Download URLs in Firebase - Time & Space Complexity

Time Complexity: Download URLs

O(n)

Understanding Time Complexity

When using Firebase to get download URLs, it's important to know how the time to get these URLs changes as you ask for more files.

We want to understand how the number of files affects the total time to get their download links.

Scenario Under Consideration

Analyze the time complexity of the following operation sequence.

const storage = getStorage();
const urls = [];
for (const filePath of filePaths) {
  const fileRef = ref(storage, filePath);
  const url = await getDownloadURL(fileRef);
  urls.push(url);
}
    

This code gets download URLs one by one for a list of file paths stored in Firebase Storage.

Identify Repeating Operations

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

• Primary operation: Calling getDownloadURL() for each file reference.
• How many times: Once per file in the list.

How Execution Grows With Input

Each file requires a separate call to get its download URL, so the total calls grow as the number of files grows.

Input Size (n)	Approx. API Calls/Operations
10	10 calls to getDownloadURL
100	100 calls to getDownloadURL
1000	1000 calls to getDownloadURL

Pattern observation: The number of calls increases directly with the number of files requested.

Final Time Complexity

Time Complexity: O(n)

This means the time to get all download URLs grows in a straight line as you ask for more files.

Common Mistake

[X] Wrong: "Getting multiple download URLs happens all at once and takes the same time no matter how many files."

[OK] Correct: Each download URL requires a separate network call, so more files mean more calls and more time.

Interview Connect

Understanding how API calls scale with input size helps you design efficient cloud operations and shows you can think about real-world performance.

Self-Check

"What if we fetched all download URLs in parallel instead of one by one? How would the time complexity change?"