ABS and MOD in MySQL - Time & Space Complexity

Time Complexity: ABS and MOD

O(n)

Understanding Time Complexity

We want to understand how the time it takes to run ABS and MOD functions changes as the amount of data grows.

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

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

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

This code calculates the absolute value of salaries and the remainder when employee IDs are divided by 10 for all employees.

Identify Repeating Operations

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

How Execution Grows With Input

Each employee row requires two simple calculations. As the number of employees grows, the total work grows proportionally.

Input Size (n)	Approx. Operations
10	20 (2 operations x 10 rows)
100	200 (2 operations x 100 rows)
1000	2000 (2 operations x 1000 rows)

Pattern observation: The total work grows directly with the number of rows; doubling rows doubles work.

Final Time Complexity

Time Complexity: O(n)

This means the time to run grows in a straight line with the number of rows processed.

Common Mistake

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

[OK] Correct: While each function is simple, they must be applied to every row, so more rows mean more total work.

Interview Connect

Understanding how simple functions scale with data size helps you explain query performance clearly and confidently.

Self-Check

"What if we applied ABS and MOD only to a filtered subset of rows? How would that affect the time complexity?"

Practice

1. What does the ABS function do in MySQL?

easy

A. Returns the positive value of a number

B. Returns the remainder of a division

C. Returns the square root of a number

D. Returns the largest number in a column

Solution

1. Step 1: Understand the purpose of ABS

   The ABS function converts any number to its positive equivalent, removing any negative sign.

2. Step 2: Compare with other options

   MOD returns remainder, SQRT returns square root, and MAX returns largest value, so they are incorrect.

3. Final Answer:

   Returns the positive value of a number -> Option A

4. Quick Check:

   ABS(-5) = 5 [OK]

Hint: ABS always makes numbers positive, no matter the sign [OK]

Common Mistakes:

• Confusing ABS with MOD function
• Thinking ABS returns square root
• Assuming ABS finds max value

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

easy

A. SELECT 17 / 5;

B. SELECT ABS(17, 5);

C. SELECT REMAINDER(17, 5);

D. SELECT MOD(17, 5);

Solution

1. Step 1: Identify correct function for remainder

   MOD is the MySQL function that returns the remainder after division.

2. Step 2: Check syntax correctness

   MOD takes two arguments: dividend and divisor. '/' operator performs division (17/5 = 3.4), ABS takes one argument, REMAINDER is not a MySQL function.

3. Final Answer:

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

4. Quick Check:

   MOD(17, 5) = 2 [OK]

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

Common Mistakes:

• Using ABS instead of MOD for remainder
• Trying to use '/' operator for remainder
• Using non-existent REMAINDER function

3. What is the output of this query?

SELECT ABS(-12) AS abs_val, MOD(29, 6) AS mod_val;

medium

A. abs_val = 12, mod_val = 5

B. abs_val = -12, mod_val = 5

C. abs_val = 12, mod_val = 23

D. abs_val = -12, mod_val = 23

Solution

1. Step 1: Calculate ABS(-12)

   ABS returns the positive value, so ABS(-12) = 12.

2. Step 2: Calculate MOD(29, 6)

   29 divided by 6 is 4 remainder 5, so MOD(29, 6) = 5.

3. Final Answer:

   abs_val = 12, mod_val = 5 -> Option A

4. Quick Check:

   ABS(-12) = 12, MOD(29,6) = 5 [OK]

Hint: ABS removes sign; MOD gives remainder after division [OK]

Common Mistakes:

• Forgetting ABS makes negative positive
• Mixing up MOD result with division quotient
• Assuming MOD returns division result

4. Identify the error in this MySQL query:

SELECT ABS(-7, 3), MOD(10);

medium

A. Both functions are used correctly

B. ABS function has too many arguments; MOD function missing second argument

C. ABS function missing second argument; MOD function has too many arguments

D. MOD function should be ABS

Solution

1. Step 1: Check ABS function arguments

   ABS takes only one argument, but here it has two (-7, 3), which is incorrect.

2. Step 2: Check MOD function arguments

   MOD requires two arguments, but only one (10) is provided, so it's missing the second argument.

3. Final Answer:

   ABS function has too many arguments; MOD function missing second argument -> Option B

4. Quick Check:

   ABS(-7) valid; MOD(10, x) needs two args [OK]

Hint: ABS needs 1 arg; MOD needs 2 args [OK]

Common Mistakes:

• Passing multiple arguments to ABS
• Using MOD with only one argument
• Assuming MOD can be called like ABS

5. You want to select all rows from a table numbers where the absolute value of the column val divided by 4 leaves a remainder of 1. Which query correctly achieves this?

hard

A. SELECT * FROM numbers WHERE ABS(MOD(val, 4)) = 1;

B. SELECT * FROM numbers WHERE MOD(val, 4) = 1;

C. SELECT * FROM numbers WHERE MOD(ABS(val), 4) = 1;

D. SELECT * FROM numbers WHERE ABS(val) / 4 = 1;

Solution

1. Step 1: Understand the condition

   We want the remainder after dividing the absolute value of val by 4 to be 1.

2. Step 2: Analyze each option

   SELECT * FROM numbers WHERE MOD(val, 4) = 1; uses val directly, ignoring absolute value. SELECT * FROM numbers WHERE MOD(ABS(val), 4) = 1; correctly applies ABS(val) inside MOD. SELECT * FROM numbers WHERE ABS(MOD(val, 4)) = 1; applies ABS after MOD, which can give wrong results if val is negative. SELECT * FROM numbers WHERE ABS(val) / 4 = 1; uses '/' which performs division, not remainder.

3. Final Answer:

   SELECT * FROM numbers WHERE MOD(ABS(val), 4) = 1; -> Option C

4. Quick Check:

   MOD(ABS(val), 4) = 1 filters correctly [OK]

Hint: Apply ABS inside MOD to get remainder of positive value [OK]

Common Mistakes:

• Applying ABS after MOD instead of before
• Using '/' operator for remainder
• Ignoring absolute value in condition