Sliding window algorithm in Rest API - Time & Space Complexity

Time Complexity: Sliding window algorithm

O(n)

Understanding Time Complexity

We want to understand how the time needed changes when using the sliding window method in a REST API context.

Specifically, how does the number of operations grow as the input size grows?

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

// Example: Find max sum of subarray of size k
function maxSumSubarray(arr, k) {
  let maxSum = 0, windowSum = 0;
  for (let i = 0; i < k; i++) {
    windowSum += arr[i];
  }
  maxSum = windowSum;
  for (let i = k; i < arr.length; i++) {
    windowSum += arr[i] - arr[i - k];
    if (windowSum > maxSum) maxSum = windowSum;
  }
  return maxSum;
}
    

This code finds the maximum sum of any subarray of size k in the array.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: Two loops that traverse the array.
• How many times: First loop runs k times, second loop runs (n - k) times, where n is array length.

How Execution Grows With Input

As the array size grows, the total steps increase roughly in a straight line.

Input Size (n)	Approx. Operations
10	About 10 steps
100	About 100 steps
1000	About 1000 steps

Pattern observation: The work grows directly with input size, not faster or slower.

Final Time Complexity

Time Complexity: O(n)

This means the time to finish grows in a straight line as the input size grows.

Common Mistake

[X] Wrong: "The sliding window always takes more time because it has two loops inside."

[OK] Correct: The loops run one after another, not nested, so total time adds up linearly, not multiplied.

Interview Connect

Understanding sliding window time complexity helps you explain efficient solutions clearly and confidently in interviews.

Self-Check

"What if we changed the window size k to be proportional to n? How would the time complexity change?"

Practice

1. What is the main advantage of using the sliding window algorithm in processing data streams?

easy

A. It processes data in fixed-size chunks efficiently by reusing previous computations.

B. It sorts the entire data before processing.

C. It stores all data in memory for faster access.

D. It processes data randomly without any order.

Solution

1. Step 1: Understand the sliding window concept

   The sliding window algorithm processes data in fixed-size chunks, moving forward by removing the oldest data and adding new data.

2. Step 2: Identify the main advantage

   This approach avoids recalculating over the entire data repeatedly, saving time and memory.

3. Final Answer:

   It processes data in fixed-size chunks efficiently by reusing previous computations. -> Option A

4. Quick Check:

   Sliding window = efficient chunk processing [OK]

Hint: Remember: sliding window reuses old results to save time [OK]

Common Mistakes:

• Thinking it sorts data first
• Assuming it stores all data in memory
• Believing it processes data randomly

2. Which of the following is the correct way to initialize a sliding window of size 3 over a list named data in Python?

easy

A. window = data[3]

B. window = data[0:3]

C. window = data(0,3)

D. window = data[:]

Solution

1. Step 1: Recall Python list slicing syntax

   To get the first 3 elements, use data[0:3], which includes indices 0, 1, and 2.

2. Step 2: Check other options

   data(0,3) is invalid syntax, data[3] gets only one element at index 3, data[:] gets the whole list.

3. Final Answer:

   window = data[0:3] -> Option B

4. Quick Check:

   Slice first 3 elements = data[0:3] [OK]

Hint: Use data[start:end] to slice lists in Python [OK]

Common Mistakes:

• Using parentheses instead of brackets
• Selecting a single element instead of a slice
• Taking the whole list instead of a window

3. Given the Python code below, what will be the output?

data = [1, 3, 5, 7, 9]
window_size = 3
result = []
for i in range(len(data) - window_size + 1):
    window_sum = sum(data[i:i+window_size])
    result.append(window_sum)
print(result)

medium

A. [1, 3, 5]

B. [15, 21, 27]

C. [3, 5, 7]

D. [9, 15, 21]

Solution

1. Step 1: Understand the loop range and slicing

   The loop runs from i=0 to i=2 (5 - 3 + 1 = 3 iterations). Each slice is data[i:i+3].

2. Step 2: Calculate sums for each window

   i=0: sum([1,3,5])=9; i=1: sum([3,5,7])=15; i=2: sum([5,7,9])=21.

3. Final Answer:

   [9, 15, 21] -> Option D

4. Quick Check:

   Sliding sums = [9, 15, 21] [OK]

Hint: Sum slices of size window_size in a loop [OK]

Common Mistakes:

• Incorrect loop range causing index errors
• Summing wrong slices
• Confusing window size with list length

4. The following code tries to implement a sliding window sum but has a bug. What is the error?

data = [2, 4, 6, 8]
window_size = 2
result = []
for i in range(len(data) - window_size):
    window_sum = sum(data[i:i+window_size])
    result.append(window_sum)
print(result)

medium

A. The result list is not initialized.

B. The sum function is used incorrectly.

C. The loop range misses the last window, causing incomplete results.

D. Window size is larger than data length.

Solution

1. Step 1: Analyze the loop range

   The loop runs from 0 to len(data) - window_size - 1, which is 4 - 2 - 1 = 1, so only indices 0 and 1.

2. Step 2: Identify missing last window

   The last valid window starts at index 2 (data[2:4]), but the loop excludes it because it should run to len(data) - window_size + 1.

3. Final Answer:

   The loop range misses the last window, causing incomplete results. -> Option C

4. Quick Check:

   Loop range must cover all windows [OK]

Hint: Use range(len(data) - window_size + 1) for full coverage [OK]

Common Mistakes:

• Using wrong loop range causing missed windows
• Misusing sum function
• Not initializing result list

5. You want to find the maximum sum of any sliding window of size 4 in a large list data. Which approach is most efficient?

hard

A. Use a sliding window by adding the new element and subtracting the oldest element from the previous sum.

B. Calculate sum of each window from scratch using sum(data[i:i+4]) in a loop.

C. Sort the entire list and pick the top 4 elements to sum.

D. Use recursion to calculate sums of all windows.

Solution

1. Step 1: Understand the problem of efficiency

   Calculating sum from scratch for each window is slow for large data because it repeats work.

2. Step 2: Apply sliding window optimization

   By keeping the previous window sum, add the new element and subtract the oldest element to get the next sum quickly.

3. Step 3: Evaluate other options

   Sorting does not help find consecutive window sums; recursion adds overhead and is inefficient here.

4. Final Answer:

   Use a sliding window by adding the new element and subtracting the oldest element from the previous sum. -> Option A

5. Quick Check:

   Sliding window sum update = add new - remove old [OK]

Hint: Update sums by adding new and removing old element [OK]

Common Mistakes:

• Recalculating sums fully each time
• Sorting unrelated to consecutive sums
• Using recursion unnecessarily