N Queens

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Problem

Place n queens on an n x n chessboard so that no two queens attack each other (no shared row, column, or diagonal), and return all distinct board configurations that achieve this.

Examples

Example 1

Input:n = 4

Output:2 distinct solutions

Constraints

1 <= n <= 9

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How to approach it: the Backtracking pattern

Explore a decision one choice at a time, undo it if it doesn't lead anywhere, and try the next option. It's a systematic way to generate every valid combination, permutation, or arrangement.

Look for this pattern when

The problem asks for "all possible" combinations, subsets, permutations, or valid arrangements.
A greedy or direct-formula approach doesn't work because you genuinely need to explore multiple branches.

Read the full Backtracking guide →

Video walkthroughs

Original problem on LeetCode ↗