Chapter 01 - Topic 1.4

Sliding Window Technique

A sliding window tracks a contiguous range and updates it by adding the new edge and removing the old edge, instead of recalculating the whole range every time.

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Definition

Sliding window is a technique for processing contiguous subarrays or substrings by maintaining one active range that expands or shrinks as needed.

Core Idea

A fixed window keeps the size constant, which is perfect for max sum of k elements or average of a subarray.

A variable window grows and shrinks based on a condition, which is useful for longest substring and minimum valid range problems.

The method works because both pointers move forward, so each element is processed only a limited number of times.

Detailed Explanation

Sliding window is one of the most valuable patterns for contiguous data. Instead of recalculating the whole range every time, you only update what changed at the edges of the window.

In a fixed window, the question usually gives you k directly. In a variable window, the question gives you a condition like no repeats, sum at least target, or must contain all required characters.

The real breakthrough is mental: you stop thinking about many separate subarrays and start thinking about one active window that grows and shrinks intelligently.

Maximum sum of a fixed window

JavaScript

function maxSumFixed(arr, k) {
  let windowSum = 0;
  for (let i = 0; i < k; i++) windowSum += arr[i];

  let maxSum = windowSum;

  for (let i = k; i < arr.length; i++) {
    windowSum += arr[i];
    windowSum -= arr[i - k];
    maxSum = Math.max(maxSum, windowSum);
  }

  return maxSum;
}

console.log(maxSumFixed([2, 1, 5, 1, 3, 2], 3));

Explanation

The first loop builds the initial window. After that, every step adds the entering element and removes the exiting element. This avoids recomputing the full sum for each new window.

Output

Real-life Example

A store can track the best 3-day sales streak by updating the rolling total each day instead of summing all 3 days from scratch every time.

When To Use It

Use fixed window when the subarray or substring size is constant.
Use variable window when the window should expand and shrink based on a rule.
Use it for contiguous range problems, not arbitrary subsets.

Common Mistakes

Using sliding window for problems where elements do not need to stay contiguous.
Forgetting to remove the outgoing value when the window moves.
Shrinking too late or too early in variable-window problems.

Key Takeaways

Use sliding window only for contiguous ranges like subarrays and substrings.
Fixed window is best when the window size is known in advance.
Variable window is best when the window must adapt to satisfy a condition.

Practice Ideas

Find maximum sum of k consecutive elements.
Find longest substring without repeating characters.
Find minimum subarray length with sum at least target.

Frequently Asked Questions

What is the difference between two pointers and sliding window?

Sliding window is a special two-pointer pattern for contiguous ranges where both pointers usually move forward across one active window.

Why is sliding window usually O(n)?

Because each pointer moves forward through the data instead of restarting work for each position.

Sliding Window Technique

Definition

Core Idea

Detailed Explanation

Maximum sum of a fixed window

When To Use It

Common Mistakes

Key Takeaways

Practice Ideas

Frequently Asked Questions

What is the difference between two pointers and sliding window?

Why is sliding window usually O(n)?

More DSA Topic Pages

Sliding Window Technique

Definition

Core Idea

Detailed Explanation

Maximum sum of a fixed window

When To Use It

Common Mistakes

Key Takeaways

Practice Ideas

Frequently Asked Questions

What is the difference between two pointers and sliding window?

Why is sliding window usually O(n)?

More DSA Topic Pages