Query execution plans in DBMS Theory - Time & Space Complexity

Time Complexity: Query execution plans

O(n)

Understanding Time Complexity

When a database runs a query, it creates a plan to get the data efficiently.

We want to understand how the time to run the query grows as the data size increases.

Scenario Under Consideration

Analyze the time complexity of the following SQL query execution plan snippet.

EXPLAIN SELECT * FROM Orders WHERE CustomerID = 123;
-- The plan shows a table scan or an index seek
-- If no index, full scan of Orders table
-- If index on CustomerID, index seek used

This query fetches all orders for a specific customer using a filter on CustomerID.

Identify Repeating Operations

Look at how the database checks rows to find matches.

• Primary operation: Scanning rows in the Orders table.
• How many times: Once for each row in the table or index.

How Execution Grows With Input

As the number of orders grows, the work to find matching rows changes.

Input Size (n)	Approx. Operations
10	10 rows checked
100	100 rows checked
1000	1000 rows checked

Pattern observation: Without an index, the database checks each row one by one, so work grows directly with data size.

Final Time Complexity

Time Complexity: O(n)

This means the time to run the query grows in direct proportion to the number of rows in the table.

Common Mistake

[X] Wrong: "The query always runs fast regardless of table size."

[OK] Correct: Without an index, the database must check every row, so bigger tables take more time.

Interview Connect

Understanding how query plans affect time helps you explain how databases handle data efficiently in real projects.

Self-Check

"What if we add an index on CustomerID? How would the time complexity change?"

Practice

1. What is the main purpose of a query execution plan in a database?

easy

A. To backup the database

B. To show how the database will execute a query step-by-step

C. To create new tables automatically

D. To store the query results permanently

Solution

1. Step 1: Understand what a query execution plan is

   A query execution plan explains the steps the database takes to run a query.

2. Step 2: Identify the main purpose

   The plan helps users see how the database processes the query to optimize performance.

3. Final Answer:

   To show how the database will execute a query step-by-step -> Option B

4. Quick Check:

   Query execution plan = execution steps [OK]

Hint: Execution plans show query steps clearly [OK]

Common Mistakes:

• Confusing plans with data storage
• Thinking plans create tables
• Assuming plans backup data

2. Which SQL command is commonly used to view the query execution plan before running a query?

easy

A. SHOW PLAN

B. RUN

C. EXPLAIN

D. DESCRIBE

Solution

1. Step 1: Recall the command to view execution plans

   The SQL command EXPLAIN is used to display how a query will be executed.

2. Step 2: Differentiate from other commands

   RUN executes queries, SHOW PLAN is not standard, and DESCRIBE shows table structure.

3. Final Answer:

   EXPLAIN -> Option C

4. Quick Check:

   View plan = EXPLAIN [OK]

Hint: Use EXPLAIN to see query plans [OK]

Common Mistakes:

• Using RUN to view plans
• Confusing DESCRIBE with EXPLAIN
• Assuming SHOW PLAN is standard

3. Given the query SELECT * FROM employees WHERE department_id = 5;, what does the execution plan likely show?

medium

A. A full table scan of employees

B. A join operation with another table

C. A sort operation on employee names

D. An index scan on department_id if indexed

Solution

1. Step 1: Analyze the query condition

   The query filters employees by department_id = 5. If department_id has an index, the database uses it.

2. Step 2: Understand execution plan behavior

   If indexed, the plan shows an index scan to quickly find matching rows instead of scanning the whole table.

3. Final Answer:

   An index scan on department_id if indexed -> Option D

4. Quick Check:

   Indexed filter = index scan [OK]

Hint: Indexed columns use index scan in plans [OK]

Common Mistakes:

• Assuming full table scan always happens
• Expecting join when none exists
• Thinking sorting is automatic

4. A query execution plan shows a full table scan but the query filters on a column that has an index. What is the likely cause?

medium

A. The query uses a function on the indexed column

B. The index is corrupted or unusable

C. The database always prefers full scans

D. The table is empty

Solution

1. Step 1: Understand why indexes may be ignored

   If a query applies a function (like LOWER or CAST) on an indexed column, the index cannot be used directly.

2. Step 2: Rule out other options

   Corrupted indexes are rare and usually cause errors; databases do not always prefer full scans; empty tables do not cause full scans.

3. Final Answer:

   The query uses a function on the indexed column -> Option A

4. Quick Check:

   Functions on indexed columns block index use [OK]

Hint: Functions on indexed columns disable index use [OK]

Common Mistakes:

• Assuming index corruption without error
• Believing full scans are default
• Thinking empty tables cause scans

5. You want to optimize a slow query that joins two large tables. The execution plan shows a nested loop join causing delays. What is a good approach to improve performance?

hard

A. Create indexes on the join columns to enable hash or merge joins

B. Remove all indexes to force full table scans

C. Rewrite the query to use subqueries instead of joins

D. Increase the database cache size without changing the query

Solution

1. Step 1: Identify the cause of slow join

   Nested loop joins are slow on large tables without indexes on join columns.

2. Step 2: Apply indexing to improve join method

   Creating indexes on join columns allows the database to use faster join methods like hash or merge joins.

3. Step 3: Evaluate other options

   Removing indexes slows queries; rewriting to subqueries may not help; increasing cache alone may not fix join inefficiency.

4. Final Answer:

   Create indexes on the join columns to enable hash or merge joins -> Option A

5. Quick Check:

   Indexes on join keys speed joins [OK]

Hint: Index join columns to speed up joins [OK]

Common Mistakes:

• Dropping indexes thinking it helps
• Assuming subqueries are always faster
• Relying only on cache size increase