$each modifier with $push in MongoDB - Time & Space Complexity

Time Complexity: $each modifier with $push

O(n)

Understanding Time Complexity

When we add multiple items to an array in MongoDB using $push with $each, it is important to understand how the time taken grows as we add more items.

We want to know how the work changes when the number of items we add increases.

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

db.collection.updateOne(
  { _id: 1 },
  { $push: { scores: { $each: [85, 90, 95] } } }
)
    

This code adds multiple scores to the scores array of a document with _id 1 using $push and $each.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: Adding each item from the $each array to the target array.
• How many times: Once for each item in the $each array.

How Execution Grows With Input

As the number of items in the $each array grows, the number of operations grows roughly the same way.

Input Size (n)	Approx. Operations
10	10 additions to the array
100	100 additions to the array
1000	1000 additions to the array

Pattern observation: The work grows directly with the number of items added.

Final Time Complexity

Time Complexity: O(n)

This means the time to add items grows in a straight line with the number of items you add.

Common Mistake

[X] Wrong: "Adding multiple items with $each is done in constant time, no matter how many items there are."

[OK] Correct: Each item must be added one by one, so more items mean more work and more time.

Interview Connect

Understanding how batch updates like $push with $each scale helps you reason about database performance and write efficient queries in real projects.

Self-Check

"What if we used $addToSet with $each instead of $push? How would the time complexity change?"

Practice

1. What does the $each modifier do when used with $push in MongoDB?

easy

A. It sorts the array elements after pushing a new value.

B. It adds multiple values to an array in a single update operation.

C. It replaces the entire array with a new set of values.

D. It removes multiple values from an array.

Solution

1. Step 1: Understand $push usage

   $push adds elements to an array field in a document.

2. Step 2: Role of $each modifier

   $each allows adding multiple elements at once inside $push, making the update efficient.

3. Final Answer:

   It adds multiple values to an array in a single update operation. -> Option B

4. Quick Check:

   $each adds many items [OK]

Hint: Remember: $each adds many items inside $push [OK]

Common Mistakes:

• Thinking $each removes items
• Using $each outside $push
• Confusing $each with sorting

2. Which of the following is the correct syntax to add multiple values ["a", "b", "c"] to the array field tags using $push with $each?

easy

A. { $push: { tags: { $each: ["a", "b", "c"] } } }

B. { $push: { tags: ["a", "b", "c"] } }

C. { $push: { tags: { $add: ["a", "b", "c"] } } }

D. { $push: { tags: { $each: "a", "b", "c" } } }

Solution

1. Step 1: Check correct $push syntax

   $push requires a field and a value or modifier object.

2. Step 2: Validate $each usage

   $each must be an array inside $push to add multiple items.

3. Final Answer:

   { $push: { tags: { $each: ["a", "b", "c"] } } } -> Option A

4. Quick Check:

   Correct $each syntax = { $push: { tags: { $each: ["a", "b", "c"] } } } [OK]

Hint: Use $each with an array inside $push [OK]

Common Mistakes:

• Passing array directly without $each
• Using invalid operator like $add
• Incorrect $each format without array brackets

3. Given the document { _id: 1, colors: ["red"] }, what will be the colors array after running this update?

{ $push: { colors: { $each: ["blue", "green"] } } }

medium

A. ["red", ["blue", "green"]]

B. ["blue", "green"]

C. ["red", "blue", "green"]

D. ["red"]

Solution

1. Step 1: Initial array and update operation

   Original array is ["red"]. The update uses $push with $each to add "blue" and "green".

2. Step 2: Effect of $each inside $push

   $each adds each element individually, so "blue" and "green" are appended to the array.

3. Final Answer:

   ["red", "blue", "green"] -> Option C

4. Quick Check:

   Array after update = ["red", "blue", "green"] [OK]

Hint: $each adds items individually, not as a nested array [OK]

Common Mistakes:

• Expecting nested array inside colors
• Replacing array instead of pushing
• Ignoring original array elements

4. What is wrong with this update operation?

{ $push: { items: { $each: "apple", "banana" } } }

medium

A. The $each value must be an array, not separate strings.

B. The $push operator cannot be used with $each.

C. The field name items is invalid.

D. The update syntax is correct and will work as expected.

Solution

1. Step 1: Analyze $each value type

   $each requires an array of values, but here it is given as separate strings without array brackets.

2. Step 2: Identify syntax error

   Passing multiple strings without array brackets causes a syntax error in MongoDB update.

3. Final Answer:

   The $each value must be an array, not separate strings. -> Option A

4. Quick Check:

   $each needs array brackets [OK]

Hint: Always wrap $each values in square brackets [OK]

Common Mistakes:

• Passing multiple values without array brackets
• Confusing $each with $addToSet
• Assuming $push alone can add multiple items

5. You want to add multiple new tags ["urgent", "review", "backend"] to the tags array of a document, but only if they are not already present. Which update operation correctly uses $push with $each and ensures no duplicates?

hard

A. { $push: { tags: { $each: ["urgent", "review", "backend"] } } }

B. { $addToSet: { tags: ["urgent", "review", "backend"] } }

C. { $push: { tags: ["urgent", "review", "backend"] } }

D. { $addToSet: { tags: { $each: ["urgent", "review", "backend"] } } }

Solution

1. Step 1: Understand requirement to avoid duplicates

   $push adds items regardless of duplicates, so it doesn't fit the requirement.

2. Step 2: Use $addToSet with $each

   $addToSet adds unique values only, and supports $each to add multiple items without duplicates.

3. Final Answer:

   { $addToSet: { tags: { $each: ["urgent", "review", "backend"] } } } -> Option D

4. Quick Check:

   $addToSet + $each avoids duplicates [OK]

Hint: Use $addToSet with $each to add unique items [OK]

Common Mistakes:

• Using $push which allows duplicates
• Not using $each with $addToSet
• Passing array directly without $each