIN is shorthand for INNER JOIN and is valid syntax. The query has no syntax errors.

❓ optimization

advanced

Optimize recursive CTE to avoid duplicates

Which option optimizes this recursive CTE to avoid revisiting nodes and duplicates in the result?

PostgreSQL

WITH RECURSIVE reachable(node) AS (
  SELECT 1
  UNION
  SELECT e.target FROM edges e
  JOIN reachable r ON e.source = r.node
)
SELECT node FROM reachable ORDER BY node;

A Use UNION ALL instead of UNION

B Add WHERE e.target NOT IN (SELECT node FROM reachable) in recursive part

C Add DISTINCT in the final SELECT

D Add a LIMIT clause to restrict recursion depth

💡 Hint

Prevent revisiting nodes by filtering them out in recursion.

Adding a WHERE clause to exclude already visited nodes prevents infinite loops and duplicates.

🧠 Conceptual

advanced

Understanding recursive CTE termination

What causes a recursive CTE for graph traversal to stop recursing?

A When no new rows are added in the recursive part

B When a maximum recursion depth is reached

C When the base case returns no rows

D When the query uses UNION ALL instead of UNION

💡 Hint

Think about how recursion ends naturally in SQL.

The recursion stops when the recursive SELECT adds no new rows to the result set.

🔧 Debug

expert

Diagnose infinite recursion in recursive CTE

Given this recursive CTE, why does it cause infinite recursion or run indefinitely?

PostgreSQL

WITH RECURSIVE reachable(node) AS (
  SELECT 1
  UNION ALL
  SELECT e.target FROM edges e
  JOIN reachable r ON e.source = r.node
)
SELECT node FROM reachable ORDER BY node;

A Missing ORDER BY in recursive part causes infinite recursion

B Base case selects node 1 incorrectly

C Using UNION instead of UNION ALL causes infinite recursion

D Edges contain cycles and no check prevents revisiting nodes

💡 Hint

Consider what happens if the graph has loops.

If the graph has cycles and the query does not exclude already visited nodes, recursion never ends.

Practice

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

easy

A. To optimize query performance by indexing graph nodes

B. To create temporary tables for storing graph data

C. To repeatedly execute a query that references itself to explore connected nodes

D. To join two unrelated tables without conditions

Solution

1. Step 1: Understand the purpose of recursive CTEs

   Recursive CTEs allow a query to call itself repeatedly, which is useful for exploring connected data like graph nodes.

2. Step 2: Identify the correct use case

   Using WITH RECURSIVE lets you traverse graph structures step-by-step by referencing the CTE inside itself.

3. Final Answer:

   To repeatedly execute a query that references itself to explore connected nodes -> Option C

4. Quick Check:

   Recursive CTE = self-referencing query [OK]

Hint: Recursive CTEs repeat queries to explore connected data [OK]

Common Mistakes:

• Confusing recursive CTE with temporary tables
• Thinking it automatically optimizes performance
• Using it for unrelated table joins

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

easy

A. WITH path RECURSIVE AS (SELECT ... UNION ALL SELECT ... FROM path ...)

B. CREATE RECURSIVE TABLE path AS SELECT ...

C. SELECT RECURSIVE * FROM path

D. WITH RECURSIVE path AS (SELECT ... UNION ALL SELECT ... FROM path ...)

Solution

1. Step 1: Recall the syntax for recursive CTEs

   The correct syntax starts with WITH RECURSIVE cte_name AS ( ... ), where the CTE references itself inside.

2. Step 2: Match the syntax options

   WITH RECURSIVE path AS (SELECT ... UNION ALL SELECT ... FROM path ...) correctly uses WITH RECURSIVE path AS (SELECT ... UNION ALL SELECT ... FROM path ...). Other options misuse keywords or order.

3. Final Answer:

   WITH RECURSIVE path AS (SELECT ... UNION ALL SELECT ... FROM path ...) -> Option D

4. Quick Check:

   WITH RECURSIVE + CTE name + self-reference [OK]

Hint: Start with WITH RECURSIVE cte_name AS (...) [OK]

Common Mistakes:

• Swapping RECURSIVE and CTE name order
• Using CREATE instead of WITH
• Omitting UNION ALL between parts

3. Given the table edges(source INT, target INT) with data:
(1, 2), (2, 3), (3, 4), (2, 5)
What will the following query return?

WITH RECURSIVE path AS (SELECT source, target FROM edges WHERE source = 1 UNION ALL SELECT e.source, e.target FROM edges e JOIN path p ON e.source = p.target) SELECT * FROM path ORDER BY source, target;

medium

A. Rows: (1,2), (2,3), (2,5), (3,4)

B. Rows: (1,2), (2,3), (3,4)

C. Rows: (1,2), (2,5)

D. Empty result

Solution

1. Step 1: Identify the anchor and recursive parts

   The anchor selects edges where source=1: (1,2). The recursive part joins edges where source matches previous target.

2. Step 2: Trace recursive expansion

   From (1,2), next edges with source=2 are (2,3) and (2,5). From (2,3), next edge with source=3 is (3,4). No further edges from 5 or 4.

3. Final Answer:

   Rows: (1,2), (2,3), (2,5), (3,4) -> Option A

4. Quick Check:

   Recursive join expands all reachable edges [OK]

Hint: Follow edges from start node stepwise [OK]

Common Mistakes:

• Ignoring multiple edges from same source
• Stopping recursion too early
• Misordering results

4. Consider this recursive CTE:

WITH RECURSIVE path(node) AS (SELECT 1 UNION ALL SELECT node + 1 FROM path WHERE node < 3) SELECT * FROM path;

What is wrong if this query runs forever without stopping?

medium

A. Not selecting from the CTE in the final SELECT

B. Missing a proper termination condition in the recursive part

C. Using UNION instead of UNION ALL

D. Incorrect anchor query syntax

Solution

1. Step 1: Analyze the recursive condition

   The recursive part adds 1 to node while node < 3, but due to UNION ALL accumulating duplicates of rows satisfying the condition, recursion continues indefinitely.

2. Step 2: Identify why it loops infinitely

   If the termination condition is incorrect or not reached, recursion never stops. Here, the condition is present but ineffective against duplicates, causing infinite loop.

3. Final Answer:

   Missing a proper termination condition in the recursive part -> Option B

4. Quick Check:

   Infinite recursion = no stop condition [OK]

Hint: Check recursive WHERE clause stops recursion [OK]

Common Mistakes:

• Confusing UNION and UNION ALL effects
• Ignoring anchor query correctness
• Forgetting to select from CTE

5. You have a table employees(id INT, manager_id INT) representing a company hierarchy. How would you write a recursive CTE to find all employees under manager with id = 10, including indirect reports?

hard

A. WITH RECURSIVE subordinates AS (
SELECT id FROM employees WHERE manager_id = 10
UNION ALL
SELECT e.id FROM employees e JOIN subordinates s ON e.manager_id = s.id
) SELECT * FROM subordinates;

B. WITH RECURSIVE subordinates AS (
SELECT id FROM employees WHERE id = 10
UNION ALL
SELECT e.id FROM employees e JOIN subordinates s ON e.id = s.manager_id
) SELECT * FROM subordinates;

C. WITH RECURSIVE subordinates AS (
SELECT id FROM employees WHERE manager_id = 10
UNION ALL
SELECT e.manager_id FROM employees e JOIN subordinates s ON e.id = s.id
) SELECT * FROM subordinates;

D. WITH RECURSIVE subordinates AS (
SELECT id FROM employees WHERE manager_id = 10
UNION ALL
SELECT e.id FROM employees e JOIN subordinates s ON e.id = s.manager_id
) SELECT * FROM subordinates;

Solution

1. Step 1: Identify the anchor query

   The anchor selects employees directly reporting to manager 10: WHERE manager_id = 10.

2. Step 2: Understand the recursive join

   The recursive part joins employees whose manager_id matches any previously found employee id, thus finding indirect reports.

3. Final Answer:

   WITH RECURSIVE subordinates AS ( SELECT id FROM employees WHERE manager_id = 10 UNION ALL SELECT e.id FROM employees e JOIN subordinates s ON e.manager_id = s.id ) SELECT * FROM subordinates; -> Option A

4. Quick Check:

   Join on e.manager_id = s.id to find subordinates [OK]

Hint: Join on manager_id = previous employee id to find reports [OK]

Common Mistakes:

• Swapping join conditions (id vs manager_id)
• Starting anchor with wrong WHERE clause
• Selecting wrong columns in recursive part