Signed URLs for temporary access in GCP - Time & Space Complexity

Time Complexity: Signed URLs for temporary access

O(n)

Understanding Time Complexity

We want to understand how the time to create signed URLs changes as we create more of them.

Specifically, how does the work grow when we generate many temporary access links?

Scenario Under Consideration

Analyze the time complexity of the following operation sequence.

from google.cloud import storage

client = storage.Client()
bucket = client.bucket('my-bucket')

for i in range(n):
    blob = bucket.blob(f'file_{i}.txt')
    url = blob.generate_signed_url(expiration=3600)
    print(url)

This code generates a signed URL for each file in a bucket to allow temporary access.

Identify Repeating Operations

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

• Primary operation: Generating a signed URL for each blob (file).
• How many times: Once per file, so n times.

How Execution Grows With Input

Each signed URL requires a separate operation, so the total work grows directly with the number of files.

Input Size (n)	Approx. Api Calls/Operations
10	10 signed URL generations
100	100 signed URL generations
1000	1000 signed URL generations

Pattern observation: The work increases evenly as you add more files.

Final Time Complexity

Time Complexity: O(n)

This means the time to generate signed URLs grows in direct proportion to the number of files.

Common Mistake

[X] Wrong: "Generating one signed URL automatically creates URLs for all files at once."

[OK] Correct: Each signed URL is created individually, so you must do the work separately for each file.

Interview Connect

Understanding how operations scale helps you design systems that handle many users or files efficiently.

Self-Check

"What if we cached signed URLs instead of generating them every time? How would the time complexity change?"