N-Queens Problem Solver

About the N-Queens Problem Solver

The N-Queens Problem Solver finds a placement of \( n \) queens on an \( n \times n \) chessboard such that no two queens can attack each other (i.e., no two queens share the same row, column, or diagonal). This tool is ideal for computer science students, puzzle enthusiasts, and those studying backtracking algorithms.

N-Queens Problem: A classic constraint satisfaction problem solved using backtracking, where each queen must be placed in a unique row and column, avoiding conflicts on diagonals.

Use this solver to explore solutions for various board sizes and visualize queen placements.

• Features:
  • Computes a valid placement of \( n \) queens on an \( n \times n \) board.
  • Supports board sizes \( n \geq 1 \) (4 to 12 recommended for visualization).
  • Keypad includes digits (0–9) and a "Next" button to cycle through solutions.
  • Visualizes the chessboard with queens (\( \text{Q} \)) and provides a textual representation.
  • Clear and backspace functionality, with a "Copy" button for results.
  • Displays backtracking steps for educational purposes.
• Practical Applications: Useful in algorithm design (backtracking, constraint satisfaction), puzzle solving, and computer science education.
• How to Use:
  • Enter the board size \( n \) using the keypad digits.
  • Click "Solve" to compute a solution, displayed as a chessboard and text.
  • Use the "Next" button to cycle through different solutions (if available).
  • Use "Clear" to reset or "⌫" to delete the last digit.
  • Use "Copy" to copy the solution text.
  • Share or embed the solver using the action buttons.
• Helpful Tips:
  • Input \( n \) must be a positive integer; \( n = 4 \) to \( 12 \) is recommended for practical visualization.
  • No solutions exist for \( n = 2 \) or \( n = 3 \).
  • The solver uses backtracking to find solutions efficiently.
  • The "Next" button cycles through a precomputed set of solutions or resets to the first.
  • Large \( n \) (e.g., \( n > 12 \)) may slow down visualization; use smaller values for best experience.
• Examples:
  • Example 1: Standard 8-Queens:
    • Input: \( n = 8 \)
    • Steps:
      • Place queen in row 0, find safe column.
      • Proceed to row 1, backtrack if conflicts arise.
      • Continue until all 8 queens are placed.
    • Result: A valid placement, e.g., queens at \( (0,0), (1,4), (2,7), (3,5), (4,2), (5,6), (6,1), (7,3) \).
  • Example 2: Small Board:
    • Input: \( n = 4 \)
    • Steps:
      • Place queens row by row, ensuring no attacks.
      • Backtrack to find a valid configuration.
    • Result: A valid placement, e.g., queens at \( (0,1), (1,3), (2,0), (3,2) \).
  • Example 3: Invalid Case:
    • Input: \( n = 2 \)
    • Steps:
      • Attempt to place 2 queens; no valid solution exists.
    • Result: No solution possible.

Explore the N-Queens problem with this interactive solver. Share or embed it on your site!