N-Queens Puzzle
Place N queens on an N×N chessboard so that no two queens can attack each other. This computational challenge requires advanced algorithm design, optimization techniques, and systematic problem-solving to find all valid solutions efficiently. Without proper optimization, solving a standard 8×8 chessboard could take exponentially longer, from milliseconds to minutes, making the algorithm unusable for interactive applications.
Find all possible arrangements of 4 queens on a 4×4 board where no queen can attack another.
Ready to Solve
Select a board size and click "Solve Puzzle" to see all possible queen arrangements.
How the Algorithm Works
BFS with explicit state management allows parallel exploration of solution paths rather than recursive backtracking, improving efficiency and memory usage.
Immediate constraint propagation eliminates all attacked squares (rows, columns, diagonals) from remaining options, preventing exploration of invalid branches.
Strategic column placement using middle-out ordering with parity tracking front-loads the pruning process, eliminating invalid solutions earlier and dramatically reducing the total number of checks required.
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