Multiple CTEs in one query in SQL - Time & Space Complexity

Time Complexity: Multiple CTEs in one query

O(n * m)

Understanding Time Complexity

When using multiple CTEs (Common Table Expressions) in one SQL query, it's important to understand how the query's work grows as the data grows.

We want to know how the time to run the query changes when the input data gets bigger.

Scenario Under Consideration

Analyze the time complexity of the following SQL query using multiple CTEs.

WITH cte1 AS (
  SELECT id, value FROM table1 WHERE value > 10
),
cte2 AS (
  SELECT id, description FROM table2
),
cte3 AS (
  SELECT cte1.id, cte1.value, cte2.description
  FROM cte1
  JOIN cte2 ON cte1.id = cte2.id
)
SELECT * FROM cte3 WHERE value < 100;
    

This query defines three CTEs: filtering table1, selecting from table2, then joining them before filtering again.

Identify Repeating Operations

Look for repeated work inside the query.

• Primary operation: Scanning and filtering rows in table1 and table2, then joining rows from both.
• How many times: Each table is scanned once, but the join compares rows from both tables, which depends on their sizes.

How Execution Grows With Input

As the number of rows in table1 and table2 grows, the work to scan and join them grows too.

Input Size (rows in each table)	Approx. Operations
10	About 10 scans + 10x10 = 100 join checks
100	About 100 scans + 100x100 = 10,000 join checks
1000	About 1000 scans + 1000x1000 = 1,000,000 join checks

Pattern observation: The join work grows much faster than scanning alone, roughly multiplying the sizes of both tables.

Final Time Complexity

Time Complexity: O(n * m)

This means the time grows roughly by multiplying the number of rows in the two tables being joined.

Common Mistake

[X] Wrong: "Using multiple CTEs means the query runs multiple times, so time multiplies by the number of CTEs."

[OK] Correct: The database usually runs each CTE once and reuses results, so time depends mostly on the size of data and join operations, not the count of CTEs.

Interview Connect

Understanding how multiple CTEs affect query time helps you explain your thought process clearly and shows you know how databases handle complex queries.

Self-Check

"What if we replaced the join with a simple union of the two CTEs? How would the time complexity change?"

Practice

1. What is the main purpose of using multiple CTEs (Common Table Expressions) in a single SQL query?

easy

A. To automatically create indexes on the tables used

B. To break down complex queries into simpler, named parts for better readability

C. To permanently store intermediate results in the database

D. To speed up the database engine by running queries in parallel

Solution

1. Step 1: Understand the role of CTEs

   CTEs are temporary named result sets used inside a query to organize complex logic.

2. Step 2: Identify the benefit of multiple CTEs

   Using multiple CTEs lets you split a big query into smaller, readable parts without permanent storage or indexing.

3. Final Answer:

   To break down complex queries into simpler, named parts for better readability -> Option B

4. Quick Check:

   Multiple CTEs improve query clarity = D [OK]

Hint: Multiple CTEs split queries into named parts for clarity [OK]

Common Mistakes:

• Thinking CTEs create permanent tables
• Assuming CTEs improve query speed automatically
• Confusing CTEs with indexes

2. Which of the following is the correct syntax to define two CTEs named cte1 and cte2 in one SQL query?

easy

A. WITH cte1 AS (SELECT * FROM table1), cte2 AS (SELECT * FROM table2) SELECT * FROM cte1 JOIN cte2 ON cte1.id = cte2.id;

B. WITH cte1 AS (SELECT * FROM table1) cte2 AS (SELECT * FROM table2) SELECT * FROM cte1 JOIN cte2 ON cte1.id = cte2.id;

C. WITH cte1 (SELECT * FROM table1); WITH cte2 (SELECT * FROM table2); SELECT * FROM cte1 JOIN cte2 ON cte1.id = cte2.id;

D. WITH cte1 = (SELECT * FROM table1), cte2 = (SELECT * FROM table2) SELECT * FROM cte1 JOIN cte2 ON cte1.id = cte2.id;

Solution

1. Step 1: Recall correct CTE syntax

   Multiple CTEs are separated by commas after WITH, each defined as name AS (query).

2. Step 2: Check each option

   WITH cte1 AS (SELECT * FROM table1), cte2 AS (SELECT * FROM table2) SELECT * FROM cte1 JOIN cte2 ON cte1.id = cte2.id; correctly uses commas and AS keyword; others miss commas or use wrong syntax.

3. Final Answer:

   WITH cte1 AS (SELECT * FROM table1), cte2 AS (SELECT * FROM table2) SELECT * FROM cte1 JOIN cte2 ON cte1.id = cte2.id; -> Option A

4. Quick Check:

   Multiple CTEs separated by commas = B [OK]

Hint: Separate multiple CTEs with commas after WITH [OK]

Common Mistakes:

• Omitting commas between CTEs
• Using semicolons between CTEs
• Using equals sign instead of AS

3. Given the following SQL query with multiple CTEs, what will be the output?

WITH cte1 AS (SELECT 1 AS num UNION ALL SELECT 2), cte2 AS (SELECT num FROM cte1 WHERE num = 2) SELECT * FROM cte2;

medium

A. 1 and 2

B. 1

C. 2

D. No rows returned

Solution

1. Step 1: Analyze cte1 content

   cte1 returns two rows with num values 1 and 2.

2. Step 2: Analyze cte2 filtering

   cte2 selects only rows from cte1 where num = 2, so only one row with num=2.

3. Final Answer:

   2 -> Option C

4. Quick Check:

   cte2 filters num=2 = A [OK]

Hint: Trace each CTE step-by-step to find final output [OK]

Common Mistakes:

• Assuming cte2 returns all rows from cte1
• Confusing UNION ALL with UNION
• Ignoring the WHERE filter in cte2

4. Identify the error in the following SQL query using multiple CTEs:

WITH cte1 AS (SELECT id, name FROM users) SELECT * FROM cte1; WITH cte2 AS (SELECT id FROM orders) SELECT * FROM cte2;

medium

A. CTEs cannot select from tables

B. CTEs must be named with different names

C. Missing JOIN condition between cte1 and cte2

D. Multiple WITH clauses are not allowed in one query

Solution

1. Step 1: Review CTE syntax rules

   Only one WITH clause is allowed per query; multiple CTEs must be separated by commas inside one WITH.

2. Step 2: Identify the error in the query

   The query uses two separate WITH clauses, which is invalid syntax.

3. Final Answer:

   Multiple WITH clauses are not allowed in one query -> Option D

4. Quick Check:

   Only one WITH clause per query = A [OK]

Hint: Use one WITH clause with commas for multiple CTEs [OK]

Common Mistakes:

• Writing multiple WITH clauses in one query
• Forgetting commas between CTEs
• Assuming CTEs create permanent tables

5. You want to calculate the average order amount per customer and then find customers whose average order is above 100. Which of the following queries correctly uses multiple CTEs to achieve this?

hard

A. WITH avg_orders AS (SELECT customer_id, AVG(amount) AS avg_amount FROM orders GROUP BY customer_id), high_avg AS (SELECT customer_id FROM avg_orders WHERE avg_amount > 100) SELECT * FROM high_avg;

B. WITH avg_orders AS (SELECT customer_id, AVG(amount) AS avg_amount FROM orders), high_avg AS (SELECT customer_id FROM avg_orders WHERE avg_amount > 100) SELECT * FROM high_avg;

C. WITH avg_orders AS (SELECT customer_id, amount FROM orders GROUP BY customer_id), high_avg AS (SELECT customer_id FROM avg_orders WHERE amount > 100) SELECT * FROM high_avg;

D. WITH avg_orders AS (SELECT customer_id, AVG(amount) AS avg_amount FROM orders GROUP BY customer_id) SELECT * FROM avg_orders WHERE avg_amount > 100;

Solution

1. Step 1: Calculate average order per customer

   WITH avg_orders AS (SELECT customer_id, AVG(amount) AS avg_amount FROM orders GROUP BY customer_id), high_avg AS (SELECT customer_id FROM avg_orders WHERE avg_amount > 100) SELECT * FROM high_avg; correctly groups orders by customer_id and calculates AVG(amount).

2. Step 2: Filter customers with avg_amount > 100

   WITH avg_orders AS (SELECT customer_id, AVG(amount) AS avg_amount FROM orders GROUP BY customer_id), high_avg AS (SELECT customer_id FROM avg_orders WHERE avg_amount > 100) SELECT * FROM high_avg; uses a second CTE to filter customers with average above 100, then selects from it.

3. Final Answer:

   WITH avg_orders AS (SELECT customer_id, AVG(amount) AS avg_amount FROM orders GROUP BY customer_id), high_avg AS (SELECT customer_id FROM avg_orders WHERE avg_amount > 100) SELECT * FROM high_avg; -> Option A

4. Quick Check:

   Multiple CTEs for calculation and filtering = C [OK]

Hint: Use one CTE to calculate, second to filter results [OK]

Common Mistakes:

• Missing GROUP BY when calculating averages
• Not filtering on aggregated column
• Incorrect CTE definitions without commas