$lt and $lte for less than in MongoDB - Time & Space Complexity

Time Complexity: $lt and $lte for less than

O(n)

Understanding Time Complexity

When using $lt and $lte in MongoDB queries, it's important to know how the query time changes as the data grows.

We want to understand how the number of documents affects the time it takes to find those less than a value.

Scenario Under Consideration

Analyze the time complexity of the following MongoDB query.

db.products.find({ price: { $lt: 100 } })
    .toArray()
    .then(results => console.log(results))
    .catch(err => console.error(err));
    

This query finds all products with a price less than 100.

Identify Repeating Operations

Look at what repeats when the query runs.

• Primary operation: Checking each document's price to see if it is less than 100.
• How many times: Once for each document in the collection if no index is used.

How Execution Grows With Input

As the number of documents grows, the query checks more prices.

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 query time grows in direct proportion to the number of documents in the collection.

Common Mistake

[X] Wrong: "Using $lt or $lte always makes the query fast no matter the data size."

[OK] Correct: Without an index, MongoDB must check every document, so the query slows down as data grows.

Interview Connect

Understanding how simple comparison queries scale helps you explain database performance clearly and confidently.

Self-Check

What if we added an index on the price field? How would the time complexity change?

Practice

1. What does the MongoDB operator $lt do in a query?

easy

A. Finds documents where the field value is less than a specified value

B. Finds documents where the field value is greater than a specified value

C. Finds documents where the field value is equal to a specified value

D. Finds documents where the field value is not equal to a specified value

Solution

1. Step 1: Understand the meaning of $lt

   The $lt operator means "less than" in MongoDB queries.

2. Step 2: Apply the operator meaning to query behavior

   It selects documents where the field value is strictly less than the given value.

3. Final Answer:

   Finds documents where the field value is less than a specified value -> Option A

4. Quick Check:

   $lt means less than [OK]

Hint: Remember: lt = less than, lte = less than or equal [OK]

Common Mistakes:

• Confusing $lt with $lte
• Thinking $lt means less than or equal
• Mixing $lt with greater than operators

2. Which of the following is the correct MongoDB query syntax to find documents where the field age is less than or equal to 30?

easy

A. { age: { $lte: 30 } }

B. { age: { $lt: 30 } }

C. { age: { $gt: 30 } }

D. { age: { $gte: 30 } }

Solution

1. Step 1: Identify the operator for less than or equal

   The operator $lte means "less than or equal to" in MongoDB.

2. Step 2: Match the operator with the query syntax

   The correct syntax to find documents where age is less than or equal to 30 is { age: { $lte: 30 } }.

3. Final Answer:

   { age: { $lte: 30 } } -> Option A

4. Quick Check:

   $lte means less than or equal [OK]

Hint: Use $lte for less than or equal, $lt for strictly less [OK]

Common Mistakes:

• Using $lt instead of $lte for less than or equal
• Using greater than operators by mistake
• Incorrect query object structure

3. Given the collection products with documents:

{ "name": "Pen", "price": 5 }

{ "name": "Notebook", "price": 10 }

{ "name": "Bag", "price": 20 }

What will be the result of the query db.products.find({ price: { $lt: 10 } })?

medium

A. []

B. [{ "name": "Pen", "price": 5 }, { "name": "Notebook", "price": 10 }]

C. [{ "name": "Pen", "price": 5 }]

D. [{ "name": "Notebook", "price": 10 }, { "name": "Bag", "price": 20 }]

Solution

1. Step 1: Understand the query condition

   The query uses $lt: 10, so it finds documents where price is less than 10.

2. Step 2: Check each document's price

   Only the "Pen" has price 5, which is less than 10. "Notebook" has price 10, which is not less than 10.

3. Final Answer:

   [{ "name": "Pen", "price": 5 }] -> Option C

4. Quick Check:

   Only prices less than 10 included [OK]

Hint: Remember $lt excludes equal values, only strictly less [OK]

Common Mistakes:

• Including documents with price equal to 10
• Confusing $lt with $lte
• Returning empty result by mistake

4. You wrote this query to find documents where score is less than or equal to 50:
db.scores.find({ score: { $lt: 50 } })
But you want to include documents where score is exactly 50. What is the error and how to fix it?

medium

A. Use $gt instead of $lt

B. No error, query is correct

C. Add $eq: 50 inside the query

D. Use $lte instead of $lt to include 50

Solution

1. Step 1: Identify the operator used

   The query uses $lt, which excludes values equal to 50.

2. Step 2: Choose the correct operator to include 50

   To include values equal to 50, use $lte (less than or equal).

3. Final Answer:

   Use $lte instead of $lt to include 50 -> Option D

4. Quick Check:

   $lte includes equal values [OK]

Hint: Use $lte to include the boundary value [OK]

Common Mistakes:

• Using $lt and expecting equal values included
• Using $gt which is wrong direction
• Trying to combine $lt and $eq unnecessarily

5. You have a collection orders with documents containing total values. You want to find all orders with total less than or equal to 100 but greater than 50. Which query correctly uses $lt and $lte to achieve this?

hard

A. { total: { $gte: 50, $lt: 100 } }

B. { total: { $gt: 50, $lte: 100 } }

C. { total: { $lt: 100, $lte: 50 } }

D. { total: { $lt: 100, $gt: 50 } }

Solution

1. Step 1: Understand the range needed

   We want totals greater than 50 and less than or equal to 100.

2. Step 2: Match operators to conditions

   $gt: 50 means strictly greater than 50, $lte: 100 means less than or equal to 100.

3. Step 3: Check query syntax

   { total: { $gt: 50, $lte: 100 } } correctly uses both operators in one object: { total: { $gt: 50, $lte: 100 } }.

4. Final Answer:

   { total: { $gt: 50, $lte: 100 } } -> Option B

5. Quick Check:

   Use $gt for greater than, $lte for less than or equal [OK]

Hint: Combine $gt and $lte for range queries [OK]

Common Mistakes:

• Mixing $lt and $lte incorrectly
• Using $gte instead of $gt when strict greater needed
• Reversing operator directions