Integer types (smallint, integer, bigint) in PostgreSQL - Time & Space Complexity

Time Complexity: Integer types (smallint, integer, bigint)

O(n)

Understanding Time Complexity

When working with integer types in PostgreSQL, it's helpful to understand how operations on these types scale as data grows.

We want to see how the time to process integers changes when using smallint, integer, or bigint types.

Scenario Under Consideration

Analyze the time complexity of inserting and querying integer values of different sizes.

-- Create a table with an integer column
CREATE TABLE numbers (
  id SERIAL PRIMARY KEY,
  value INTEGER
);

-- Insert n integer values
INSERT INTO numbers (value)
SELECT generate_series(1, n);

-- Query all values
SELECT * FROM numbers WHERE value > 0;
    

This code inserts n integer values and then queries all rows with a simple condition.

Identify Repeating Operations

Look for repeated actions that affect performance.

• Primary operation: Inserting and scanning n rows in the table.
• How many times: Each row is inserted once and scanned once during the query.

How Execution Grows With Input

As the number of rows n increases, the work to insert and query grows roughly in proportion.

Input Size (n)	Approx. Operations
10	About 10 insert and 10 scan operations
100	About 100 insert and 100 scan operations
1000	About 1000 insert and 1000 scan operations

Pattern observation: The operations increase linearly as n grows.

Final Time Complexity

Time Complexity: O(n)

This means the time to insert and query grows directly with the number of rows.

Common Mistake

[X] Wrong: "Using bigint instead of integer will slow down queries significantly because bigger numbers are harder to process."

[OK] Correct: The difference in processing time between smallint, integer, and bigint is very small and usually does not affect query time noticeably. The main factor is the number of rows, not the integer size.

Interview Connect

Understanding how data size affects query time helps you write efficient database code and explain your reasoning clearly in interviews.

Self-Check

"What if we added an index on the integer column? How would the time complexity of queries change?"

Practice

1. Which PostgreSQL integer type is best suited for storing very large whole numbers?

easy

A. bigint

B. smallint

C. integer

D. decimal

Solution

1. Step 1: Understand integer types and their sizes

   smallint stores small numbers, integer stores medium-sized numbers, and bigint stores very large numbers.

2. Step 2: Identify the type for very large whole numbers

   Since the question asks for very large whole numbers, bigint is the correct choice.

3. Final Answer:

   bigint -> Option A

4. Quick Check:

   Very large whole numbers = bigint [OK]

Hint: Biggest integer type is bigint for very large numbers [OK]

Common Mistakes:

• Confusing smallint with bigint
• Choosing decimal which is for decimals, not integers
• Picking integer which is medium size

2. Which of the following is the correct way to declare a column named age as a 2-byte integer in PostgreSQL?

easy

A. age INT2(2);

B. age INTEGER(2);

C. age BIGINT(2);

D. age SMALLINT;

Solution

1. Step 1: Recall PostgreSQL integer type syntax

   PostgreSQL uses SMALLINT for 2-byte integers. The syntax is simply column_name SMALLINT;.

2. Step 2: Evaluate each option

   age SMALLINT; uses correct syntax. The other options incorrectly use size in parentheses (like INT2(2), INTEGER(2), BIGINT(2)), which is invalid for integer types in PostgreSQL.

3. Final Answer:

   age SMALLINT; -> Option D

4. Quick Check:

   2-byte integer = SMALLINT syntax [OK]

Hint: Use SMALLINT keyword for 2-byte integers, no size in parentheses [OK]

Common Mistakes:

• Adding size in parentheses like INTEGER(2)
• Using BIGINT for small numbers
• Specifying size like INT2(2) for integer types

3. What will be the result of this PostgreSQL query?

CREATE TABLE test_numbers (num SMALLINT); INSERT INTO test_numbers VALUES (40000); SELECT * FROM test_numbers;

medium

A. 40000

B. Error: integer out of range

C. 0

D. NULL

Solution

1. Step 1: Understand SMALLINT range

   SMALLINT can store values from -32768 to 32767 only.

2. Step 2: Check inserted value against range

   40000 is greater than 32767, so inserting it causes an error.

3. Final Answer:

   Error: integer out of range -> Option B

4. Quick Check:

   40000 > SMALLINT max 32767 = error [OK]

Hint: Check value fits type range; else error occurs [OK]

Common Mistakes:

• Assuming value truncates silently
• Expecting 0 or NULL instead of error
• Confusing SMALLINT range with INTEGER

4. You wrote this table definition:

CREATE TABLE sales (id INTEGER, amount SMALLINT);

But when inserting a large amount like 40000, you get an error. How do you fix it?

medium

A. Change amount column type to INTEGER

B. Change id column type to SMALLINT

C. Insert smaller values only

D. Change amount column type to tinyint

Solution

1. Step 1: Identify cause of error

   Amount column is SMALLINT which maxes at 32767, so 40000 is too large.

2. Step 2: Choose appropriate type to hold 40000

   INTEGER can hold values up to 2,147,483,647, so changing amount to INTEGER fixes the error.

3. Final Answer:

   Change amount column type to INTEGER -> Option A

4. Quick Check:

   40000 fits INTEGER but not SMALLINT [OK]

Hint: Use INTEGER for values larger than 32767 [OK]

Common Mistakes:

• Changing unrelated column type
• Trying to insert smaller values only
• Choosing tinyint which is a MySQL type, not PostgreSQL

5. You need to store user IDs that can be very large numbers, possibly exceeding 2 billion. Which PostgreSQL integer type should you choose and why?

hard

A. smallint because it uses less storage

B. integer because it supports up to 2 billion

C. bigint because it supports numbers larger than 2 billion

D. serial because it auto-increments

Solution

1. Step 1: Understand size limits of integer types

   smallint max is 32767, integer max is about 2,147,483,647, bigint supports much larger numbers.

2. Step 2: Match requirement to type

   User IDs may exceed 2 billion, so integer is insufficient. bigint is needed to store larger values.

3. Final Answer:

   bigint because it supports numbers larger than 2 billion -> Option C

4. Quick Check:

   IDs > 2 billion need bigint [OK]

Hint: Use bigint for numbers larger than 2 billion [OK]

Common Mistakes:

• Choosing smallint for large IDs
• Assuming integer supports >2 billion
• Confusing serial with integer size