Solve N-Queens Problem

Explore how to solve the N-Queens problem by placing N queens on an N×N chessboard so that no two queens attack each other. Learn to apply backtracking techniques to reduce unnecessary checks, understand the algorithm's recursive structure, and analyze the solution's time and space complexity. This lesson helps you develop problem-solving skills with backtracking for coding interviews.

We'll cover the following...

Statement

Example 1
Example 2
Sample input
Expected output

Try it yourself
Solution 1

Time complexity
Space complexity

Solution 2

Time complexity
Space complexity

Statement

Given a chessboard of size $N \times N$ , determine how many ways $N$ queens can be placed on the board, such that no two queens attack each other.

A queen can move horizontally, vertically, and diagonally on a chessboard. One queen can be attacked by another queen if it is present in the same row, column, or diagonal of that queen.

Example 1

Below is a valid placement of $4$ queens on a $4 \times 4$ chessboard. The $X$ on the board represents a square where a queen is placed:

1.Getting Started

2.Arrays

3.Linked Lists

4.Math & Stats

5.Strings

6.Trees

7.Stacks and Queues

8.Graphs

9.Back Tracking

10.Dynamic Programming

11.Miscellaneous

12.Appendix

13.Conclusion

Solve N-Queens Problem

Statement

Example 1