Hierarchical resource paths in Rest API - Time & Space Complexity

Time Complexity: Hierarchical resource paths

O(n)

Understanding Time Complexity

When working with hierarchical resource paths in REST APIs, it's important to understand how the number of operations grows as the API handles nested resources.

We want to know how the time to process requests changes when the depth or number of nested resources increases.

Scenario Under Consideration

Analyze the time complexity of the following REST API path handling.

GET /users/{userId}/orders/{orderId}/items

// The server fetches user data,
// then fetches the order for that user,
// then fetches all items in that order.
    

This code represents a hierarchical path where each resource depends on the previous one.

Identify Repeating Operations

Look for repeated actions or loops in handling nested resources.

• Primary operation: Fetching items in the order (likely a list traversal)
• How many times: Once per item in the order, which depends on the number of items

How Execution Grows With Input

As the number of items in an order grows, the time to fetch all items grows too.

Input Size (n)	Approx. Operations
10 items	About 10 fetch operations
100 items	About 100 fetch operations
1000 items	About 1000 fetch operations

Pattern observation: The operations increase directly with the number of items.

Final Time Complexity

Time Complexity: O(n)

This means the time to handle the request grows linearly with the number of items in the nested resource.

Common Mistake

[X] Wrong: "Fetching nested resources is always constant time because it's just one API call."

[OK] Correct: Even though the path looks like one call, the server often fetches each nested resource separately, so time grows with the number of nested items.

Interview Connect

Understanding how nested resource paths affect time helps you explain API performance clearly and shows you can think about real-world data sizes.

Self-Check

What if the API used pagination to limit items returned per request? How would that change the time complexity?

Practice

1. What does a hierarchical resource path in a REST API represent?

easy

A. A nested structure showing relationships between resources

B. A random list of unrelated resources

C. A single resource without any relation

D. A method to encrypt API data

Solution

1. Step 1: Understand resource organization

   Hierarchical paths show how resources are connected, like folders inside folders.

2. Step 2: Identify the purpose of hierarchical paths

   They help represent parent-child relationships clearly in the API URL.

3. Final Answer:

   A nested structure showing relationships between resources -> Option A

4. Quick Check:

   Hierarchical paths = nested resource relationships [OK]

Hint: Think of folders inside folders to understand hierarchy [OK]

Common Mistakes:

• Confusing hierarchy with unrelated resource lists
• Ignoring the relationship between resources
• Thinking it's about data encryption

2. Which of the following is the correct syntax for a hierarchical resource path to access comments of a post with ID 10?

easy

A. /posts/10/comments

B. /comments/posts/10

C. /posts/comments/10

D. /10/posts/comments

Solution

1. Step 1: Identify the parent resource and its ID

   The parent resource is 'posts' with ID 10, so it comes first in the path.

2. Step 2: Append the child resource

   Comments belong to the post, so '/comments' follows '/posts/10'.

3. Final Answer:

   /posts/10/comments -> Option A

4. Quick Check:

   Parent resource + ID + child resource = /posts/10/comments [OK]

Hint: Parent resource and ID come before child resource [OK]

Common Mistakes:

• Placing child resource before parent
• Swapping resource names and IDs
• Using incorrect order of segments

3. Given the REST API path /users/5/orders/12/items, what resource does this path represent?

medium

A. All orders of all users

B. Order 12 of user 5

C. User 5's profile information

D. Items in order 12 of user 5

Solution

1. Step 1: Break down the path segments

   /users/5 means user with ID 5, /orders/12 means order with ID 12 for that user, and /items means the items in that order.

2. Step 2: Understand the full resource

   The path points to the items inside order 12 which belongs to user 5.

3. Final Answer:

   Items in order 12 of user 5 -> Option D

4. Quick Check:

   Path shows nested resources = items in order 12 of user 5 [OK]

Hint: Read path left to right as parent to child resources [OK]

Common Mistakes:

• Ignoring the nested order and item relationship
• Confusing order with user profile
• Assuming it lists all users or orders

4. Identify the error in this hierarchical REST API path: /projects//tasks/7

medium

A. Missing task ID before 7

B. Double slash between 'projects' and 'tasks' is invalid

C. Resource names should be capitalized

D. The path should end with a slash

Solution

1. Step 1: Check the path syntax

   The path has two slashes '//' between 'projects' and 'tasks', which is not valid in REST API paths.

2. Step 2: Understand correct path format

   Only one slash should separate resource names and IDs to maintain proper hierarchy.

3. Final Answer:

   Double slash between 'projects' and 'tasks' is invalid -> Option B

4. Quick Check:

   Only single slashes separate path segments [OK]

Hint: Check for extra or missing slashes in paths [OK]

Common Mistakes:

• Ignoring double slashes as harmless
• Thinking resource names must be capitalized
• Believing trailing slash is mandatory

5. You want to design a REST API path to access all reviews for a specific product variant. The product ID is 20 and the variant ID is 5. Which path correctly represents this hierarchical resource?

hard

A. /products/reviews/20/variants/5

B. /reviews/products/20/variants/5

C. /products/20/variants/5/reviews

D. /variants/5/products/20/reviews

Solution

1. Step 1: Identify the resource hierarchy

   Reviews belong to a variant, which belongs to a product. So the path should start with product ID, then variant ID, then reviews.

2. Step 2: Construct the path in correct order

   The correct order is /products/20/variants/5/reviews to show this nested relationship clearly.

3. Final Answer:

   /products/20/variants/5/reviews -> Option C

4. Quick Check:

   Parent to child order: product -> variant -> reviews [OK]

Hint: Order path segments from general to specific resource [OK]

Common Mistakes:

• Placing reviews before products or variants
• Mixing order of product and variant IDs
• Using unrelated resource order