Percent of total with window functions in SQL - Time & Space Complexity

Time Complexity: Percent of total with window functions

O(n)

Understanding Time Complexity

When we use window functions to calculate percent of total, we want to know how the work grows as the data grows.

How does the time to run the query change when the number of rows increases?

Scenario Under Consideration

Analyze the time complexity of the following SQL query using window functions.

SELECT
  category,
  sales,
  sales * 100.0 / SUM(sales) OVER () AS percent_of_total
FROM
  sales_data;
    

This query calculates each category's sales and what percent it is of the total sales.

Identify Repeating Operations

Look for repeated work done by the query.

• Primary operation: Scanning all rows once to compute the total sales and then computing percent for each row.
• How many times: The total sum is computed once, and then each row is processed once to calculate the percent.

How Execution Grows With Input

As the number of rows grows, the total sum calculation scans all rows once, then each row gets its percent calculated.

Input Size (n)	Approx. Operations
10	About 20 operations (10 to sum, 10 to calculate percent)
100	About 200 operations
1000	About 2000 operations

Pattern observation: The work grows roughly in direct proportion to the number of rows.

Final Time Complexity

Time Complexity: O(n)

This means the time to run the query grows linearly as the number of rows increases.

Common Mistake

[X] Wrong: "Using window functions means the query runs multiple times for each row, so it's much slower than a simple sum."

[OK] Correct: The window function computes the total sum once over all rows, then applies the calculation per row without repeating the full sum each time.

Interview Connect

Understanding how window functions scale helps you explain query performance clearly and shows you know how databases handle calculations efficiently.

Self-Check

What if we changed the window function to partition by category? How would the time complexity change?

Practice

1. What does the SQL window function SUM(column) OVER () compute in a query?

easy

A. The maximum value of the column

B. The total sum of the column across all rows without grouping

C. The average of the column values

D. The sum of the column for each group defined by GROUP BY

Solution

1. Step 1: Understand window function syntax

   The syntax SUM(column) OVER () means sum over all rows without partitioning or grouping.

2. Step 2: Compare with GROUP BY sum

   Unlike GROUP BY, this sums the entire column across all rows, returning the same total for each row.

3. Final Answer:

   The total sum of the column across all rows without grouping -> Option B

4. Quick Check:

   SUM() OVER () = total sum [OK]

Hint: SUM() OVER () gives total sum for all rows, no grouping [OK]

Common Mistakes:

• Confusing window sum with GROUP BY sum
• Thinking it calculates average
• Assuming it returns max value

2. Which of the following SQL queries correctly calculates the percent of total sales per product using window functions?

easy

A. SELECT product, sales, (sales / SUM(sales) OVER ()) * 100 AS percent_total FROM sales_table;

B. SELECT product, sales, (SUM(sales) OVER () / sales) * 100 AS percent_total FROM sales_table;

C. SELECT product, sales, (sales / SUM(sales)) * 100 AS percent_total FROM sales_table GROUP BY product;

D. SELECT product, sales, (sales / COUNT(*) OVER ()) * 100 AS percent_total FROM sales_table;

Solution

1. Step 1: Identify correct window function usage

   SELECT product, sales, (sales / SUM(sales) OVER ()) * 100 AS percent_total FROM sales_table; uses SUM(sales) OVER () to get total sales across all rows, then divides each sales value by this total.

2. Step 2: Check other options for errors

   SELECT product, sales, (SUM(sales) OVER () / sales) * 100 AS percent_total FROM sales_table; divides total by sales (wrong direction). SELECT product, sales, (sales / SUM(sales)) * 100 AS percent_total FROM sales_table GROUP BY product; uses SUM(sales) without OVER(), which requires GROUP BY and won't work as intended. SELECT product, sales, (sales / COUNT(*) OVER ()) * 100 AS percent_total FROM sales_table; divides sales by count of rows, not sum.

3. Final Answer:

   SELECT product, sales, (sales / SUM(sales) OVER ()) * 100 AS percent_total FROM sales_table; -> Option A

4. Quick Check:

   Percent = sales / total sales * 100 [OK]

Hint: Divide sales by SUM() OVER () and multiply by 100 [OK]

Common Mistakes:

• Reversing numerator and denominator
• Using SUM() without OVER() in window context
• Using COUNT() instead of SUM() for total

3. Given the table sales_data with columns product and amount, what is the output of this query?

SELECT product, amount, ROUND((amount / SUM(amount) OVER ()) * 100, 1) AS percent_total FROM sales_data ORDER BY product;

Assume the data:
product | amount
-------|-------
A | 50
B | 30
C | 20

medium

A. [{"product": "A", "amount": 50, "percent_total": 100.0}, {"product": "B", "amount": 30, "percent_total": 100.0}, {"product": "C", "amount": 20, "percent_total": 100.0}]

B. [{"product": "A", "amount": 50, "percent_total": 33.3}, {"product": "B", "amount": 30, "percent_total": 20.0}, {"product": "C", "amount": 20, "percent_total": 13.3}]

C. [{"product": "A", "amount": 50, "percent_total": 25.0}, {"product": "B", "amount": 30, "percent_total": 15.0}, {"product": "C", "amount": 20, "percent_total": 10.0}]

D. [{"product": "A", "amount": 50, "percent_total": 50.0}, {"product": "B", "amount": 30, "percent_total": 30.0}, {"product": "C", "amount": 20, "percent_total": 20.0}]

Solution

1. Step 1: Calculate total amount

   Total = 50 + 30 + 20 = 100.

2. Step 2: Calculate percent for each product

   Percent = (amount / total) * 100 rounded to 1 decimal:
   A: (50/100)*100 = 50.0
   B: (30/100)*100 = 30.0
   C: (20/100)*100 = 20.0

3. Final Answer:

   [{"product": "A", "amount": 50, "percent_total": 50.0}, {"product": "B", "amount": 30, "percent_total": 30.0}, {"product": "C", "amount": 20, "percent_total": 20.0}] -> Option D

4. Quick Check:

   Percent totals sum to 100% [OK]

Hint: Sum amounts, divide each by total, multiply by 100 [OK]

Common Mistakes:

• Not rounding results
• Using COUNT() instead of SUM()
• Calculating percent incorrectly (e.g., reversed division)

4. You wrote this query to calculate percent of total sales:

SELECT product, sales, (sales / SUM(sales)) * 100 AS percent_total FROM sales_table;

But it gives an error. What is the problem?

medium

A. SUM(sales) requires a GROUP BY clause or window function syntax

B. sales column does not exist

C. Multiplying by 100 is invalid syntax

D. Missing WHERE clause

Solution

1. Step 1: Analyze use of SUM() without OVER()

   SUM(sales) without GROUP BY or window function context causes error because SQL doesn't know how to aggregate without grouping.

2. Step 2: Correct usage

   Use either GROUP BY product with SUM(sales) or use window function SUM(sales) OVER () to get total sum without grouping.

3. Final Answer:

   SUM(sales) requires a GROUP BY clause or window function syntax -> Option A

4. Quick Check:

   SUM() needs GROUP BY or OVER() [OK]

Hint: Use SUM() OVER () or GROUP BY with SUM() [OK]

Common Mistakes:

• Ignoring need for GROUP BY with aggregate functions
• Assuming multiplication by 100 causes error
• Thinking WHERE clause is mandatory here

5. You have a table orders with columns category and amount. Write a query to show each category, total amount per category, and percent of total amount across all categories. Which query is correct?

hard

A. SELECT category, SUM(amount) AS category_total, (SUM(amount) / COUNT(*) OVER ()) * 100 AS percent_total FROM orders GROUP BY category;

B. SELECT category, amount, (amount / SUM(amount) OVER ()) * 100 AS percent_total FROM orders ORDER BY category;

C. SELECT category, SUM(amount) AS category_total, (SUM(amount) / SUM(SUM(amount)) OVER ()) * 100 AS percent_total FROM orders GROUP BY category ORDER BY category;

D. SELECT category, SUM(amount) AS category_total, (SUM(amount) / SUM(amount)) * 100 AS percent_total FROM orders GROUP BY category;

Solution

1. Step 1: Calculate total per category

   Use SUM(amount) GROUP BY category to get total per category.

2. Step 2: Calculate percent of total across all categories

   Use window function SUM(SUM(amount)) OVER () to get grand total across all categories, then divide category total by this and multiply by 100.

3. Step 3: Verify query correctness

   SELECT category, SUM(amount) AS category_total, (SUM(amount) / SUM(SUM(amount)) OVER ()) * 100 AS percent_total FROM orders GROUP BY category ORDER BY category; correctly combines GROUP BY with window function for total sum. SELECT category, amount, (amount / SUM(amount) OVER ()) * 100 AS percent_total FROM orders ORDER BY category; uses amount per row, not category total. SELECT category, SUM(amount) AS category_total, (SUM(amount) / COUNT(*) OVER ()) * 100 AS percent_total FROM orders GROUP BY category; incorrectly uses COUNT() for total. SELECT category, SUM(amount) AS category_total, (SUM(amount) / SUM(amount)) * 100 AS percent_total FROM orders GROUP BY category; divides sum by itself, always 100%.

4. Final Answer:

   SELECT category, SUM(amount) AS category_total, (SUM(amount) / SUM(SUM(amount)) OVER ()) * 100 AS percent_total FROM orders GROUP BY category ORDER BY category; -> Option C

5. Quick Check:

   Percent = category sum / total sum * 100 [OK]

Hint: Use GROUP BY with SUM() and window SUM(SUM(amount)) OVER () for total [OK]

Common Mistakes:

• Using row amount instead of category sum
• Using COUNT() instead of SUM() for total
• Dividing sum by itself always gives 100%