Fixed window algorithm in Rest API - Time & Space Complexity

Time Complexity: Fixed window algorithm

O(1)

Understanding Time Complexity

We want to understand how the time it takes to check and update request counts grows as more requests come in.

How does the fixed window algorithm handle many requests efficiently?

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

// Pseudocode for fixed window rate limiting
function isRequestAllowed(userId) {
  currentWindow = getCurrentTime() / windowSize
  count = getCount(userId, currentWindow) // get count from storage
  if (count < limit) {
    incrementCount(userId, currentWindow)
    return true
  } else {
    return false
  }
}

This code checks if a user has made fewer requests than the limit in the current time window, then increments the count if allowed.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: Accessing and updating the count for the user in the current time window.
• How many times: Once per request received.

How Execution Grows With Input

Each request triggers a single check and update operation regardless of how many requests happened before.

Input Size (n)	Approx. Operations
10	10 checks and updates
100	100 checks and updates
1000	1000 checks and updates

Pattern observation: The number of operations grows directly with the number of requests.

Final Time Complexity

Time Complexity: O(1)

This means each request is handled in constant time, no matter how many requests have come before.

Common Mistake

[X] Wrong: "The time to check requests grows as more requests come in because we have to look at all previous requests."

[OK] Correct: The fixed window algorithm only checks the count for the current window, not all past requests, so it stays constant time.

Interview Connect

Understanding fixed window time complexity shows you can reason about how systems handle many requests efficiently, a useful skill for real-world API design.

Self-Check

"What if we changed the fixed window to a sliding window algorithm? How would the time complexity change?"

Practice

1.

What is the main idea behind the Fixed window algorithm in rate limiting?

easy

A. Count requests in fixed time intervals and block if limit exceeded

B. Allow unlimited requests without any restrictions

C. Count requests over a sliding time window for smooth limiting

D. Block all requests after the first one

Solution

1. Step 1: Understand fixed window concept

   The fixed window algorithm divides time into fixed intervals (windows) and counts requests in each interval.

2. Step 2: Identify how blocking works

   If the number of requests in the current window exceeds the limit, further requests are blocked until the next window.

3. Final Answer:

   Count requests in fixed time intervals and block if limit exceeded -> Option A

4. Quick Check:

   Fixed window = count + block in fixed intervals [OK]

Hint: Fixed window counts requests per fixed time block [OK]

Common Mistakes:

• Confusing fixed window with sliding window algorithm
• Thinking it allows unlimited requests
• Assuming it blocks all requests immediately

2.

Which of the following is the correct way to check the current window start time in a fixed window algorithm using Python?

import time
window_size = 60  # seconds
current_time = int(time.time())
window_start = ?

easy

A. current_time - (current_time % window_size)

B. current_time % window_size

C. current_time + window_size

D. window_size - current_time

Solution

1. Step 1: Calculate window start using modulo

   The window start is the current time minus the remainder when divided by window size, to align to window boundary.

2. Step 2: Apply formula

   Using current_time - (current_time % window_size) gives the start of the current fixed window.

3. Final Answer:

   current_time - (current_time % window_size) -> Option A

4. Quick Check:

   Window start = current_time - remainder [OK]

Hint: Use modulo to find window start time [OK]

Common Mistakes:

• Using modulo alone without subtraction
• Adding window size instead of subtracting remainder
• Confusing window start with window end

3.

Given the following Python code snippet implementing a fixed window rate limiter, what will be the output?

requests = [1, 1, 1, 1, 1]
limit = 3
window_start = 0
count = 0
for req in requests:
    if count < limit:
        count += req
        print("Allowed")
    else:
        print("Blocked")

medium

A. Allowed Allowed Allowed Allowed Allowed

B. Blocked Blocked Blocked Blocked Blocked

C. Allowed Allowed Allowed Blocked Blocked

D. Allowed Allowed Blocked Allowed Blocked

Solution

1. Step 1: Trace request counts

   Count starts at 0. For each request (value 1), count increases until it reaches limit 3.

2. Step 2: Determine allowed or blocked

   First 3 requests increase count to 3 and print "Allowed". Next requests exceed limit, so print "Blocked".

3. Final Answer:

   Allowed Allowed Allowed Blocked Blocked -> Option C

4. Quick Check:

   Count ≤ 3 allowed, else blocked [OK]

Hint: Count requests and block after limit reached [OK]

Common Mistakes:

• Assuming all requests allowed
• Resetting count incorrectly
• Confusing count comparison operator

4.

Identify the bug in this fixed window rate limiter code snippet and select the fix:

limit = 5
window_size = 60
count = 0
window_start = int(time.time())

if int(time.time()) - window_start > window_size:
    count = 0

count += 1
if count > limit:
    print("Blocked")
else:
    print("Allowed")

medium

A. Increase limit to 10

B. Change count += 1 to count = 1

C. Remove the if condition checking time difference

D. Move window_start update inside the if block to reset window

Solution

1. Step 1: Identify window reset logic

   The code resets count when window expires but does not update window_start, so window never moves forward.

2. Step 2: Fix by updating window start time

   Inside the if block, update window_start = int(time.time()) to start a new window correctly.

3. Final Answer:

   Move window_start update inside the if block to reset window -> Option D

4. Quick Check:

   Reset count and window start together [OK]

Hint: Update window start when resetting count [OK]

Common Mistakes:

• Not updating window start time
• Resetting count incorrectly
• Ignoring time difference condition

5.

You want to implement a fixed window rate limiter that allows 10 requests per minute per user. Which approach correctly handles multiple users without mixing counts?

hard

A. Store counts in a list without user identification

B. Use a dictionary with user IDs as keys and counts as values, reset counts per user each window

C. Use a single global count for all users and reset every minute

D. Allow unlimited requests for all users

Solution

1. Step 1: Understand per-user counting

   Each user must have a separate count to avoid mixing requests between users.

2. Step 2: Use dictionary keyed by user ID

   A dictionary with user IDs as keys and counts as values allows tracking each user's requests independently and resetting counts per window.

3. Final Answer:

   Use a dictionary with user IDs as keys and counts as values, reset counts per user each window -> Option B

4. Quick Check:

   Separate counts per user = dictionary keyed by user [OK]

Hint: Track counts per user with dictionary keys [OK]

Common Mistakes:

• Using a single global count for all users
• Not resetting counts per user
• Ignoring user identification in counting