Fixed-Size Window Sums
Slide a window of length k in O(n).
Fixed-Size Window Sums is a free Coding Interview Prep lesson on CoddyKit — lesson 1 of 4. You can read the complete lesson below for free — then practise it hands-on in the browser with a built-in code editor and a 24/7 AI tutor. It is part of the Coding Interview Prep learning path, one of 4 lessons in the course, and your progress syncs across the web and the CoddyKit app.
The Repeated-Sum Problem
Many tasks ask for the sum of every block of k consecutive elements. Recomputing each block from scratch is wasteful, and you can do better. 🪟
The Slow Way First
The naive idea adds up each window of length k separately. That repeats work and costs O(n times k), which is too slow for large inputs.
for i in range(n - k + 1):
s = sum(a[i:i + k])The Key Insight
Neighboring windows overlap almost completely. Moving one step right only removes the leftmost element and adds one new element on the right.
Seed the First Window
Start by summing the first k elements once. This single sum is the base you will keep updating as the window slides forward.
window = sum(a[:k])
best = windowSlide One Step
To move the window, add the entering element and subtract the leaving one. That keeps each step at constant O(1) work.
for i in range(k, n):
window += a[i] - a[i - k]Track Your Answer
After each slide, update whatever you need, such as the maximum window sum seen so far. The window value is always ready instantly.
best = max(best, window)Total Cost Is Linear
You touch each element to add it and once more to remove it, so the whole scan is O(n). That easily passes large constraints.
Mind the Indices
The element leaving the window is a[i - k], not a[i - 1]. Getting this offset right is the most common fixed-window bug.
Averages Come Free
Need the maximum window average instead of sum? Just divide the tracked window sum by k. The sliding logic does not change at all.
avg = window / kHandle Small Arrays
If the array is shorter than k, no full window exists. Check len(a) against k up front and return early to avoid an index error.
if n < k:
return NoneWhen Fixed Windows Fit
Use this pattern whenever the window length is fixed and you combine values cheaply, like sums, counts, or simple running statistics.
Quick Check
You slide a window of size k one step to the right across an array.
Recap
Seed the first window once, then add and subtract at each step to slide in O(1). The whole fixed-size scan runs in linear time. ✅
Frequently asked questions
Is the “Fixed-Size Window Sums” lesson free?
Yes — the full text of “Fixed-Size Window Sums” is free to read here on the web, and the Coding Interview Prep course includes 4 lessons in total. To practise it interactively (a built-in code editor and a 24/7 AI tutor) and unlock the rest of the Coding Interview Prep course, upgrade to CoddyKit PRO.
What will I learn in “Fixed-Size Window Sums”?
Slide a window of length k in O(n). You practise Coding Interview Prep with hands-on code you run directly in the browser, and a 24/7 AI tutor answers your questions as you work through the lesson.
Do I need any experience to start Coding Interview Prep?
No prior experience is required. Coding Interview Prep on CoddyKit is structured for beginners through advanced learners; this is — lesson 1 of 4, so you can start here or from the beginning and move at your own pace.
How long does the “Fixed-Size Window Sums” lesson take?
Most CoddyKit lessons take about 5–10 minutes. Each one is bite-sized and interactive, so you make steady progress and pick up exactly where you left off across the web and the app.
Can I write and run code in this Coding Interview Prep lesson?
Yes. Every Coding Interview Prep lesson includes a built-in code editor, so you write and run real code right in your browser and get instant AI feedback — no local setup required.