Redirect and rewrite rules in Firebase - Time & Space Complexity

Time Complexity: Redirect and rewrite rules

O(n)

Understanding Time Complexity

We want to understand how the time it takes to apply redirect and rewrite rules changes as we add more rules.

Specifically, how does the number of rules affect the processing time when a user requests a page?

Scenario Under Consideration

Analyze the time complexity of applying redirect and rewrite rules in Firebase Hosting.

"hosting": {
  "rewrites": [
    { "source": "/old-path/**", "destination": "/new-path/index.html" },
    { "source": "/blog/**", "function": "blogHandler" }
  ],
  "redirects": [
    { "source": "/home", "destination": "/index.html", "type": 301 }
  ]
}
    

This configuration applies multiple rewrite and redirect rules to incoming requests.

Identify Repeating Operations

When a request comes in, Firebase Hosting checks each rule in order.

• Primary operation: Matching the request URL against each redirect and rewrite rule.
• How many times: Once per rule, until a match is found or all rules are checked.

How Execution Grows With Input

As the number of rules increases, the system checks more rules one by one.

Input Size (n rules)	Approx. Rule Checks per Request
10	Up to 10 checks
100	Up to 100 checks
1000	Up to 1000 checks

Pattern observation: The number of checks grows directly with the number of rules.

Final Time Complexity

Time Complexity: O(n)

This means the time to process a request grows linearly with the number of redirect and rewrite rules.

Common Mistake

[X] Wrong: "Adding more rules won't affect request speed because they run in parallel."

[OK] Correct: The rules are checked one after another until a match is found, so more rules mean more checks and longer processing time.

Interview Connect

Understanding how rule checks scale helps you design efficient configurations and shows you can think about performance in real systems.

Self-Check

"What if Firebase Hosting used a tree structure to organize rules instead of checking them one by one? How would the time complexity change?"