N-Queens
Place n queens on an n x n board so that none attack each other.
Pattern fit
This is a classic constraint backtracking problem where pruning matters more than raw recursion, because invalid board states should be rejected immediately.
Key observation
At each row you only need to know which columns and diagonals are already occupied.
Target complexity
Exponential / O(n)
How to break down the solution cleanly
This is a classic constraint backtracking problem where pruning matters more than raw recursion, because invalid board states should be rejected immediately.
At each row you only need to know which columns and diagonals are already occupied.
Model the decision tree explicitly.
Choose the next candidate set for the current depth.
Reference implementation
Python# Generic pattern template
def backtrack(path):
if complete(path):
answer.append(path[:])
return
for choice in choices(path):
if not valid(choice, path):
continue
path.append(choice)
backtrack(path)
path.pop()
Common pitfalls
Checking the whole board for every candidate instead of maintaining sets.
Forgetting diagonal indexing rules.
Common follow-ups
How do diagonal sets map to row and column?
Could bitmasks speed this up?
Continue with related problems
Build repeatable depth inside the Backtracking cluster before moving on.