Mastering the Sliding Window Technique: A Visual Guide with Mind Map

5 min readSep 10, 2023

Hey there! Ever heard of the “Sliding Window” technique in programming? Don’t worry if it sounds a bit perplexing; we’re here to break it down for you in plain, conversational terms. In this chat, we’ll explore what the sliding window pattern is, how to spot scenarios where it comes in handy, and we’ll even discuss its time and space complexities.

What’s This Sliding Window Pattern All About?

Now, let’s talk about when to pull out this technique from your programming toolbox. You’d want to consider using the sliding window pattern in situations like these:

1. Subarray or Substring Problems: Imagine you need to find the longest or shortest subarray or substring that meets certain criteria (like having the maximum sum or distinct elements). Well, that’s the sliding window’s sweet spot.

2. Fixed-Size Data Extraction: Sometimes, you need to process data within a fixed-size window or subarray. Think of it as extracting insights from a particular chunk of data. This pattern makes it a breeze.

3. Two-Pointer Approach: In some cases, you can think of the sliding window as a two-pointer approach, where two pointers (usually the left and right) roam through your data while maintaining a specific window size.

How Do You Actually Use It?

So, you’re sold on trying out the sliding window pattern? Awesome! Here’s a quick guide on how to implement it:

Step 1: Define Your Window: First things first, you define the window size or boundaries. Most of the time, you’ll have two pointers, one marking the start and the other the end of the window. Set them up accordingly.

Step 2: Slide the Window: Now comes the fun part! Start moving your window by incrementing the end pointer. While you do this, keep track of any relevant data within that window.

Step 3: Check the Constraints: At each step, give a look-see to check if the current window satisfies your problem’s constraints or requirements. If it does, update your result or do whatever needs to be done.

Step 4: Adjust the Window: If the window no longer meets the constraints, don’t fret. Simply adjust it by incrementing the start pointer while ensuring the window’s size stays constant.

Step 5: Rinse and Repeat: Keep sliding and adjusting that window until you’ve worked through the entire array or list. Eventually, you’ll get the result you’re aiming for.

Are there any types?

Yes, the sliding window pattern can be categorized into two main types: fixed-size windows and dynamic-size windows.

Let’s explore each type with examples:

1. Fixed-Size Window: In a fixed-size window, the size of the window remains constant as it slides through the data. This type of sliding window is particularly useful when you need to process data within a fixed range or for a specific length of elements.

Example: Maximum Sum Subarray (Fixed-Size Window)

Suppose you have an array of integers and want to find the maximum sum of a subarray with a fixed size `k`. Here’s an example in Python:

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

Example usage

arr = [2, 1, 5, 1, 3, 2]
k = 3
result = max_sum_subarray(arr, k)
print(result)  # Output: 9

In this example, the sliding window has a fixed size of `k=3`, and it moves through the array to find the maximum sum subarray of that size.

2. Dynamic-Size Window: In a dynamic-size window, the size of the window can change as it slides through the data. This type of sliding window is used when the problem requires adjusting the window size based on specific conditions or constraints.

Example: Longest Subarray with Sum at Most K (Dynamic-Size Window)

Let’s say you have an array of positive integers and a target sum `k`, and you want to find the length of the longest subarray whose sum is at most `k`. Here’s an example in Python:

def max_length_subarray(arr, k):
    max_len = 0
    window_sum = 0
    left = 0

    for right in range(len(arr)):
        window_sum += arr[right]

        while window_sum > k:
            window_sum -= arr[left]
            left += 1

        max_len = max(max_len, right - left + 1)

    return max_len

Example Usage

arr = [1, 2, 3, 4, 1, 1, 1]
k = 5
result = max_length_subarray(arr, k)
print(result)  # Output: 3 (Subarray [2, 3, 4])

In this dynamic-size window example, the window adjusts its size based on the condition that the sum of elements within the window should be at most `k`.

Both fixed-size and dynamic-size sliding window patterns have their applications and are powerful tools for efficiently solving a wide range of problems in programming and data analysis.

Time and Space Complexity?

Now, let’s chat about efficiency. The sliding window pattern’s time complexity usually falls in the range of O(N) to O(N²), depending on the specific problem and window size. In most cases, it’s a significant improvement over brute force approaches, which can have a time complexity of O(N³) or even worse.

When it comes to space, the sliding window is a minimalist. Its space complexity is generally O(1), meaning it only requires a constant amount of extra memory. This makes it memory-efficient, even when dealing with massive datasets.

In Conclusion

So, there you have it — a friendly chat about the sliding window pattern. It’s a versatile tool for efficient array and list processing, and it’s surprisingly easy to implement once you get the hang of it. As you gain more coding experience, you’ll become a pro at recognizing when the sliding window can work its magic to streamline your code and find elegant solutions to complex problems. So, next time you’re faced with a tricky programming challenge, remember to slide your way to success with the sliding window pattern!

Mind Map

Let’s have a look at a visual mind map that summarizes all the things we just discussed. This acts as a cheat sheet: