Mastering the Sliding Window Pattern Series — Introducing Basic Questions

Algorithm challenges can sometimes seem daunting, especially when facing problems that require keeping track of a subset of data in a larger set. However, the sliding window pattern is a powerful technique that can simplify these challenges, making them more manageable and solvable within optimal time and space complexities. In this blog, we’ll delve into the sliding window pattern, explore its general structure through code, and tackle a variety of problems that illustrate its utility and adaptability.

Introduction to the Sliding Window Pattern

The sliding window pattern is an algorithmic technique for efficiently solving problems that involve sequences or arrays, especially those that ask for longest or shortest subarrays meeting certain criteria. It involves moving a window of elements through the sequence to examine different subsets of data.

This pattern is particularly useful for dealing with continuous or contiguous blocks of elements and is often applied in string or array manipulation problems. Its beauty lies in its ability to reduce potentially complex operations to simple, linear time executions.

How to Identify Sliding Window Problems

Recognizing when to apply the sliding window technique is as crucial as understanding the pattern itself. Problems suitable for this approach often share common characteristics that hint at the efficiency of a sliding window solution. Here’s a rundown, inspired by insights from GeeksforGeeks:

1. Problem Involves a Subarray or Substring: If the problem asks for the longest or shortest(min/max) substring or subarray that meets certain criteria, it’s a strong candidate for the sliding window technique.
2. Looking for Optimal Subsets of particular size K: The sliding window shines in problems where you need to find an optimal range within a larger set — be it for maximum sum, minimum length, or meeting specific constraints.
3. Linear Complexity is Suggested: Brute Force solution can be O(n**2) but problems requires a solution with linear time complexity (O(n)). Easiest way to impose that constraint will be to take N in power of 10**6
4. Continuous or Contiguous Data Segment Requirements: When the problem is focused on continuous or contiguous segments of data within an array or string, the sliding window approach is often ideal. This is because the pattern inherently deals with segments of data by adjusting the start and end points (or left and right pointers) of the window.
5. Incremental Changes in Conditions: If the problem’s condition changes incrementally as you move through the dataset (for example, summing elements, counting distinct elements, etc.), sliding window can efficiently adjust to these changes without redoing calculations from scratch.

Practical Example:

Consider the problem of finding the maximum sum of any contiguous subarray of a given size. This scenario directly hints at a sliding window approach because:

• It involves a subarray (a contiguous segment).
• The goal is to find an optimal subset (maximum sum).
• The problem requires examining segments of the data in a manner that suggests linear complexity could be achieved.

Here is basic Code structure we can follow :

def sliding_window(arr, k):
    # Initialize any required variables
    # For example, to keep track of the current sum, maximum sum, or count of distinct elements, etc.
    window_sum = 0
    max_sum = 0
    left = 0

    for right in range(len(arr)):
        # Update the window_sum or any other relevant variable by considering the element at the 'right' pointer
        window_sum += arr[right]
        
        # Check if the window size is greater than k (or meets the specific problem's condition)
        # Then, adjust the window size and update the variables accordingly
        while right - left + 1 > k:
            # Update window_sum or other variables by removing the element at the 'left' pointer
            window_sum -= arr[left]
            # Move the left pointer to the right to shrink the window size
            left += 1
        
        # Update the result (e.g., max_sum, count) based on the current window's properties
        max_sum = max(max_sum, window_sum)
    
    # Return the result (e.g., max_sum, the number of subarrays meeting a condition, etc.)
    return max_sum

To get a grasp of this topic, I recommend trying the following LeetCode Problems

1. 713. Subarray Product Less Than K : Solution
2. 2958. Length of Longest Subarray With at Most K Frequency : Solution
3. 2962. Count Subarrays Where Max Element Appears at Least K Times : Solution

References :

https://www.geeksforgeeks.org/window-sliding-technique/