Difference Arrays for Range Updates
Apply many add-on-range operations fast.
Difference Arrays for Range Updates is a free Coding Interview Prep lesson on CoddyKit — lesson 4 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.
Flip the Problem
Prefix sums answered range queries fast. A difference array flips that to apply many range updates fast. 🔁
The Slow Way
Adding a value to every element in a range, repeated many times, costs O(n) per update. Across q updates that cost explodes.
Store the Changes
Instead of touching every cell, record only where a change starts and where it ends. Mark the edges, not the middle.
What a Diff Array Holds
A difference array stores the gap between each element and the one before it. Editing one gap shifts a whole stretch later.
The Two-Mark Trick
To add v over l to r, add v at index l and subtract v at index r + 1. Just two edits cover the entire range.
diff[l] += v
diff[r + 1] -= vWhy the Minus
The plus at l turns the change on; the minus at r + 1 turns it back off. Together they fence the update to one range.
Apply All Updates Cheaply
Each update is just two array writes, so q updates take O(q) total. The heavy lifting is deferred to the end.
Recover the Final Array
After all marks are placed, take a prefix sum of the difference array. That single pass reconstructs every final value.
for i in range(1, n):
diff[i] += diff[i - 1]Size with a Guard Slot
Make the array one cell longer so r + 1 never falls off the end. That extra guard slot avoids index errors.
The Total Cost
You spend O(q) marking updates and one O(n) pass to rebuild. The combined cost is far below the naive O(n times q).
Where It Wins
Difference arrays shine for booking counts, road tolls, and any problem with many range-add operations and one final read.
Quick Check
You add v to every element from index l to r.
Recap
You can batch range updates with a difference array: mark l and r + 1, then prefix-sum once to rebuild. Fast updates, single read. ✅
Frequently asked questions
Is the “Difference Arrays for Range Updates” lesson free?
Yes — the full text of “Difference Arrays for Range Updates” 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 “Difference Arrays for Range Updates”?
Apply many add-on-range operations fast. 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 4 of 4, so you can start here or from the beginning and move at your own pace.
How long does the “Difference Arrays for Range Updates” 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.
All lessons in this course
- Build a Prefix Sum Array
- Sum Any Range with Subtraction
- Count Subarrays with a Target Sum
- Difference Arrays for Range Updates