How does a fixed-size sliding window work?

Compute the sum of the first k values once. Each time the window moves one place, add the value entering on the right and subtract the value leaving on the left, and compare the new sum with the best.

How does this solve Maximum Average Subarray I (LeetCode 643)?

Every window has the same length k, so the window with the largest sum also has the largest average. Find the maximum sum this way and divide it by k.

What is the time complexity of the fixed-size window?

O(n): the first sum costs O(k) and each of the remaining n − k moves costs O(1). Extra space is O(1).

Overview (Fixed Length)

Master the fixed-size sliding window pattern: slide one element out, slide one element in.

Medium

15 min

Solve on LeetCode

What is a Fixed Length Window?

In a Fixed Length sliding window, the size of the window k never changes. Visualizing it is simple: imagine a rigid frame of size k sliding across your array one step at a time.

The Golden Rule:
At each step, we do exactly two things in O(1) time:

Remove the element leaving the window (the one at i - k).
Add the element entering the window (the one at i).

This "Add-Remove" strategy avoids re-calculating the window content from scratch, turning an O(N*K) brute force algorithm into an O(N) linear solution.

Core Problem: Maximum Sum Subarray of Size K

The classic problem to learn this pattern:

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

Example:

Input: nums = [2, 1, 5, 1, 3, 2], k = 3
Output: 9
Explanation: Subarray [5, 1, 3] has the largest sum.

The LeetCode problem linked above, 643. Maximum Average Subarray I, asks for the maximum average of a length-k subarray. It uses exactly the same windows: this lesson computes the maximum sum, and the answer to 643 is bestSum / k.

Algorithm Strategy

Initialize: Calculate the sum of the first k elements. Set this as your initial current_sum and max_sum.
Slide: Iterate from index k to the end of the array.
Update: For each new element at index i:
- Add nums[i] to current_sum.
- Subtract nums[i - k] (the element falling out) from current_sum.
- Update max_sum = max(max_sum, current_sum).
Return: max_sum.

Visual Walkthrough

Watch how the window slides. Notice that we don't re-add the middle elements; we purely adjust for the entering and leaving numbers.

Dry Run: [2, 1, 5, 1, 3, 2], k=3

Step	Window Indices	Window Values	Operation	Current Sum	Max Sum
Init	`[0, 2]`	`[2, 1, 5]`	Sum first 3	`2+1+5 = 8`	8
Slide 1	`[1, 3]`	`[1, 5, 1]`	Add 1, Remove 2	`8 + 1 - 2 = 7`	8
Slide 2	`[2, 4]`	`[5, 1, 3]`	Add 3, Remove 1	`7 + 3 - 1 = 9`	9
Slide 3	`[3, 5]`	`[1, 3, 2]`	Add 2, Remove 5	`9 + 2 - 5 = 6`	9
End					Result: 9

Edge Cases & Common Mistakes

Edge Cases:

Array length < k: Checking should happen immediately. Usually return 0 or error.
k = 1: The problem reduces to finding the maximum element in the array.

Common Mistakes:

Off-by-one errors: Calculating the index of the element leaving (i - k vs i - k + 1 etc). If iterating i from 0 to end, the leaving element is i - k only after i >= k-1.
Re-summing: Using a loop inside the loop to sum the window elements, leading to O(N*K) complexity.

The Code Template

This template applies to almost any fixed-window problem (Generic inputs are used).

Overview (Fixed Length) Code

1function maxSumSubarray(nums, k) {
2    if (nums.length < k) return 0;
3    
4    let currentSum = 0;
5    for (let i = 0; i < k; i++) {
6        currentSum += nums[i];
7    }
8    
9    let maxSum = currentSum;
10    
11    for (let i = k; i < nums.length; i++) {
12        currentSum += nums[i];
13        currentSum -= nums[i - k];
14        maxSum = Math.max(maxSum, currentSum);
15    }
16    return maxSum;
17}

Minimum Window Substring

Maximum Points You Can Obtain from Cards

Overview (Fixed Length)

What is a Fixed Length Window?

Core Problem: Maximum Sum Subarray of Size K

Algorithm Strategy

Visual Walkthrough

Dry Run: [2, 1, 5, 1, 3, 2], k=3

Edge Cases & Common Mistakes

The Code Template

Overview (Fixed Length) Code

The approach, step by step

Sum the first window

Slide one place

Keep the maximum

Frequently asked questions

How does a fixed-size sliding window work?

How does this solve Maximum Average Subarray I (LeetCode 643)?

What is the time complexity of the fixed-size window?

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