Combining comparison operators in MongoDB - Time & Space Complexity

Time Complexity: Combining comparison operators

O(n)

Understanding Time Complexity

When we combine comparison operators in MongoDB queries, it affects how many documents the database checks.

We want to understand how the work grows as the data size grows when using these combined conditions.

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

    db.products.find({
      price: { $gt: 10, $lt: 50 },
      rating: { $gte: 4 }
    })
    

This query finds products with price greater than 10 and less than 50, and rating at least 4.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: Scanning documents to check if they meet all combined conditions.
• How many times: Each document is checked once against all conditions.

How Execution Grows With Input

Explain the growth pattern intuitively.

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

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

Final Time Complexity

Time Complexity: O(n)

This means the time to run the query grows linearly with the number of documents in the collection.

Common Mistake

[X] Wrong: "Combining multiple comparison operators makes the query run faster because it narrows results."

[OK] Correct: While it narrows results, the database still checks each document to see if it matches all conditions, so the work grows with data size.

Interview Connect

Understanding how combined conditions affect query time helps you explain database performance clearly and shows you know how queries scale with data.

Self-Check

"What if we added an index on price and rating? How would the time complexity change?"

Practice

1. Which MongoDB query correctly finds documents where the field age is greater than 20 and less than 30?

easy

A. { age: { $gte: 20, $lte: 30 } }

B. { age: { $gt: 20, $lt: 30 } }

C. { age: { $ne: 20, $ne: 30 } }

D. { age: { $gt: 20 }, $lt: 30 }

Solution

1. Step 1: Understand the requirement for age range

   The question asks for documents where age is strictly greater than 20 and strictly less than 30.

2. Step 2: Identify the correct MongoDB syntax for combined conditions

   Using { age: { $gt: 20, $lt: 30 } } combines both conditions on the same field correctly.

3. Final Answer:

   { age: { $gt: 20, $lt: 30 } } -> Option B

4. Quick Check:

   Combined $gt and $lt on same field = { age: { $gt: 20, $lt: 30 } } [OK]

Hint: Use $gt and $lt together inside one field object [OK]

Common Mistakes:

• Using $gte and $lte includes boundary values, not strictly between
• Placing $lt outside the field object causes syntax error
• Using $ne does not check range but excludes specific values

2. Which of the following is the correct syntax to find documents where score is not equal to 50 and less than or equal to 100?

easy

A. { score: { $ne: 50, $lte: 100 } }

B. { score: { $ne: 50 }, $lte: 100 }

C. { score: { $ne: 50, $lt: 100 } }

D. { score: { $ne: 50, $gte: 100 } }

Solution

1. Step 1: Combine $ne and $lte inside the same field object

   Both conditions must apply to score, so they go together inside one object.

2. Step 2: Check each option's syntax

   { score: { $ne: 50, $lte: 100 } } correctly combines $ne: 50 and $lte: 100 inside score. { score: { $ne: 50 }, $lte: 100 } separates $lte outside, which is invalid syntax.

3. Final Answer:

   { score: { $ne: 50, $lte: 100 } } -> Option A

4. Quick Check:

   Combine $ne and $lte inside one field object = { score: { $ne: 50, $lte: 100 } } [OK]

Hint: Put all comparison operators inside one field object [OK]

Common Mistakes:

• Placing $lte outside the field object causes syntax error
• Using $gte instead of $lte changes the condition
• Separating operators into different objects breaks query

3. Given the collection products with documents like { price: 150, stock: 30 }, what will the query { price: { $gt: 100, $lt: 200 }, stock: { $gte: 20, $lte: 40 } } return?

medium

A. Documents where price is greater than 100 or stock is less than 40

B. Documents where price is exactly 100 and stock is exactly 20

C. Documents where price is between 100 and 200, and stock is between 20 and 40

D. Documents where price is less than 100 and stock is greater than 40

Solution

1. Step 1: Understand the combined conditions on price and stock

   The query uses $gt and $lt on price to find values strictly between 100 and 200, and $gte and $lte on stock to find values between 20 and 40 inclusive.

2. Step 2: Interpret the logical AND behavior of MongoDB queries

   Both conditions must be true for a document to match, so only documents with price in (100,200) and stock in [20,40] are returned.

3. Final Answer:

   Documents where price is between 100 and 200, and stock is between 20 and 40 -> Option C

4. Quick Check:

   Combined conditions on fields = Documents where price is between 100 and 200, and stock is between 20 and 40 [OK]

Hint: All conditions on different fields combine with AND logic [OK]

Common Mistakes:

• Thinking conditions combine with OR instead of AND
• Confusing inclusive ($gte/$lte) with exclusive ($gt/$lt)
• Assuming exact matches instead of ranges

4. Identify the error in this MongoDB query: { quantity: { $gt: 10 }, $lt: 50 }

medium

A. The query is correct and will work as expected

B. The $gt operator should be $gte

C. The field name 'quantity' is missing

D. The $lt operator is outside the field object and causes syntax error

Solution

1. Step 1: Analyze the placement of comparison operators

   The $lt operator is placed outside the quantity field object, which is invalid syntax in MongoDB queries.

2. Step 2: Correct syntax requires all operators on the same field inside one object

   Both $gt and $lt must be inside the quantity object like { quantity: { $gt: 10, $lt: 50 } }.

3. Final Answer:

   The $lt operator is outside the field object and causes syntax error -> Option D

4. Quick Check:

   All operators must be inside field object = The $lt operator is outside the field object and causes syntax error [OK]

Hint: Keep all comparison operators inside the same field object [OK]

Common Mistakes:

• Placing operators outside the field object
• Confusing $gt with $gte unnecessarily
• Assuming query works despite syntax error

5. You want to find documents where rating is greater than 3 but not equal to 5, and reviews are between 10 and 100 inclusive. Which query correctly combines these conditions?

hard

A. { rating: { $gt: 3, $ne: 5 }, reviews: { $gte: 10, $lte: 100 } }

B. { rating: { $gt: 3 }, rating: { $ne: 5 }, reviews: { $gte: 10, $lte: 100 } }

C. { rating: { $gt: 3, $ne: 5, $gte: 10 }, reviews: { $lte: 100 } }

D. { rating: { $gt: 3, $ne: 5 }, reviews: { $gt: 10, $lt: 100 } }

Solution

1. Step 1: Combine multiple comparison operators on the same field correctly

   Both $gt: 3 and $ne: 5 must be inside the same rating object to apply both conditions.

2. Step 2: Use inclusive range operators for reviews

   Since reviews should be between 10 and 100 inclusive, use $gte: 10 and $lte: 100 inside the reviews object.

3. Step 3: Check for syntax errors and logical correctness

   { rating: { $gt: 3, $ne: 5 }, reviews: { $gte: 10, $lte: 100 } } correctly combines all conditions. { rating: { $gt: 3 }, rating: { $ne: 5 }, reviews: { $gte: 10, $lte: 100 } } repeats the rating field, which is invalid. { rating: { $gt: 3, $ne: 5, $gte: 10 }, reviews: { $lte: 100 } } incorrectly adds $gte: 10 to rating. { rating: { $gt: 3, $ne: 5 }, reviews: { $gt: 10, $lt: 100 } } uses exclusive operators for reviews, which is incorrect.

4. Final Answer:

   { rating: { $gt: 3, $ne: 5 }, reviews: { $gte: 10, $lte: 100 } } -> Option A

5. Quick Check:

   Combine all conditions inside field objects correctly = { rating: { $gt: 3, $ne: 5 }, reviews: { $gte: 10, $lte: 100 } } [OK]

Hint: Put all conditions for one field inside one object, use correct operators [OK]

Common Mistakes:

• Repeating the same field multiple times in query
• Mixing inclusive and exclusive operators incorrectly
• Adding unrelated operators inside wrong field objects