$push operator for adding to arrays in MongoDB - Time & Space Complexity

Time Complexity: $push operator for adding to arrays

O(1)

Understanding Time Complexity

When we add items to arrays in MongoDB using the $push operator, it is important to understand how the time it takes grows as the array gets bigger.

We want to know how the work changes when the array has more elements.

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

    db.collection.updateOne(
      { _id: 1 },
      { $push: { items: "newItem" } }
    )
    

This code adds a new element to the end of the items array inside a document with _id 1.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: Adding one element to the end of an array.
• How many times: This happens once per update call.

How Execution Grows With Input

Adding one item to the end of an array usually takes the same amount of time no matter how big the array is.

Input Size (n)	Approx. Operations
10	1
100	1
1000	1

Pattern observation: The time to add one element stays about the same even if the array grows larger.

Final Time Complexity

Time Complexity: O(1)

This means adding an element with $push takes a constant amount of time regardless of the array size.

Common Mistake

[X] Wrong: "Adding an item with $push takes longer as the array gets bigger because it has to move all elements."

[OK] Correct: MongoDB stores arrays so it can add items at the end quickly without moving existing elements, so the time stays constant.

Interview Connect

Understanding how simple operations like $push scale helps you explain database performance clearly and confidently in interviews.

Self-Check

"What if we used $push with $each to add multiple items at once? How would the time complexity change?"

Practice

1. What does the $push operator do in MongoDB?

easy

A. Adds a new element to the end of an array field in a document

B. Removes an element from an array field in a document

C. Replaces the entire array field with a new array

D. Creates a new collection in the database

Solution

1. Step 1: Understand the purpose of $push

   The $push operator is used to add elements to an existing array field inside a MongoDB document.

2. Step 2: Compare with other options

   Options A, C, and D describe different operations: removing elements, replacing arrays, or creating collections, which are not what $push does.

3. Final Answer:

   Adds a new element to the end of an array field in a document -> Option A

4. Quick Check:

   $push adds elements [OK]

Hint: Remember: $push always adds to array end [OK]

Common Mistakes:

• Confusing $push with $pull (which removes items)
• Thinking $push replaces the whole array
• Mixing $push with collection creation commands

2. Which of the following is the correct syntax to add the value 5 to the array field numbers in a document where _id is 1?

easy

A. db.collection.updateOne({_id: 1}, {$push: {numbers: 5}})

B. db.collection.updateOne({_id: 1}, {$push: numbers: 5})

C. db.collection.updateOne({_id: 1}, {$push: {numbers => 5}})

D. db.collection.updateOne({_id: 1}, {$push: {numbers: [5]}})

Solution

1. Step 1: Identify correct $push syntax

   The correct syntax uses an object with the field name as key and the value to add as value: {$push: {field: value}}.

2. Step 2: Analyze each option

   db.collection.updateOne({_id: 1}, {$push: {numbers: 5}}) matches the correct syntax. db.collection.updateOne({_id: 1}, {$push: numbers: 5}) misses curly braces around the field-value pair. db.collection.updateOne({_id: 1}, {$push: {numbers => 5}}) uses an invalid arrow syntax. db.collection.updateOne({_id: 1}, {$push: {numbers: [5]}}) pushes the array [5] as a single element instead of adding the scalar value 5.

3. Final Answer:

   db.collection.updateOne({_id: 1}, {$push: {numbers: 5}}) -> Option A

4. Quick Check:

   Correct $push syntax uses {$push: {field: value}} [OK]

Hint: Use {$push: {field: value}} with braces [OK]

Common Mistakes:

• Omitting braces around field-value pair
• Using wrong symbols like => instead of :
• Pushing an array when a single value is intended

3. Given the document { _id: 1, tags: ["red", "blue"] }, what will be the tags array after running db.collection.updateOne({_id: 1}, {$push: {tags: "green"}})?

medium

A. ["red", "blue"]

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

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

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

Solution

1. Step 1: Understand $push effect on array

   The $push operator adds the new element to the end of the existing array.

2. Step 2: Apply $push to the given array

   Starting with ["red", "blue"], pushing "green" adds it at the end, resulting in ["red", "blue", "green"].

3. Final Answer:

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

4. Quick Check:

   New item added at array end [OK]

Hint: Remember $push adds at the end of array [OK]

Common Mistakes:

• Assuming $push adds at the start
• Replacing the whole array instead of adding
• Confusing order of elements after push

4. You want to add multiple values ["yellow", "purple"] to the colors array in a document with _id: 2. Which update command will NOT work correctly?

medium

A. db.collection.updateOne({_id: 2}, {$push: {colors: { $each: ["yellow", "purple"] }}})

B. db.collection.updateOne({_id: 2}, {$push: {colors: ["yellow", "purple"]}})

C. db.collection.updateOne({_id: 2}, {$push: {colors: {$each: ["yellow", "purple"]}}})

D. db.collection.updateOne({_id: 2}, {$push: {colors: { $each: ["yellow", "purple" ] }}})

Solution

1. Step 1: Understand how to push multiple items

   To add multiple items to an array, $push must be combined with $each inside the update document.

2. Step 2: Analyze each option

   Options B, C, and D correctly use $each to add multiple values. db.collection.updateOne({_id: 2}, {$push: {colors: ["yellow", "purple"]}}) tries to push an array directly, which will add the entire array as a single element, not multiple elements.

3. Final Answer:

   db.collection.updateOne({_id: 2}, {$push: {colors: ["yellow", "purple"]}}) -> Option B

4. Quick Check:

   Use $each to push multiple items [OK]

Hint: Use $each inside $push for multiple items [OK]

Common Mistakes:

• Pushing an array directly instead of using $each
• Forgetting curly braces around $each
• Using wrong operators like $addToSet instead of $push

5. You have a document { _id: 3, tasks: ["task1"] }. You want to add "task2" and "task3" only if they are not already in the array. Which update command correctly achieves this?

hard

A. db.collection.updateOne({_id: 3}, {$push: {tasks: { $each: ["task2", "task3"] }}})

B. db.collection.updateOne({_id: 3}, {$push: {tasks: { $addToSet: ["task2", "task3"] }}})

C. db.collection.updateOne({_id: 3}, {$addToSet: {tasks: { $each: ["task2", "task3"] }}})

D. db.collection.updateOne({_id: 3}, {$push: {tasks: ["task2", "task3"]}})

Solution

1. Step 1: Understand difference between $push and $addToSet

   $push adds items regardless of duplicates. $addToSet adds items only if they don't exist already.

2. Step 2: Analyze the commands

   db.collection.updateOne({_id: 3}, {$addToSet: {tasks: { $each: ["task2", "task3"] }}}) uses $addToSet with $each to add multiple unique items. Options A and D use $push which can add duplicates. db.collection.updateOne({_id: 3}, {$push: {tasks: { $addToSet: ["task2", "task3"] }}}) incorrectly nests $addToSet inside $push, which is invalid syntax.

3. Final Answer:

   db.collection.updateOne({_id: 3}, {$addToSet: {tasks: { $each: ["task2", "task3"] }}}) -> Option C

4. Quick Check:

   Use $addToSet with $each for unique additions [OK]

Hint: Use $addToSet with $each to avoid duplicates [OK]

Common Mistakes:

• Using $push when duplicates should be avoided
• Nesting $addToSet inside $push incorrectly
• Forgetting $each when adding multiple items