Is N-Queens easy or hard?

N-Queens is considered a hard problem because it requires recursive search with pruning and careful state tracking. The challenge comes from efficiently eliminating invalid placements while exploring all valid board configurations.

How to solve N-Queens in O(n)?

N-Queens cannot be solved in O(N) time when generating all valid board configurations. The search space grows factorially, leading to about O(N!) complexity. Optimizations like bitmasking reduce constant overhead but do not change the overall factorial growth.

What is the best approach for N-Queens?

Backtracking with row-wise construction is the most common and interview-friendly approach. It places one queen per row and tracks used columns and diagonals to prune invalid states. The algorithm explores placements recursively with about O(N!) time complexity and O(N) extra space for tracking constraints.

What data structure is used in N-Queens?

Typical implementations use arrays or sets to track occupied columns and diagonals. Optimized versions replace these structures with integer bitmasks, allowing constant-time checks using bit operations and reducing memory overhead.

What is the time complexity of N-Queens?

The typical N-Queens backtracking solution runs in approximately O(N!) time because each row can branch into multiple column choices while pruning invalid placements. Space complexity is O(N) for recursion depth and tracking columns and diagonals, or O(N²) if the board is stored explicitly.

N-Queens Python or Java solution approach?

Python and Java solutions usually implement recursive backtracking. Track used columns, major diagonals (row - col), and minor diagonals (row + col) using sets or boolean arrays, then recursively place queens row by row until a full board configuration is built.

Is N-Queens asked at Google, Amazon, or Meta?

N-Queens is a classic backtracking problem commonly used in interviews at companies like Amazon, Google, and Meta to evaluate recursion, pruning strategies, and constraint satisfaction reasoning. Variants may appear that focus on counting solutions or validating queen placements.

Description Solution Video 17:51

51. N-Queens

Hard76.3% acceptance16 companies

The n-queens puzzle is the problem of placing n queens on an n x n chessboard such that no two queens attack each other.

Given an integer n, return all distinct solutions to the n-queens puzzle. You may return the answer in any order.

Each solution contains a distinct board configuration of the n-queens' placement, where 'Q' and '.' both indicate a queen and an empty space, respectively.

Example 1:

Input: n = 4
Output: [[".Q..","...Q","Q...","..Q."],["..Q.","Q...","...Q",".Q.."]]
Explanation: There exist two distinct solutions to the 4-queens puzzle as shown above

Example 2: