Lambda with API Gateway pattern in AWS - Time & Space Complexity

Time Complexity: Lambda with API Gateway pattern

O(n)

Understanding Time Complexity

When using Lambda with API Gateway, we want to know how the number of requests affects the work done.

We ask: How does the system handle more users calling the API?

Scenario Under Consideration

Analyze the time complexity of the following operation sequence.

// API Gateway receives HTTP request
// API Gateway triggers Lambda function
// Lambda processes request and returns response
// API Gateway sends response back to client
    

This sequence shows how each API call triggers a Lambda function to handle it.

Identify Repeating Operations

Identify the API calls, resource provisioning, data transfers that repeat.

• Primary operation: Lambda function invocation triggered by API Gateway request
• How many times: Once per each API request received

How Execution Grows With Input

Each new API request causes one Lambda invocation, so the work grows directly with the number of requests.

Input Size (n)	Approx. Api Calls/Operations
10	10 Lambda invocations
100	100 Lambda invocations
1000	1000 Lambda invocations

Pattern observation: The number of Lambda calls grows linearly as requests increase.

Final Time Complexity

Time Complexity: O(n)

This means the total work grows in direct proportion to the number of API requests.

Common Mistake

[X] Wrong: "Lambda runs once and handles all requests at the same time."

[OK] Correct: Each request triggers a separate Lambda run, so work grows with requests, not fixed.

Interview Connect

Understanding this helps you explain how serverless scales and costs relate to usage, a key cloud skill.

Self-Check

"What if the Lambda function called another Lambda inside it for each request? How would the time complexity change?"

Practice

1. What is the primary role of AWS API Gateway when used with Lambda in a serverless architecture?

easy

A. To receive HTTP requests and trigger Lambda functions

B. To store data permanently

C. To run long-running background tasks

D. To manage virtual machines

Solution

1. Step 1: Understand API Gateway's function

   API Gateway acts as a front door to accept and process HTTP requests from clients.

2. Step 2: Connect API Gateway to Lambda

   API Gateway triggers Lambda functions to execute backend logic upon receiving requests.

3. Final Answer:

   To receive HTTP requests and trigger Lambda functions -> Option A

4. Quick Check:

   API Gateway triggers Lambda = A [OK]

Hint: API Gateway handles HTTP, Lambda runs code [OK]

Common Mistakes:

• Confusing API Gateway with data storage
• Thinking Lambda manages servers
• Assuming API Gateway runs background tasks

2. Which of the following is the correct way to configure an API Gateway method to trigger a Lambda function?

easy

A. Set the integration type to HTTP and specify the Lambda URL

B. Set the integration type to VPC Link and attach Lambda

C. Set the integration type to Lambda Function and select the function ARN

D. Set the integration type to MOCK and provide Lambda code inline

Solution

1. Step 1: Identify correct integration type

   API Gateway uses 'Lambda Function' integration to directly invoke Lambda functions.

2. Step 2: Specify Lambda function ARN

   You must provide the ARN (Amazon Resource Name) of the Lambda function to link it properly.

3. Final Answer:

   Set the integration type to Lambda Function and select the function ARN -> Option C

4. Quick Check:

   Integration type Lambda Function + ARN = D [OK]

Hint: Use 'Lambda Function' integration with ARN [OK]

Common Mistakes:

• Using HTTP integration instead of Lambda Function
• Confusing MOCK integration with Lambda
• Incorrectly using VPC Link for Lambda

3. Consider this AWS Lambda function triggered by API Gateway:

exports.handler = async (event) => {
  return { statusCode: 200, body: JSON.stringify({ message: event.queryStringParameters.name }) };
};

What will be the response body if the API Gateway is called with URL ?name=Alice?

medium

A. {"message":"Alice"}

B. {"message":null}

C. {"message":"name"}

D. Error: event.queryStringParameters undefined

Solution

1. Step 1: Understand event object from API Gateway

   API Gateway passes query parameters inside event.queryStringParameters, so event.queryStringParameters.name equals 'Alice'.

2. Step 2: Check Lambda return value

   Lambda returns JSON string with message key set to 'Alice', so response body is '{"message":"Alice"}'.

3. Final Answer:

   {"message":"Alice"} -> Option A

4. Quick Check:

   Query param 'name=Alice' -> message = 'Alice' [OK]

Hint: Query params in event.queryStringParameters [OK]

Common Mistakes:

• Assuming queryStringParameters is null
• Returning raw object instead of JSON string
• Confusing parameter name with literal string

4. You deployed an API Gateway with Lambda integration but receive a 502 Bad Gateway error when calling the API. What is the most likely cause?

medium

A. API Gateway endpoint URL is incorrect

B. Lambda function is not returning a properly formatted response

C. Lambda function has no execution role assigned

D. API Gateway method is set to MOCK integration

Solution

1. Step 1: Understand 502 Bad Gateway meaning

   502 error usually means API Gateway received an invalid response from Lambda.

2. Step 2: Check Lambda response format

   Lambda must return an object with statusCode and body as string; missing or malformed response causes 502.

3. Final Answer:

   Lambda function is not returning a properly formatted response -> Option B

4. Quick Check:

   502 error = bad Lambda response format [OK]

Hint: 502 means Lambda response format error [OK]

Common Mistakes:

• Assuming wrong API Gateway URL causes 502
• Ignoring Lambda execution role issues (causes 403)
• Confusing MOCK integration with Lambda integration

5. You want to design a serverless API using API Gateway and Lambda that handles high traffic with unpredictable spikes. Which design choice best ensures scalability and cost efficiency?

hard

A. Use API Gateway with Lambda proxy integration and enable Lambda reserved concurrency

B. Use API Gateway with HTTP integration to EC2 instances behind an autoscaling group

C. Use API Gateway with MOCK integration and pre-warm Lambda functions manually

D. Use API Gateway with Lambda proxy integration and rely on Lambda's default scaling without reserved concurrency

Solution

1. Step 1: Understand Lambda scaling behavior

   Lambda scales automatically with incoming requests without needing reserved concurrency unless limiting concurrency is required.

2. Step 2: Evaluate cost and scalability

   Relying on default Lambda scaling avoids paying for reserved concurrency and handles unpredictable spikes efficiently.

3. Step 3: Compare other options

   EC2 autoscaling adds server management and cost; MOCK integration doesn't run real code; reserved concurrency limits scaling.

4. Final Answer:

   Use API Gateway with Lambda proxy integration and rely on Lambda's default scaling without reserved concurrency -> Option D

5. Quick Check:

   Default Lambda scaling + proxy integration = C [OK]

Hint: Default Lambda scaling handles spikes best [OK]

Common Mistakes:

• Setting reserved concurrency unnecessarily limits scaling
• Using EC2 adds complexity and cost
• Using MOCK integration doesn't run Lambda code