Comparison expressions ($eq, $gt in aggregation) in MongoDB - Time & Space Complexity

Time Complexity: Comparison expressions ($eq, $gt in aggregation)

O(n)

Understanding Time Complexity

When using comparison expressions like $eq and $gt in MongoDB aggregation, it's important to understand how the time to run these checks grows as the data grows.

We want to know how the number of comparisons affects the total work done.

Scenario Under Consideration

Analyze the time complexity of the following aggregation pipeline snippet.

    db.collection.aggregate([
      { $match: { $expr: { $gt: ["$score", 50] } } },
      { $project: { name: 1, passed: { $eq: ["$status", "passed"] } } }
    ])
    

This pipeline filters documents where the score is greater than 50, then adds a field passed that is true if status equals "passed".

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: The aggregation processes each document once, applying $gt and $eq comparisons.
• How many times: Each comparison runs once per document in the input collection.

How Execution Grows With Input

As the number of documents grows, the number of comparisons grows at the same rate.

Input Size (n)	Approx. Operations
10	About 10 comparisons
100	About 100 comparisons
1000	About 1000 comparisons

Pattern observation: The work grows directly with the number of documents, doubling the documents doubles the comparisons.

Final Time Complexity

Time Complexity: O(n)

This means the time to run these comparisons grows in a straight line with the number of documents.

Common Mistake

[X] Wrong: "Comparison expressions like $eq and $gt run once and don't depend on data size."

[OK] Correct: Each document must be checked, so the number of comparisons grows with the number of documents.

Interview Connect

Understanding how comparison operations scale helps you explain query performance clearly and shows you know how MongoDB processes data step-by-step.

Self-Check

"What if we added a $lookup stage before the $match? How would that affect the time complexity of the comparison expressions?"

Practice

1. What does the $eq operator do in a MongoDB aggregation pipeline?

easy

A. Checks if one value is greater than another

B. Sorts documents in ascending order

C. Checks if two values are equal

D. Filters documents by existence of a field

Solution

1. Step 1: Understand the purpose of $eq

   The $eq operator compares two values to see if they are exactly the same.

2. Step 2: Compare with other operators

   Unlike $gt which checks if one value is greater, $eq checks equality.

3. Final Answer:

   Checks if two values are equal -> Option C

4. Quick Check:

   $eq means equal [OK]

Hint: Remember: eq means equal, gt means greater [OK]

Common Mistakes:

• Confusing $eq with $gt
• Thinking $eq sorts data
• Using $eq to check field existence

2. Which of the following is the correct syntax to use $gt in a MongoDB aggregation $match stage to find documents where age is greater than 30?

easy

A. { $match: { $gt: { age: 30 } } }

B. { $match: { age: { $gt: 30 } } }

C. { $match: { age: $gt(30) } }

D. { $match: { age: { gt: 30 } } }

Solution

1. Step 1: Recall correct operator syntax

   MongoDB operators like $gt are used as keys inside an object with the field name as the key.

2. Step 2: Match correct structure

   The correct syntax is { field: { $gt: value } }, so { age: { $gt: 30 } } is correct.

3. Final Answer:

   { $match: { age: { $gt: 30 } } } -> Option B

4. Quick Check:

   Correct operator syntax = { $match: { age: { $gt: 30 } } } [OK]

Hint: Operators go inside field object with $ prefix [OK]

Common Mistakes:

• Placing $gt outside the field object
• Using parentheses like a function
• Missing $ before gt

3. Given the aggregation pipeline stage:

{ $match: { score: { $gt: 80 } } }

Which documents will be matched if the collection has documents with scores: 75, 80, 85, 90?

medium

A. Documents with scores 75, 85, and 90

B. Documents with scores 75 and 80

C. Documents with scores 80, 85, and 90

D. Documents with scores 85 and 90

Solution

1. Step 1: Understand $gt meaning

   The $gt operator matches values strictly greater than the given number, here 80.

2. Step 2: Check which scores are greater than 80

   Scores 85 and 90 are greater than 80; 75 and 80 are not.

3. Final Answer:

   Documents with scores 85 and 90 -> Option D

4. Quick Check:

   Only scores > 80 match = Documents with scores 85 and 90 [OK]

Hint: Remember $gt excludes equal values [OK]

Common Mistakes:

• Including values equal to 80
• Confusing $gt with $gte
• Selecting lower values by mistake

4. Identify the error in this aggregation $match stage:

{ $match: { $eq: ["$status", "active"] } }

medium

A. Incorrect use of $eq outside a field key

B. Missing $gt operator

C. Wrong array syntax for $eq

D. No error, syntax is correct

Solution

1. Step 1: Check $eq usage in $match

   The $eq operator is usually used inside $expr or aggregation expressions, not directly as a key in $match.

2. Step 2: Understand correct placement

   To compare fields with $eq, it must be inside $expr, like { $match: { $expr: { $eq: ["$status", "active"] } } }.

3. Final Answer:

   Incorrect use of $eq outside a field key -> Option A

4. Quick Check:

   $eq needs $expr for expressions [OK]

Hint: Use $expr to compare fields with $eq [OK]

Common Mistakes:

• Using $eq directly in $match without $expr
• Confusing $eq array syntax
• Assuming $eq works like a filter key

5. You want to filter documents where price is greater than 100 and category equals "electronics" using aggregation. Which $match stage correctly uses $gt and $eq together?

hard

A. { $match: { price: { $gt: 100 }, category: "electronics" } }

B. { $match: { $and: [ { price: { $gt: 100 } }, { category: { eq: "electronics" } } ] } }

C. { $match: { price: { $gt: 100 }, category: { eq: "electronics" } } }

D. { $match: { $expr: { $and: [ { gt: ["$price", 100] }, { eq: ["$category", "electronics"] } ] } } }

Solution

1. Step 1: Understand simple field comparisons

   For simple equality, you can directly write category: "electronics" without using $eq.

2. Step 2: Combine conditions in $match

   MongoDB $match supports multiple field conditions combined with AND by default, so { price: { $gt: 100 }, category: "electronics" } works.

3. Step 3: Check other options

   { $match: { price: { $gt: 100 }, category: { $eq: "electronics" } } } misuses $eq inside $match (not needed). { $match: { $and: [ { price: { $gt: 100 } }, { category: { $eq: "electronics" } } ] } } uses $and unnecessarily. { $match: { $expr: { $and: [ { $gt: ["$price", 100] }, { $eq: ["$category", "electronics"] } ] } } } uses $expr which is more complex than needed.

4. Final Answer:

   { $match: { price: { $gt: 100 }, category: "electronics" } } -> Option A

5. Quick Check:

   Simple conditions combine directly in $match [OK]

Hint: Use direct equality for fields, $gt for ranges [OK]

Common Mistakes:

• Overusing $eq inside $match
• Using $and unnecessarily
• Using $expr when not needed