Link relations in responses in Rest API - Time & Space Complexity

Time Complexity: Link relations in responses

O(n)

Understanding Time Complexity

When a REST API includes link relations in its responses, it adds extra steps to build those links.

We want to know how the time to create these links grows as the response size grows.

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

function buildResponse(items) {
  return items.map(item => ({
    data: item,
    links: {
      self: `/items/${item.id}`,
      related: `/items/${item.id}/related`
    }
  }));
}

This code creates a response array where each item includes its data and two link relations.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: The map function loops over each item once.
• How many times: Exactly once per item in the input array.

How Execution Grows With Input

As the number of items grows, the number of link creations grows the same way.

Input Size (n)	Approx. Operations
10	20 link creations (2 per item)
100	200 link creations
1000	2000 link creations

Pattern observation: The work grows directly with the number of items, doubling for twice as many items.

Final Time Complexity

Time Complexity: O(n)

This means the time to build the response grows in a straight line with the number of items.

Common Mistake

[X] Wrong: "Adding link relations does not affect time because it’s just a small addition."

[OK] Correct: Even small additions happen for every item, so the total time adds up as the list grows.

Interview Connect

Understanding how adding links affects response time helps you design APIs that stay fast as data grows.

Self-Check

What if we added nested link relations inside each related item? How would the time complexity change?

Practice

1. What is the main purpose of using link relations in REST API responses?

easy

A. To define the HTTP methods allowed on a resource

B. To encrypt the data sent between client and server

C. To specify the data format like JSON or XML

D. To describe how different resources are connected and provide URLs for related actions

Solution

1. Step 1: Understand link relations concept

   Link relations describe the relationship between resources and provide URLs to related resources or actions.

2. Step 2: Identify the purpose in REST API responses

   They help clients navigate the API by following links instead of hardcoding URLs.

3. Final Answer:

   To describe how different resources are connected and provide URLs for related actions -> Option D

4. Quick Check:

   Link relations = resource connections and URLs [OK]

Hint: Link relations connect resources with URLs in responses [OK]

Common Mistakes:

• Confusing link relations with data encryption
• Thinking link relations define data format
• Mixing link relations with HTTP method definitions

2. Which of the following is the correct way to include a link relation in a JSON REST API response?

easy

A. "_links": { "self": { "href": "/users/123" } }

B. "links": [ { "url": "/users/123" } ]

C. "link": "/users/123"

D. "href": { "self": "/users/123" }

Solution

1. Step 1: Recall standard link relation format in JSON

   Standard uses a _links object with named relations like self containing an href URL.

2. Step 2: Match the correct JSON structure

   "_links": { "self": { "href": "/users/123" } } matches this format exactly, others do not follow the standard naming or structure.

3. Final Answer:

   "_links": { "self": { "href": "/users/123" } } -> Option A

4. Quick Check:

   Standard link relation = _links with self and href [OK]

Hint: Look for _links with self and href keys [OK]

Common Mistakes:

• Using 'links' instead of '_links'
• Missing 'href' inside the relation object
• Using arrays instead of objects for link relations

3. Given this JSON response snippet:

{
  "_links": {
    "self": { "href": "/orders/42" },
    "cancel": { "href": "/orders/42/cancel" }
  }
}

What URL should a client use to cancel order 42?

medium

A. /orders/42

B. /orders/cancel/42

C. /orders/42/cancel

D. /orders/42/cancelled

Solution

1. Step 1: Locate the 'cancel' link relation in the JSON

   The 'cancel' relation has the href value "/orders/42/cancel" which is the URL to cancel the order.

2. Step 2: Confirm the correct URL for cancellation

   The client should use the URL exactly as given in the 'cancel' href to perform the cancel action.

3. Final Answer:

   /orders/42/cancel -> Option C

4. Quick Check:

   Cancel URL = /orders/42/cancel [OK]

Hint: Use the href under the 'cancel' link relation [OK]

Common Mistakes:

• Using the 'self' URL instead of 'cancel'
• Rearranging URL parts incorrectly
• Guessing URL instead of reading from response

4. You receive this partial JSON response:

{
  "_links": {
    "self": { "href": "/products/7" },
    "edit": { "url": "/products/7/edit" }
  }
}

What is wrong with the link relations in this response?

medium

A. The 'edit' relation uses 'url' instead of 'href'

B. The 'self' relation should not be included

C. The 'href' value for 'self' is missing a domain

D. The '_links' key should be named 'links'

Solution

1. Step 1: Check the property names inside link relations

   Standard link relations use 'href' to specify the URL, not 'url'.

2. Step 2: Identify the incorrect property

   The 'edit' relation incorrectly uses 'url' instead of 'href'.

3. Final Answer:

   The 'edit' relation uses 'url' instead of 'href' -> Option A

4. Quick Check:

   Link relation URLs must use 'href' key [OK]

Hint: Link URLs always use 'href', not 'url' [OK]

Common Mistakes:

• Thinking 'url' is acceptable instead of 'href'
• Expecting full domain in href for relative URLs
• Renaming '_links' to 'links' incorrectly

5. You want to design a REST API response for a blog post that includes links to the post itself, the author's profile, and comments. Which JSON structure correctly uses link relations to represent these?

hard

A. { "links": [ { "rel": "self", "url": "/posts/10" }, { "rel": "author", "url": "/users/5" }, { "rel": "comments", "url": "/posts/10/comments" } ] }

B. { "_links": { "self": { "href": "/posts/10" }, "author": { "href": "/users/5" }, "comments": { "href": "/posts/10/comments" } } }

C. { "_links": { "self": "/posts/10", "author": "/users/5", "comments": "/posts/10/comments" } }

D. { "_links": { "self": { "url": "/posts/10" }, "author": { "url": "/users/5" }, "comments": { "url": "/posts/10/comments" } } }

Solution

1. Step 1: Recall the correct link relation format

   Each link relation should be an object with an 'href' key inside the '_links' object.

2. Step 2: Evaluate each option's structure

   { "_links": { "self": { "href": "/posts/10" }, "author": { "href": "/users/5" }, "comments": { "href": "/posts/10/comments" } } } correctly uses '_links' with 'self', 'author', and 'comments' keys, each having an 'href' URL. Options B and D use 'url' instead of 'href', and C uses strings instead of objects.

3. Final Answer:

   { "_links": { "self": { "href": "/posts/10" }, "author": { "href": "/users/5" }, "comments": { "href": "/posts/10/comments" } } } -> Option B

4. Quick Check:

   Use '_links' with objects containing 'href' URLs [OK]

Hint: Use '_links' with 'href' keys for each relation [OK]

Common Mistakes:

• Using 'url' instead of 'href' for links
• Using arrays instead of objects for link relations
• Assigning string URLs directly without 'href' objects