How to Master the Sliding Window Pattern: A Detailed Guide

The Sliding Window pattern is like looking through a small window that moves across a long line of objects (like an array or string). This pattern helps us solve problems quickly by focusing on a small part of the data at a time.

What is the Sliding Window Pattern ?

Imagine you have a long list of numbers or letters. Instead of looking at the whole list at once, you look at a small part of it (a window) and then move this window one step at a time. The window can be a fixed size or can change size based on certain rules.

Key Concepts

1. Window Size: How many elements you look at in the window.

2. Window Start and End: Where the window begins and ends in the list.

3. Sliding Mechanism: Moving the window one element at a time from start to end.

Types of Sliding Windows

1. Fixed-Size Sliding Window: The window size stays the same as it moves.

2. Dynamic Sliding Window: The window size can grow or shrink based in certain conditions.

Common Application

1. Finding the maximum or minimum sum of a subarray of size k.

2. Finding the longest substring with at most k distinct characters.

3. Detecting anagrams in a string.

4. Finding the smallest subarray with a sum greater than or equal to a give value.

Example Problems

1. Maximum Sum Subarray of Size k

   Problem Statement: Given an array of integers and a number k, find the maximum sum of a subarray of size k.

2. Longest Substring with At Most K Distinct Characters

   Problem Statement: Given a string, find the length of the longest substring that contains at most K

3. Smallest subarray with a given sum

   Problem Statement: Given an array of positive integers and a positive integer S, find the length of the smallest contiguous subarray whose sum is greater than or equal to S. return 0 if no such subarray exists.

4. Longest repeating character replacement

5. Permutation in a String