Build a Prefix Sum Array
Precompute running totals once.
Build a Prefix Sum Array 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
Imagine answering hundreds of range-sum questions on one array. Summing each range from scratch is slow. A prefix sum fixes that. 🚀
What a Prefix Sum Is
A prefix sum array stores, at each index, the total of all elements up to that point. One precompute pass turns slow sums into instant answers.
A Tiny Example
For [3, 1, 4], the running totals are 3, then 4, then 8. That growing list of totals is exactly your prefix sum.
The Core Recurrence
Each entry is the previous total plus the current element. This one-line recurrence is the heart of the whole technique.
prefix[i] = prefix[i - 1] + a[i]Build It in Code
Walk the array once, carrying a running total. Each step appends the new sum, so building the array is a single linear pass.
prefix = [0]
for x in a:
prefix.append(prefix[-1] + x)Why a Leading Zero Helps
Starting prefix with a leading zero means prefix[i] holds the sum of the first i elements. This makes range math clean later.
Indexing Convention
With the zero in front, prefix[k] equals a[0] + ... + a[k-1]. Keeping this convention straight prevents painful off-by-one bugs.
Cost of Building
Building the prefix array touches each element exactly once, so it costs O(n) time. You pay this once, then reuse it forever.
Precompute Once, Query Often
The big win is the tradeoff: spend one linear pass up front so every later sum query becomes a quick lookup instead of a loop.
A Pythonic Shortcut
The standard library can build totals for you. itertools.accumulate produces the running sums in one clean call.
from itertools import accumulate
prefix = [0] + list(accumulate(a))Watch the Memory
The prefix array is the same length as your input plus one. For huge inputs, remember it doubles your memory footprint.
Quick Check
You build a prefix array. What does index 0 usually hold?
Recap
You learned to build a prefix sum array in one O(n) pass, with a leading zero for clean indexing. Precompute once, then reuse. ✅
Frequently asked questions
Is the “Build a Prefix Sum Array” lesson free?
Yes — the full text of “Build a Prefix Sum Array” 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 “Build a Prefix Sum Array”?
Precompute running totals once. 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 “Build a Prefix Sum Array” 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.