The 10^8 Rule of Thumb
Map operation counts to the time limit.
The 10^8 Rule of Thumb is a free Coding Interview Prep lesson on CoddyKit — lesson 2 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 Magic Budget
A typical online judge runs about 10^8 simple operations per second. That number is your spending budget for the whole program. 💡
From Steps to Seconds
Multiply your operation count by the work per step, then compare to the time limit. If steps fit in the budget, you likely pass.
Linear Is Cheap
An O(n) scan over n = 10^6 is only a million steps, far under the budget. Linear solutions almost always pass comfortably.
n log n Is Safe
For n = 10^6, an O(n log n) sort is about 2 times 10^7 steps. Still well inside the one-second budget, so sorting is rarely the bottleneck.
Quadratic Has a Ceiling
An O(n^2) approach hits the budget near n = 10^4, where it costs 10^8 steps. Past that, quadratic starts to time out.
Cubic Is Tiny Only
An O(n^3) solution survives only up to about n = 500. Cube that and you reach roughly 10^8 steps, the edge of the budget.
Exponential Stays Small
O(2^n) doubles each step, so it works only for tiny n around 20 to 25. Beyond that the operation count explodes past 10^8.
Python Pays a Tax
Python is slower per step, so treat the budget as closer to 10^7 for tight loops. Stay conservative when constraints feel borderline.
Mind the Hidden Constant
The 10^8 rule counts simple steps. Heavy work inside a loop, like string building, adds a constant factor that shrinks your real budget.
Read the Limit
The time limit is often 1 or 2 seconds. A 2-second limit roughly doubles your budget, giving a little more breathing room.
Estimate Before You Type
Always plug n into your complexity and compare to 10^8 first. This quick sanity check saves you from coding a doomed solution.
Quick Check
Put the 10^8 rule to work.
Recap
You now map operations to time: roughly 10^8 per second. Linear and n log n are safe, quadratic caps near 10^4, and you check before coding. ✅
Frequently asked questions
Is the “The 10^8 Rule of Thumb” lesson free?
Yes — the full text of “The 10^8 Rule of Thumb” 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 “The 10^8 Rule of Thumb”?
Map operation counts to the time limit. 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 2 of 4, so you can start here or from the beginning and move at your own pace.
How long does the “The 10^8 Rule of Thumb” 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.