$push accumulator for building arrays in MongoDB - Time & Space Complexity

Time Complexity: $push accumulator for building arrays

O(n)

Understanding Time Complexity

We want to understand how the time needed to build arrays using the $push accumulator changes as the input data grows.

Specifically, how does adding elements to arrays during aggregation scale with more data?

Scenario Under Consideration

Analyze the time complexity of the following MongoDB aggregation snippet using $push.

db.orders.aggregate([
  { $group: {
      _id: "$customerId",
      items: { $push: "$item" }
    }
  }
])

This groups orders by customer and builds an array of items each customer ordered.

Identify Repeating Operations

Look for repeated actions that affect time.

• Primary operation: Adding each order's item to the customer's array using $push.
• How many times: Once for every order document processed.

How Execution Grows With Input

As the number of orders grows, the number of pushes grows the same way.

Input Size (n)	Approx. Operations
10	10 pushes to arrays
100	100 pushes to arrays
1000	1000 pushes to arrays

Pattern observation: The number of operations grows directly with the number of input documents.

Final Time Complexity

Time Complexity: O(n)

This means the time to build the arrays grows linearly as more documents are processed.

Common Mistake

[X] Wrong: "Using $push is instant and does not depend on input size."

[OK] Correct: Each $push adds one element per document, so more documents mean more pushes and more time.

Interview Connect

Understanding how accumulators like $push scale helps you explain data aggregation efficiency clearly in real projects.

Self-Check

What if we replaced $push with $addToSet? How would the time complexity change?

Practice

1. What does the $push accumulator do in a MongoDB aggregation pipeline?

easy

A. It removes duplicate values from an array.

B. It adds values to an array for each group in the aggregation.

C. It sorts the documents in the aggregation result.

D. It counts the number of documents in each group.

Solution

1. Step 1: Understand the purpose of $push

   The $push accumulator collects values into an array for each group during aggregation.

2. Step 2: Compare with other accumulators

   Unlike $addToSet which removes duplicates, $push simply appends values, allowing duplicates.

3. Final Answer:

   It adds values to an array for each group in the aggregation. -> Option B

4. Quick Check:

   $push = add values to array [OK]

Hint: Remember: $push always appends values to arrays [OK]

Common Mistakes:

• Confusing $push with $addToSet which removes duplicates
• Thinking $push sorts the array automatically
• Assuming $push counts documents instead of collecting values

2. Which of the following is the correct syntax to use $push in a MongoDB aggregation $group stage?

easy

A. { $group: { _id: "$category", items: { $push: { "$item" } } } }

B. { $group: { _id: "$category", items: { $push: ["$item"] } } }

C. { $group: { _id: "$category", items: { $push: "$item" } } }

D. { $group: { _id: "$category", items: { push: "$item" } } }

Solution

1. Step 1: Review correct $push syntax

   The $push operator requires a field name with a value to push, like $push: "$item".

2. Step 2: Identify syntax errors in options

   { $group: { _id: "$category", items: { $push: ["$item"] } } } incorrectly uses an array around "$item". { $group: { _id: "$category", items: { $push: { "$item" } } } } uses braces instead of quotes. { $group: { _id: "$category", items: { push: "$item" } } } misses the $ sign before push.

3. Final Answer:

   { $group: { _id: "$category", items: { $push: "$item" } } } -> Option C

4. Quick Check:

   Correct $push syntax = { $group: { _id: "$category", items: { $push: "$item" } } } [OK]

Hint: Use $push: "fieldName" inside $group stage [OK]

Common Mistakes:

• Forgetting the $ before push
• Using arrays or objects incorrectly inside $push
• Misplacing quotes around field names

3. Given the collection orders with documents:

{ "customer": "Alice", "product": "Pen" }

{ "customer": "Alice", "product": "Notebook" }

{ "customer": "Bob", "product": "Pen" }

What will be the result of this aggregation?

{ $group: { _id: "$customer", products: { $push: "$product" } } }

medium

A. [{ "_id": "Alice", "products": ["Pen", "Notebook"] }, { "_id": "Bob", "products": ["Pen"] }]

B. [{ "_id": "Alice", "products": "Pen" }, { "_id": "Bob", "products": "Pen" }]

C. [{ "_id": "Alice", "products": ["Notebook"] }, { "_id": "Bob", "products": ["Pen"] }]

D. [{ "_id": "Alice", "products": [] }, { "_id": "Bob", "products": [] }]

Solution

1. Step 1: Group documents by customer

   The aggregation groups documents by the "customer" field, so Alice and Bob form separate groups.

2. Step 2: Use $push to collect products

   For each group, $push collects all "product" values into an array. Alice has "Pen" and "Notebook", Bob has "Pen".

3. Final Answer:

   [{ "_id": "Alice", "products": ["Pen", "Notebook"] }, { "_id": "Bob", "products": ["Pen"] }] -> Option A

4. Quick Check:

   Group by customer + $push products = [{ "_id": "Alice", "products": ["Pen", "Notebook"] }, { "_id": "Bob", "products": ["Pen"] }] [OK]

Hint: Group by field, $push collects all matching values in array [OK]

Common Mistakes:

• Expecting $push to return single value instead of array
• Confusing $push with $first or $last accumulator
• Ignoring grouping effect on output structure

4. You wrote this aggregation but it throws an error:

{ $group: { _id: "$category", items: { $push: "$item" } } }

What is the likely cause of the error?

medium

A. The field names "category" or "item" do not exist in the documents.

B. You forgot to include the $match stage before $group.

C. The $push operator cannot be used inside $group.

D. The _id field cannot be a string.

Solution

1. Step 1: Check field existence in documents

   If the fields "category" or "item" do not exist in the documents, $push will fail because it tries to access missing fields.

2. Step 2: Validate other options

   $push is valid inside $group, $match is optional, and _id can be a string. So these are not causes of error.

3. Final Answer:

   The field names "category" or "item" do not exist in the documents. -> Option A

4. Quick Check:

   Missing fields cause $push error [OK]

Hint: Verify fields exist before using $push on them [OK]

Common Mistakes:

• Assuming $push requires $match stage
• Thinking _id cannot be string
• Believing $push is invalid inside $group

5. You want to group sales by store and collect all product names sold, but only unique products without duplicates. Which aggregation pipeline correctly uses $push and another operator to achieve this?

hard

A. { $group: { _id: "$store", products: { $push: "$product" } } }

B. { $group: { _id: "$store", products: { $push: { $each: "$product" } } } }

C. { $group: { _id: "$store", products: { $push: { $addToSet: "$product" } } } }

D. { $group: { _id: "$store", products: { $addToSet: "$product" } } }

Solution

1. Step 1: Understand $push vs $addToSet

   $push collects all values including duplicates. $addToSet collects unique values only.

2. Step 2: Identify correct usage for unique array

   To get unique products per store, use $addToSet: "$product" inside $group.

3. Step 3: Analyze other options

   { $group: { _id: "$store", products: { $push: "$product" } } } uses $push (duplicates allowed). { $group: { _id: "$store", products: { $push: { $addToSet: "$product" } } } } nests $addToSet inside $push which is invalid. { $group: { _id: "$store", products: { $push: { $each: "$product" } } } } misuses $each inside $push.

4. Final Answer:

   { $group: { _id: "$store", products: { $addToSet: "$product" } } } -> Option D

5. Quick Check:

   Unique array needs $addToSet, not $push [OK]

Hint: Use $addToSet for unique arrays, $push allows duplicates [OK]

Common Mistakes:

• Using $push when unique values are needed
• Nesting $addToSet inside $push incorrectly
• Misusing $each inside $push accumulator