Sliding Window on Arrays in DSA Python - Time & Space Complexity

Time Complexity: Sliding Window on Arrays

O(n)

Understanding Time Complexity

We want to understand how the time taken by a sliding window approach changes as the input array grows.

Specifically, how many steps does it take to process all windows in the array?

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

def max_sum_subarray(arr, k):
    max_sum = 0
    window_sum = 0
    for i in range(k):
        window_sum += arr[i]
    max_sum = window_sum
    for i in range(k, len(arr)):
        window_sum += arr[i] - arr[i - k]
        max_sum = max(max_sum, window_sum)
    return max_sum

This code finds the maximum sum of any subarray of size k using a sliding window.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: Two loops that traverse parts of 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 grow roughly in a straight line with n.

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

Pattern observation: The number of operations increases directly with input size.

Final Time Complexity

Time Complexity: O(n)

This means the time to complete grows linearly as the array gets bigger.

Common Mistake

[X] Wrong: "Sliding window always takes O(k) time because the window size is k."

[OK] Correct: The window moves across the entire array, so the total work depends on n, not just k.

Interview Connect

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

Self-Check

"What if we used nested loops instead of sliding window? How would the time complexity change?"