$mul operator for multiplication in MongoDB - Time & Space Complexity

Time Complexity: $mul operator for multiplication

O(n)

Understanding Time Complexity

We want to understand how the time it takes to multiply fields in MongoDB grows as the number of documents increases.

How does using the $mul operator affect the work done when updating many records?

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

db.products.updateMany(
  { category: "books" },
  { $mul: { price: 1.1 } }
)

This code multiplies the price field by 1.1 for all products in the "books" category.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: Multiplying the price field for each matching document.
• How many times: Once for each document that matches the filter (all "books" products).

How Execution Grows With Input

As the number of matching documents grows, the total work grows proportionally.

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

Pattern observation: Doubling the number of documents doubles the work.

Final Time Complexity

Time Complexity: O(n)

This means the time to complete the multiplication grows linearly with the number of documents updated.

Common Mistake

[X] Wrong: "Using $mul updates all documents instantly regardless of count."

[OK] Correct: Each document must be processed individually, so more documents mean more work and more time.

Interview Connect

Understanding how update operations scale helps you explain database performance clearly and confidently in real situations.

Self-Check

"What if we added a filter that matches only a fixed number of documents regardless of total size? How would the time complexity change?"

Practice

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

easy

A. It multiplies the value of a field by a specified number.

B. It adds a specified number to the value of a field.

C. It divides the value of a field by a specified number.

D. It subtracts a specified number from the value of a field.

Solution

1. Step 1: Understand the purpose of $mul

   The $mul operator is used to multiply the value of a numeric field by a given number in an update operation.

2. Step 2: Compare with other arithmetic operators

   Unlike $inc which adds, or $div which divides, $mul specifically multiplies the field value.

3. Final Answer:

   It multiplies the value of a field by a specified number. -> Option A

4. Quick Check:

   $mul = multiply [OK]

Hint: Remember: $mul means multiply field by number [OK]

Common Mistakes:

• Confusing $mul with $inc (addition)
• Thinking $mul divides instead of multiplies
• Assuming $mul works on non-numeric fields

2. Which of the following is the correct syntax to multiply the field price by 3 in a MongoDB update?

easy

A. { $mul: { price: price * 3 } }

B. { $mul: { 3: price } }

C. { $mul: { price: "3" } }

D. { $mul: { price: 3 } }

Solution

1. Step 1: Identify correct operator usage

   The $mul operator requires a field name as key and a numeric multiplier as value.

2. Step 2: Check each option's structure

   { $mul: { price: 3 } } correctly uses { $mul: { price: 3 } }. { $mul: { 3: price } } reverses key and value. { $mul: { price: "3" } } uses a string instead of number. { $mul: { price: price * 3 } } uses an invalid expression.

3. Final Answer:

   { $mul: { price: 3 } } -> Option D

4. Quick Check:

   Correct syntax = { $mul: { price: 3 } } [OK]

Hint: Use field name as key and number as value inside $mul [OK]

Common Mistakes:

• Using string instead of number for multiplier
• Swapping key and value inside $mul
• Trying to use expressions inside $mul

3. Given a document { _id: 1, quantity: 5, price: 10 }, what will be the document after running db.collection.updateOne({ _id: 1 }, { $mul: { quantity: 2, price: 3 } })?

medium

A. { _id: 1, quantity: 2, price: 3 }

B. { _id: 1, quantity: 10, price: 30 }

C. { _id: 1, quantity: 5, price: 10 }

D. { _id: 1, quantity: 7, price: 13 }

Solution

1. Step 1: Understand the update operation

   The $mul operator multiplies each specified field by the given number. Here, quantity is multiplied by 2 and price by 3.

2. Step 2: Calculate new field values

   Original quantity 5 * 2 = 10, original price 10 * 3 = 30.

3. Final Answer:

   { _id: 1, quantity: 10, price: 30 } -> Option B

4. Quick Check:

   5*2=10 and 10*3=30 [OK]

Hint: Multiply each field value by given number in $mul [OK]

Common Mistakes:

• Adding instead of multiplying
• Not updating all specified fields
• Confusing field names or values

4. You run this update: db.products.updateOne({ _id: 2 }, { $mul: { stock: '2' } }). What is the issue?

medium

A. The update query is missing $set operator.

B. The field name 'stock' is invalid.

C. The multiplier '2' is a string, should be a number.

D. The filter {_id: 2} is incorrect.

Solution

1. Step 1: Check the multiplier type

   The $mul operator requires the multiplier to be a number, not a string.

2. Step 2: Identify the error in the update

   Here, '2' is a string (in quotes), which causes a type error in MongoDB.

3. Final Answer:

   The multiplier '2' is a string, should be a number. -> Option C

4. Quick Check:

   Multiplier must be numeric, not string [OK]

Hint: Multiplier must be a number, not a string [OK]

Common Mistakes:

• Using quotes around numbers in $mul
• Assuming $set is needed with $mul
• Blaming filter instead of multiplier type

5. You want to double the score field only if it is greater than 10 in documents. Which update query correctly uses $mul with a filter?

hard

A. db.collection.updateMany({ score: { $gt: 10 } }, { $mul: { score: 2 } })

B. db.collection.updateMany({}, { $mul: { score: { $gt: 10, $mul: 2 } } })

C. db.collection.updateMany({ $mul: { score: 2 } }, { score: { $gt: 10 } })

D. db.collection.updateMany({ score: 2 }, { $mul: { score: 10 } })

Solution

1. Step 1: Understand filtering in updateMany

   The first argument is the filter to select documents where score is greater than 10.

2. Step 2: Apply $mul only to filtered documents

   The second argument uses $mul to multiply score by 2 for those documents.

3. Final Answer:

   db.collection.updateMany({ score: { $gt: 10 } }, { $mul: { score: 2 } }) -> Option A

4. Quick Check:

   Filter then multiply = db.collection.updateMany({ score: { $gt: 10 } }, { $mul: { score: 2 } }) [OK]

Hint: Filter documents first, then apply $mul in update [OK]

Common Mistakes:

• Trying to use $mul inside filter
• Swapping filter and update arguments
• Using invalid syntax mixing filter and update