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Introduction to Sliding Window

· 3 min read
Mr. Frugal
Mr. Frugal
I'm afraid of paying full price.

Overview​

The Sliding Window pattern is a powerful technique used for efficiently solving problems related to sequential data, including arrays and strings. This approach allows us to process subarrays or substrings dynamically by maintaining a window that adjusts as it slides across the data.

Understanding the Pattern​

The Sliding Window technique helps in solving problems that involve sequential data by maintaining a dynamic window that moves through an array or string. Instead of recalculating values from scratch, the window adjusts by adding new elements and removing old ones as it slides.

Think of it as looking through a narrow frame while walking down a long hallway filled with paintings. As you move, new paintings come into view while others disappear. Similarly, this technique processes only a subset of the data at any time, improving efficiency.

Why is Sliding Window Efficient?​

Consider a problem where we need to find k consecutive integers with the highest sum in an array. A naive approach would involve calculating the sum of all possible subarrays of size k, resulting in a time complexity of O(kn).

However, using the Sliding Window technique, instead of recalculating sums entirely, we update the sum dynamically:

  • Subtract the element that leaves the window.
  • Add the element that enters the window.
  • Update the maximum sum accordingly.

This reduces the time complexity to O(n), as each window update takes constant time O(1). The goal is to ensure that the computation per window move remains minimal, ideally in O(1) or a slow-growing function like log(n).

Example Problems​

1. Maximum Sum Subarray of Size K​

Given an array of integers and a positive integer k, find the maximum sum of any contiguous subarray of size k.

2. Longest Substring Without Repeating Characters​

Given a string, determine the length of the longest substring that does not contain duplicate characters.

Does Your Problem Fit This Pattern?​

Your problem likely benefits from the Sliding Window approach if:

  • Contiguous Data: The input is stored as a contiguous structure, such as an array or string.
  • Processing Subsets: The problem requires computations on a contiguous subset of elements that slide through the data. The window size may be fixed or dynamic.
  • Efficient Computation: The per-move calculations should be constant-time or nearly constant.

Real-World Applications​

  • Telecommunications: Determine the peak number of users connected to a cellular network’s base station within a k-millisecond window.
  • Video Streaming: Compute the median buffering events over each one-minute interval in a streaming session.
  • Social Media Mining: Identify the shortest sequence of posts by one user that includes all topics mentioned by another user.

Example: Repeated DNA Sequences​

Given a DNA sequence (dna) and an integer k, return all contiguous subsequences of length k that appear more than once. If no such sequence exists, return an empty set.

Solution Approach​

  1. Iterate through all substrings of length k in the given string.
  2. Store the hash of each substring to track uniqueness.
  3. If a hash is found again, the substring is repeated and should be added to the output.
  4. Return the set of repeated substrings after processing the entire string.