Permutations and the N-Queens Idea
Place items and backtrack on conflicts.
Permutations and the N-Queens Idea is a free Coding Interview Prep lesson on CoddyKit — lesson 3 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.
From Subsets to Orderings
A permutation is an arrangement of all elements in some order. Generating them is the next backtracking skill after subsets. 🔀
How Many Permutations
There are n factorial permutations of n items, because the first slot has n choices, the next n minus one, and so on. It grows fast.
Place One Item at a Time
The recursion fills positions left to right. At each step you pick an unused element, place it, and recurse on the rest.
Track What Is Used
A boolean used array marks which elements are already placed, so each appears exactly once in every permutation.
Permutations in Code
This backtracking places an unused value, recurses, then frees it for the next branch.
def perm(cur):
if len(cur) == n:
out.append(cur[:]); return
for x in a:
if x not in cur:
perm(cur + [x])Use itertools When Allowed
For quick contests, Python's itertools.permutations gives every ordering without writing the recursion yourself.
from itertools import permutations
for p in permutations(a):
print(p)The N-Queens Problem
N-Queens asks you to place n queens on an n by n board so none attack each other. It is the classic backtracking puzzle. 👑
One Queen Per Row
Since no two queens share a row, you place exactly one queen per row and only choose its column. That shrinks the search hugely.
Check the Three Conflicts
Before placing, reject any column or diagonal already taken. Track used columns and both diagonal directions in sets.
if c in cols or r-c in d1 or r+c in d2:
continueBacktrack on a Dead End
If no column works in a row, the branch fails. You backtrack, remove the last queen, and try its next option.
The Shared Pattern
Permutations and N-Queens share one shape: choose, recurse, undo. Once you see it, most placement puzzles fall to the same template.
Quick Check
Why does N-Queens place just one queen per row?
Recap: Choose, Recurse, Undo
You generated permutations by placing unused items and learned that N-Queens uses the same choose-recurse-undo pattern with conflict checks. 🎯
Frequently asked questions
Is the “Permutations and the N-Queens Idea” lesson free?
Yes — the full text of “Permutations and the N-Queens Idea” 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 “Permutations and the N-Queens Idea”?
Place items and backtrack on conflicts. 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 3 of 4, so you can start here or from the beginning and move at your own pace.
How long does the “Permutations and the N-Queens Idea” 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
- Think Recursively: Base & Recurse
- Generate All Subsets
- Permutations and the N-Queens Idea
- Prune to Survive the Time Limit