API keys and usage plans in AWS - Time & Space Complexity

Time Complexity: API keys and usage plans

O(n)

Understanding Time Complexity

When managing API keys and usage plans, it is important to understand how the number of API keys affects the operations needed to enforce usage limits.

We want to know how the work grows as more API keys are added to a usage plan.

Scenario Under Consideration

Analyze the time complexity of the following operation sequence.

// Attach multiple API keys to a usage plan
for (let i = 0; i < apiKeys.length; i++) {
  aws.apigateway.createUsagePlanKey({
    usagePlanId: usagePlanId,
    keyId: apiKeys[i].id,
    keyType: 'API_KEY'
  });
}
    

This sequence attaches each API key to a usage plan to enforce usage limits per key.

Identify Repeating Operations

• Primary operation: createUsagePlanKey API call to attach one API key to the usage plan
• How many times: Once for each API key in the list

How Execution Grows With Input

Each API key requires one separate call to attach it to the usage plan, so the total calls grow directly with the number of keys.

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

Pattern observation: The number of calls increases one-to-one with the number of API keys.

Final Time Complexity

Time Complexity: O(n)

This means the work grows linearly as you add more API keys to the usage plan.

Common Mistake

[X] Wrong: "Attaching multiple API keys can be done in a single API call, so time stays the same regardless of keys."

[OK] Correct: Each API key must be attached individually, so the number of calls grows with the number of keys.

Interview Connect

Understanding how API calls scale with input size shows you can predict system behavior and design efficient cloud solutions.

Self-Check

"What if the usage plan allowed attaching multiple API keys in one batch call? How would the time complexity change?"

Practice

1. What is the main purpose of an API key in AWS API Gateway?

easy

A. To monitor server CPU usage

B. To store user data securely

C. To encrypt API responses

D. To identify and control who can access the API

Solution

1. Step 1: Understand API key role

   An API key is used to identify the client calling the API.

2. Step 2: Identify purpose in AWS API Gateway

   It helps control and track who can access the API, not data storage or encryption.

3. Final Answer:

   To identify and control who can access the API -> Option D

4. Quick Check:

   API key = identify and control access [OK]

Hint: API keys identify users, not store or encrypt data [OK]

Common Mistakes:

• Confusing API keys with encryption keys
• Thinking API keys store user data
• Assuming API keys monitor server metrics

2. Which of the following is the correct way to associate an API key with a usage plan in AWS API Gateway?

easy

A. Create a usage plan, then add the API key to it

B. Create an API key, then add a usage plan to it

C. Create a usage plan and API key separately without linking

D. Create an API key inside the usage plan settings

Solution

1. Step 1: Understand usage plan and API key relationship

   Usage plans define limits and must have API keys linked to enforce them.

2. Step 2: Correct linking process

   You create a usage plan first, then add API keys to it to apply limits.

3. Final Answer:

   Create a usage plan, then add the API key to it -> Option A

4. Quick Check:

   Usage plan first, then add API key [OK]

Hint: Link API keys by adding them to usage plans [OK]

Common Mistakes:

• Trying to add usage plans to API keys
• Not linking keys and plans at all
• Assuming API keys are created inside usage plans

3. Given this AWS CLI command output showing usage plan limits:

{"throttle": {"rateLimit": 100, "burstLimit": 200}, "quota": {"limit": 1000, "period": "DAY"}}

What does this usage plan enforce?

medium

A. Max 1000 requests per second, burst up to 200, and 100 requests per day

B. Max 200 requests per second, burst up to 100, and 1000 requests per day

C. Max 100 requests per second, burst up to 200, and 1000 requests per day

D. No limits on requests per second or daily quota

Solution

1. Step 1: Interpret throttle limits

   RateLimit 100 means 100 requests per second max, burstLimit 200 allows short bursts up to 200 requests.

2. Step 2: Interpret quota limits

   Quota limit 1000 per DAY means max 1000 requests allowed in one day.

3. Final Answer:

   Max 100 requests per second, burst up to 200, and 1000 requests per day -> Option C

4. Quick Check:

   Throttle = 100/sec + 200 burst, Quota = 1000/day [OK]

Hint: Throttle = per second, quota = daily limit [OK]

Common Mistakes:

• Mixing burstLimit with rateLimit
• Confusing quota limit with per second limit
• Ignoring the quota period

4. You created an API key and a usage plan, but API calls with the key are not limited by the usage plan. What is the most likely cause?

medium

A. The usage plan has no throttle or quota limits set

B. The API key is not associated with the usage plan

C. The API key is expired

D. The API Gateway stage is not deployed

Solution

1. Step 1: Check API key and usage plan link

   Usage plans only apply limits if the API key is linked to them.

2. Step 2: Verify other causes

   While no limits or deployment can cause issues, the key not linked means no limits apply.

3. Final Answer:

   The API key is not associated with the usage plan -> Option B

4. Quick Check:

   Key must be linked to usage plan for limits [OK]

Hint: Check if API key is linked to usage plan [OK]

Common Mistakes:

• Assuming usage plan limits apply without linking keys
• Ignoring deployment status
• Confusing expired keys with unlinked keys

5. You want to create a usage plan that limits users to 5000 requests per month and 50 requests per second with a burst of 100. You also want to track usage per API key. Which steps correctly achieve this?

hard

A. Create usage plan with quota 5000/month and throttle 50/sec burst 100, then add API keys to the plan

B. Create API keys with limits, then assign usage plan to each key

C. Create usage plan with limits, deploy API, no need to link API keys

D. Set limits on API Gateway stage, then create API keys without usage plan

Solution

1. Step 1: Define usage plan with required limits

   Set quota to 5000 per month and throttle to 50 requests per second with burst 100.

2. Step 2: Link API keys to usage plan

   Adding API keys to the usage plan enables tracking and enforcement of limits per key.

3. Final Answer:

   Create usage plan with quota 5000/month and throttle 50/sec burst 100, then add API keys to the plan -> Option A

4. Quick Check:

   Usage plan sets limits + keys linked for tracking [OK]

Hint: Set limits in usage plan, then add API keys [OK]

Common Mistakes:

• Trying to set limits on API keys directly
• Not linking API keys to usage plan
• Setting limits only on API Gateway stage