N-Queens Solver

Description

This JavaScript program solves the classic N-Queens problem, which involves placing N queens on an N×N chessboard such that no two queens attack each other. The program implements a backtracking algorithm to find all valid solutions and displays them in a readable format using emojis.

Features

• Uses backtracking to explore all possible queen placements efficiently.
• Supports different board sizes by changing the value of n.
• Displays the solutions in a visual format using 👑 for queens and ⬜ for empty spaces.
• Provides the total number of solutions found for a given n.

How It Works

1. The nQueens(n) function initializes an empty chessboard of size n × n.
2. The solveNQueens(board, row, n, solutions) function attempts to place queens row by row while ensuring they do not attack each other.
3. The isSafe(board, row, col, n) function checks if a queen can be placed in a given position.
4. If a valid placement is found for all rows, a solution is added to the results.
5. The program prints each solution using printBoard(board).

Usage

1. Install Node.js if you haven't already.
2. Save the script as nQueens.js.
3. Open a terminal and run the script using:

   node nQueens.js

4. Modify the n variable in the script to test different board sizes.

Example Output

For n = 4, the script outputs:

Number of solutions for 4-Queens: 2

Solution 1:
1 ⬜ 👑 ⬜ ⬜
2 ⬜ ⬜ ⬜ 👑
3 👑 ⬜ ⬜ ⬜
4 ⬜ ⬜ 👑 ⬜

Solution 2:
1 ⬜ ⬜ 👑 ⬜
2 👑 ⬜ ⬜ ⬜
3 ⬜ ⬜ ⬜ 👑
4 ⬜ 👑 ⬜ ⬜

Complexity

• The time complexity of the backtracking approach is O(N!) in the worst case.
• The space complexity is O(N²) due to the board storage.

Notes

• The N-Queens problem has no solutions for ******n = 2**** or ******n = 3.
• The algorithm can be optimized using bitwise operations for larger values of n.

License

This project is open-source and free to use.

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Happy Coding! 🚀