ABS and MOD functions in SQL - Time & Space Complexity

Time Complexity: ABS and MOD functions

O(n)

Understanding Time Complexity

We want to understand how the time it takes to run ABS and MOD functions changes as we use them on more data.

How does the work grow when we apply these functions to many rows?

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

SELECT
  ABS(salary) AS absolute_salary,
  MOD(employee_id, 10) AS mod_result
FROM employees;

This query calculates the absolute value of salaries and the remainder when employee IDs are divided by 10 for every employee.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: Applying ABS and MOD functions to each row in the employees table.
• How many times: Once for each employee row.

How Execution Grows With Input

Each row requires a fixed amount of work to compute ABS and MOD. So, as the number of rows grows, the total work grows proportionally.

Input Size (n)	Approx. Operations
10	20 function calls
100	200 function calls
1000	2000 function calls

Pattern observation: The total work grows in a straight line with the number of rows.

Final Time Complexity

Time Complexity: O(n)

This means the time to run the query grows directly with the number of rows processed.

Common Mistake

[X] Wrong: "ABS and MOD functions take the same time no matter how many rows there are."

[OK] Correct: Each row needs its own calculation, so more rows mean more total work.

Interview Connect

Understanding how simple functions like ABS and MOD scale helps you explain query performance clearly and confidently.

Self-Check

"What if we added a nested query that calls ABS and MOD multiple times per row? How would the time complexity change?"

Practice

1. What does the SQL function ABS(-15) return?

easy

A. 15

B. -15

C. 0

D. Error

Solution

1. Step 1: Understand the ABS function

   The ABS function returns the absolute value, which means it removes any negative sign from a number.

2. Step 2: Apply ABS to -15

   Applying ABS to -15 gives 15 because it converts the negative number to positive.

3. Final Answer:

   15 -> Option A

4. Quick Check:

   ABS(-15) = 15 [OK]

Hint: ABS always returns a positive number or zero [OK]

Common Mistakes:

• Thinking ABS changes positive numbers
• Confusing ABS with MOD
• Expecting ABS to return negative values

2. Which of the following is the correct syntax to get the remainder of 17 divided by 5 using SQL?

easy

A. SELECT MOD(17, 5);

B. SELECT REMAINDER(17, 5);

C. SELECT 17 % 5;

D. SELECT ABS(17, 5);

Solution

1. Step 1: Identify the correct function for remainder

   In standard SQL, the MOD function returns the remainder after division.

2. Step 2: Check syntax correctness

   MOD takes two arguments: dividend and divisor, so MOD(17, 5) is correct syntax.

3. Final Answer:

   SELECT MOD(17, 5); -> Option A

4. Quick Check:

   MOD syntax = MOD(dividend, divisor) [OK]

Hint: Use MOD(a, b) to get remainder in SQL [OK]

Common Mistakes:

• Using ABS instead of MOD
• Using % which is not standard SQL
• Using REMAINDER which is not standard SQL

3. What is the result of this SQL query?

SELECT ABS(-7) + MOD(20, 6) AS result;

medium

A. 2

B. 8

C. 14

D. 9

Solution

1. Step 1: Calculate ABS(-7)

   ABS(-7) returns 7 because it converts negative to positive.

2. Step 2: Calculate MOD(20, 6)

   20 divided by 6 is 3 with remainder 2, so MOD(20, 6) = 2.

3. Step 3: Add the two results

   7 + 2 = 9.

4. Final Answer:

   9 -> Option D

5. Quick Check:

   ABS(-7) + MOD(20, 6) = 9 [OK]

Hint: Calculate ABS and MOD separately, then add [OK]

Common Mistakes:

• Adding MOD result incorrectly
• Confusing ABS with MOD
• Ignoring negative sign in ABS

4. Identify the error in this SQL query:

SELECT ABS(10, -5) FROM dual;

medium

A. MOD function should be used instead

B. ABS function takes only one argument

C. Missing FROM clause

D. ABS cannot be used with negative numbers

Solution

1. Step 1: Check ABS function argument count

   ABS accepts only one argument, but here it has two (10, -5), which is invalid.

2. Step 2: Understand correct usage

   To get remainder, MOD should be used, but the question asks about error in ABS usage.

3. Final Answer:

   ABS function takes only one argument -> Option B

4. Quick Check:

   ABS single argument only [OK]

Hint: ABS needs exactly one number inside parentheses [OK]

Common Mistakes:

• Using multiple arguments in ABS
• Confusing ABS with MOD
• Ignoring function argument rules

5. You want to find all rows in a table numbers where the absolute value of value is less than 10 and the remainder when value is divided by 3 is 1. Which SQL WHERE clause is correct?

hard

A. WHERE MOD(ABS(value), 3) = 1 AND value < 10

B. WHERE ABS(value) > 10 OR MOD(value, 3) = 1

C. WHERE ABS(value) < 10 AND MOD(value, 3) = 1

D. WHERE ABS(value) < 10 AND MOD(value, 3) = 0

Solution

1. Step 1: Understand the conditions

   We want rows where absolute value of 'value' is less than 10 and remainder of 'value' divided by 3 equals 1.

2. Step 2: Translate conditions into SQL

   ABS(value) < 10 ensures absolute value less than 10; MOD(value, 3) = 1 ensures remainder 1.

3. Step 3: Check options

   WHERE ABS(value) < 10 AND MOD(value, 3) = 1 matches both conditions exactly with AND.

4. Final Answer:

   WHERE ABS(value) < 10 AND MOD(value, 3) = 1 -> Option C

5. Quick Check:

   Use AND to combine ABS and MOD conditions [OK]

Hint: Combine ABS and MOD with AND for multiple conditions [OK]

Common Mistakes:

• Using OR instead of AND
• Mixing up MOD values
• Applying MOD to ABS result incorrectly