Rewrite directive in Nginx - Time & Space Complexity

Time Complexity: Rewrite directive

O(n)

Understanding Time Complexity

We want to understand how the time it takes for nginx to process rewrite rules changes as we add more rules.

Specifically, how does the number of rewrite directives affect the work nginx does?

Scenario Under Consideration

Analyze the time complexity of the following nginx rewrite rules.

server {
    listen 80;
    server_name example.com;

    rewrite ^/oldpath/(.*)$ /newpath/$1 permanent;
    rewrite ^/blog/(.*)$ /news/$1 last;
    rewrite ^/user/(.*)$ /profile/$1 break;
}

This snippet shows three rewrite directives that change URLs based on patterns.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: nginx checks each rewrite rule one by one to see if the URL matches the pattern.
• How many times: It tries each rewrite directive in order until one matches or all are checked.

How Execution Grows With Input

As the number of rewrite rules grows, nginx has to check more patterns for each request.

Input Size (n)	Approx. Operations
3	3 pattern checks
10	10 pattern checks
100	100 pattern checks

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

Final Time Complexity

Time Complexity: O(n)

This means the time to process rewrites grows linearly with the number of rewrite directives.

Common Mistake

[X] Wrong: "Adding more rewrite rules does not affect performance because nginx is very fast."

[OK] Correct: Even though nginx is fast, each rewrite rule adds work because nginx checks them one by one, so more rules mean more checks and more time.

Interview Connect

Understanding how rewrite rules affect processing time helps you design efficient server configurations and shows you can think about performance in real setups.

Self-Check

What if we combined multiple rewrite rules into one using a more complex pattern? How would the time complexity change?