Exact match (=) in Nginx - Time & Space Complexity

Time Complexity: Exact match (=)

O(n)

Understanding Time Complexity

We want to understand how the time it takes for nginx to find an exact match in its configuration grows as the number of rules increases.

Specifically, how does nginx check for an exact match when processing requests?

Scenario Under Consideration

Analyze the time complexity of the following nginx exact match configuration snippet.

location = /about {
    return 200 "About page";
}
location = /contact {
    return 200 "Contact page";
}
location / {
    return 404;
}
    

This snippet defines exact match locations for "/about" and "/contact" URLs, and a default catch-all location.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: nginx checks each exact match location one by one to find a matching URL.
• How many times: It compares the request URI against each exact match rule until it finds a match or exhausts all.

How Execution Grows With Input

As the number of exact match locations grows, nginx must check more rules one after another.

Input Size (n)	Approx. Operations
10	Up to 10 string comparisons
100	Up to 100 string comparisons
1000	Up to 1000 string comparisons

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

Final Time Complexity

Time Complexity: O(n)

This means the time to find an exact match grows linearly as you add more exact match locations.

Common Mistake

[X] Wrong: "nginx finds exact matches instantly no matter how many rules there are."

[OK] Correct: nginx checks exact matches one by one, so more rules mean more checks and longer time.

Interview Connect

Understanding how nginx processes exact matches helps you reason about request handling speed and configuration design in real projects.

Self-Check

"What if nginx used a hash table for exact matches? How would the time complexity change?"

Practice

1. What does the = sign mean in an nginx location block?

easy

A. It matches URLs ending with the given path.

B. It matches the exact URL path only.

C. It matches URLs containing the given path anywhere.

D. It matches any URL starting with the given path.

Solution

1. Step 1: Understand nginx location matching

   The = sign in nginx location means the URL must match exactly the specified path.

2. Step 2: Compare with other matching types

   Other types like prefix matching use location /path without =, which matches URLs starting with that path.

3. Final Answer:

   It matches the exact URL path only. -> Option B

4. Quick Check:

   Exact match = exact URL [OK]

Hint: Exact match uses = sign, no extra path allowed [OK]

Common Mistakes:

• Thinking = matches URL prefixes
• Confusing = with regex matching
• Assuming = matches URLs containing the path

2. Which of the following is the correct syntax to define an exact match location for URL /about in nginx?

easy

A. location /about { }

B. location /about = { }

C. location ~ /about { }

D. location = /about { }

Solution

1. Step 1: Recall nginx exact match syntax

   Exact match uses location = /path { } syntax, where = comes immediately after location.

2. Step 2: Check other options

   location /about = { } places = after path, which is invalid. location ~ /about { } uses regex (~), not exact match. location /about { } is prefix match.

3. Final Answer:

   location = /about { } -> Option D

4. Quick Check:

   Exact match syntax = location = /path [OK]

Hint: Put = right after location for exact match [OK]

Common Mistakes:

• Placing = after the path
• Using regex (~) instead of = for exact match
• Omitting = for exact match

3. Given this nginx config snippet:

location = /test {
  return 200 'Exact match';
}
location /test {
  return 200 'Prefix match';
}

What will be the response body when accessing URL /test?

medium

A. Exact match

B. Prefix match

C. 404 Not Found

D. 500 Internal Server Error

Solution

1. Step 1: Identify matching location for /test

   The URL /test matches exactly the location = /test block because of the exact match sign =.

2. Step 2: Understand nginx location priority

   Exact match locations have higher priority than prefix matches, so the first block is used and returns 'Exact match'.

3. Final Answer:

   Exact match -> Option A

4. Quick Check:

   Exact match location wins for exact URL [OK]

Hint: Exact match location overrides prefix for exact URL [OK]

Common Mistakes:

• Choosing prefix match response for exact URL
• Assuming 404 if exact match exists
• Confusing order of location blocks

4. You wrote this nginx config:

location = /home {
  proxy_pass http://backend;
}
location /home {
  proxy_pass http://frontend;
}

But requests to /home are always sent to http://frontend. What is the likely problem?

medium

A. The exact match location block is not matched because of a syntax error.

B. The exact match location block is missing a trailing slash.

C. The exact match location is overridden by prefix match due to order.

D. The exact match location block is ignored because proxy_pass is invalid.

Solution

1. Step 1: Check syntax of exact match location

   The exact match location location = /home { ... } may have a syntax error like missing semicolon after proxy_pass, causing nginx to ignore it.

2. Step 2: Consider nginx matching rules

   Exact match locations have highest priority and should be matched first. If requests go to frontend, likely the exact match block is ignored due to a syntax error or config reload issue.

3. Step 3: Identify common mistake

   Often, missing semicolons or incorrect proxy_pass URL cause nginx to ignore the block silently.

4. Final Answer:

   The exact match location block is not matched because of a syntax error. -> Option A

5. Quick Check:

   Syntax errors cause nginx to ignore blocks [OK]

Hint: Check syntax errors if exact match ignored [OK]

Common Mistakes:

• Assuming order affects exact match priority
• Missing semicolon after proxy_pass
• Confusing trailing slash importance

5. You want to serve a special static page only when the URL is exactly /special. Which nginx config snippet correctly achieves this without affecting other URLs starting with /special?

hard

A. location /special { root /var/www/special; }

B. location ~ /special { root /var/www/special; }

C. location = /special { root /var/www/special; }

D. location ^~ /special { root /var/www/special; }

Solution

1. Step 1: Understand exact match requirement

   To serve only the exact URL /special, use location = /special which matches exactly that path.

2. Step 2: Analyze other options

   location /special { root /var/www/special; } matches any URL starting with /special. location ~ /special { root /var/www/special; } uses regex to match URLs containing /special anywhere. location ^~ /special { root /var/www/special; } uses prefix match with ^~, which matches prefixes but not exact only.

3. Final Answer:

   location = /special { root /var/www/special; } -> Option C

4. Quick Check:

   Exact match = location = /path [OK]

Hint: Use = for exact URL, not prefix or regex [OK]

Common Mistakes:

• Using prefix match for exact URL
• Overcomplicating with regex
• Confusing ^~ with exact match