Computed pattern for pre-aggregation in MongoDB - Time & Space Complexity

Time Complexity: Computed pattern for pre-aggregation

O(n)

Understanding Time Complexity

When we use computed patterns for pre-aggregation in MongoDB, we want to know how the work grows as data grows.

We ask: How does the time to compute aggregated results change when more data is added?

Scenario Under Consideration

Analyze the time complexity of the following MongoDB aggregation pipeline.

db.orders.aggregate([
  { $match: { status: "completed" } },
  { $group: { _id: "$customerId", totalSpent: { $sum: "$amount" } } },
  { $project: { customerId: "$_id", totalSpent: 1, _id: 0 } }
])

This pipeline filters completed orders, groups them by customer, and sums the amount spent per customer.

Identify Repeating Operations

Look for repeated work inside the pipeline.

• Primary operation: Scanning each order document once to filter and group.
• How many times: Once per document in the orders collection.

How Execution Grows With Input

As the number of orders grows, the pipeline processes each order once.

Input Size (n)	Approx. Operations
10	About 10 document checks and group updates
100	About 100 document checks and group updates
1000	About 1000 document checks and group updates

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

Final Time Complexity

Time Complexity: O(n)

This means the time to compute the aggregation grows linearly with the number of input documents.

Common Mistake

[X] Wrong: "Grouping by customer means the time depends on the number of customers only."

[OK] Correct: The pipeline must still scan every order document to group them, so time depends on total orders, not just customers.

Interview Connect

Understanding how aggregation scales helps you explain data processing costs clearly and shows you can reason about real database workloads.

Self-Check

"What if we added an index on the status field used in $match? How would that affect the time complexity?"

Practice

1. What is the main purpose of using a computed pattern for pre-aggregation in MongoDB?

easy

A. To delete all raw data after aggregation

B. To create indexes on every field automatically

C. To calculate and store summary data ahead of time for faster queries

D. To replicate data across multiple servers

Solution

1. Step 1: Understand pre-aggregation concept

   Pre-aggregation means computing summary data before queries run, so queries are faster.

2. Step 2: Identify the main goal

   The goal is to store computed summaries to avoid recalculating on every query.

3. Final Answer:

   To calculate and store summary data ahead of time for faster queries -> Option C

4. Quick Check:

   Pre-aggregation = faster queries [OK]

Hint: Pre-aggregation means compute summaries before queries [OK]

Common Mistakes:

• Confusing pre-aggregation with data deletion
• Thinking it automatically creates indexes
• Mixing it with data replication

2. Which MongoDB aggregation stage is primarily used to compute grouped summary data for pre-aggregation?

easy

A. $match

B. $group

C. $project

D. $sort

Solution

1. Step 1: Recall aggregation stages

   $group is used to group documents and compute summary values like sums or counts.

2. Step 2: Identify correct stage for pre-aggregation

   Pre-aggregation requires grouping and computing, so $group is the right stage.

3. Final Answer:

   $group -> Option B

4. Quick Check:

   $group = grouping and computing summaries [OK]

Hint: Use $group to compute grouped summaries [OK]

Common Mistakes:

• Choosing $match which filters but does not compute
• Confusing $project with grouping
• Selecting $sort which only orders data

3. Given the following aggregation pipeline, what will be the output?

[{ $group: { _id: "$category", total: { $sum: "$amount" } } }]

Assuming the collection has documents: {category: "A", amount: 10}, {category: "B", amount: 5}, {category: "A", amount: 15}.

medium

A. [{_id: null, total: 30}]

B. [{_id: "A", total: 10}, {_id: "B", total: 5}, {_id: "A", total: 15}]

C. [{_id: "A", total: 15}, {_id: "B", total: 5}]

D. [{_id: "A", total: 25}, {_id: "B", total: 5}]

Solution

1. Step 1: Group documents by category

   Documents with category "A" are grouped together, and category "B" separately.

2. Step 2: Sum amounts per group

   For "A": 10 + 15 = 25; for "B": 5.

3. Final Answer:

   [{_id: "A", total: 25}, {_id: "B", total: 5}] -> Option D

4. Quick Check:

   Sum amounts by category = correct totals [OK]

Hint: Sum amounts grouped by _id field [OK]

Common Mistakes:

• Not grouping sums correctly
• Returning individual documents instead of grouped
• Using null _id which sums all documents

4. Identify the error in this aggregation pipeline for pre-aggregation:

[{ $group: { _id: "$category", total: { $sum: "amount" } } }]

medium

A. Missing $ before amount in $sum operator

B. Incorrect use of $group stage

C. Missing $match stage before $group

D. Using _id field incorrectly

Solution

1. Step 1: Check $sum operator syntax

   $sum requires a field path starting with $, but "amount" is missing the $.

2. Step 2: Confirm correct syntax

   It should be $sum: "$amount" to sum the amount field values.

3. Final Answer:

   Missing $ before amount in $sum operator -> Option A

4. Quick Check:

   $sum needs $field syntax [OK]

Hint: Field names in aggregation need $ prefix [OK]

Common Mistakes:

• Forgetting $ before field names in operators
• Assuming $match is mandatory before $group
• Misusing _id field in $group

5. You want to pre-aggregate sales data by month and product category, storing total sales and average price. Which aggregation pipeline correctly computes these values?

hard

A. [{ $group: { _id: { month: { $month: "$date" }, category: "$category" }, totalSales: { $sum: "$amount" }, avgPrice: { $avg: "$price" } } }]

B. [{ $group: { _id: "$date", totalSales: { $sum: "$amount" }, avgPrice: { $avg: "$price" } } }]

C. [{ $group: { _id: { month: "$date", category: "$category" }, totalSales: { $sum: "$amount" }, avgPrice: { $avg: "$price" } } }]

D. [{ $group: { _id: { month: { $month: "$date" }, category: "$category" }, totalSales: { $sum: "$price" }, avgPrice: { $avg: "$amount" } } }]

Solution

1. Step 1: Group by month and category correctly

   Use $month operator on "$date" to extract month, and include "$category" as second key.

2. Step 2: Compute total sales and average price correctly

   Sum the "$amount" field for totalSales and average the "$price" field for avgPrice.

3. Final Answer:

   [{ $group: { _id: { month: { $month: "$date" }, category: "$category" }, totalSales: { $sum: "$amount" }, avgPrice: { $avg: "$price" } } }] -> Option A

4. Quick Check:

   Group by month+category, sum amount, avg price [OK]

Hint: Use $month for date grouping and correct fields for sum/avg [OK]

Common Mistakes:

• Grouping by full date instead of month
• Swapping sum and avg fields
• Not using $month operator for month extraction