$gt and $gte for greater than in MongoDB - Time & Space Complexity

Time Complexity: $gt and $gte for greater than

O(n)

Understanding Time Complexity

When we use $gt or $gte in MongoDB queries, we want to find documents with values greater than a number.

We ask: How does the time to find these documents grow as the collection gets bigger?

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

db.products.find({ price: { $gt: 100 } })

// or

db.products.find({ price: { $gte: 100 } })

This code finds all products with a price greater than (or equal to) 100.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: Scanning documents to check the price field.
• 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 time to find matching documents grows in a straight line as the collection gets bigger.

Common Mistake

[X] Wrong: "Using $gt or $gte always makes queries fast because they are simple comparisons."

[OK] Correct: Without an index on the field, MongoDB must check every document, so the query time grows with collection size.

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 $gt operator do in a MongoDB query?

easy

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

B. Finds documents where the field value is equal to the specified value.

C. Finds documents where the field value is strictly greater than the specified value.

D. Finds documents where the field value is greater than or equal to the specified value.

Solution

1. Step 1: Understand the meaning of $gt

   The $gt operator means "greater than" and selects values strictly larger than the given number.

2. Step 2: Compare with other operators

   $gte means "greater than or equal to", so it includes the number itself, unlike $gt.

3. Final Answer:

   Finds documents where the field value is strictly greater than the specified value. -> Option C

4. Quick Check:

   $gt = strictly greater than [OK]

Hint: Remember: $gt means strictly greater than [OK]

Common Mistakes:

• Confusing $gt with $gte
• Thinking $gt includes equal values
• Mixing $gt with less than operators

2. Which of the following is the correct syntax to find documents where the field age is greater than or equal to 18 in MongoDB?

easy

A. { age: { $gte: 18 } }

B. { age: { $gt: 18 } }

C. { age: { $gte: "18" } }

D. { age: { $gte: > 18 } }

Solution

1. Step 1: Check the operator and syntax

   The correct operator for "greater than or equal to" is $gte, and it must be used as { field: { $gte: value } }.

2. Step 2: Validate the value type and format

   The value should be a number (18), not a string or invalid syntax like > 18.

3. Final Answer:

   { age: { $gte: 18 } } -> Option A

4. Quick Check:

   Correct syntax uses $gte with number [OK]

Hint: Use { field: { $gte: number } } for greater or equal [OK]

Common Mistakes:

• Using quotes around numbers
• Writing invalid syntax like $gte: > 18
• Confusing $gt and $gte

3. Given the collection products with documents:

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

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

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

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

medium

A. [{ "name": "Notebook", "price": 10 }, { "name": "Backpack", "price": 20 }]

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

C. []

D. [{ "name": "Backpack", "price": 20 }]

Solution

1. Step 1: Understand the query condition

   The query uses $gt: 10, so it selects documents where price is strictly greater than 10.

2. Step 2: Check each document's price

   "Pen" has price 5 (not > 10), "Notebook" has price 10 (not > 10), "Backpack" has price 20 (greater than 10).

3. Final Answer:

   [{ "name": "Backpack", "price": 20 }] -> Option D

4. Quick Check:

   Only price > 10 matches [OK]

Hint: Remember $gt excludes equal values [OK]

Common Mistakes:

• Including documents with price equal to 10
• Confusing $gt with $gte
• Selecting documents with price less than 10

4. You wrote the query db.users.find({ age: { $gte: 21 } }) but it returns no results even though some users are 21 or older. What is the likely problem?

medium

A. You should use $gt instead of $gte.

B. The field name age is misspelled in the documents.

C. The query syntax is incorrect; $gte cannot be used here.

D. MongoDB does not support $gte operator.

Solution

1. Step 1: Check the query syntax

   The syntax { age: { $gte: 21 } } is correct and supported by MongoDB.

2. Step 2: Consider data issues

   If no results appear, likely the field age is misspelled or missing in documents, so no matches occur.

3. Final Answer:

   The field name age is misspelled in the documents. -> Option B

4. Quick Check:

   Field name mismatch causes no results [OK]

Hint: Check field names carefully if no results [OK]

Common Mistakes:

• Assuming $gte is unsupported
• Switching $gte to $gt unnecessarily
• Ignoring possible typos in field names

5. You want to find all orders with a total amount greater than or equal to 100 but less than 200. Which MongoDB query correctly uses $gte and $gt to achieve this?

hard

A. { total: { $gte: 100, $lt: 200 } }

B. { total: { $gt: 100, $gte: 200 } }

C. { total: { $gte: 100, $gt: 200 } }

D. { total: { $gte: 100, $gt: 199 } }

Solution

1. Step 1: Understand the range conditions

   You want totals >= 100 and < 200, so use $gte: 100 and $lt: 200 (less than 200).

2. Step 2: Check each option's operators

   { total: { $gte: 100, $lt: 200 } } correctly uses $gte: 100 and $lt: 200. Other options misuse operators or values.

3. Final Answer:

   { total: { $gte: 100, $lt: 200 } } -> Option A

4. Quick Check:

   Use $gte for lower bound, $lt for upper bound [OK]

Hint: Use $gte for start, $lt for end of range [OK]

Common Mistakes:

• Using $gt instead of $gte for lower bound
• Using $gte for upper bound instead of $lt
• Mixing operator directions incorrectly