What is the N-Queens problem and how can it be solved?

What is the N-Queens problem and how can it be solved?

The N-Queens problem is a classic algorithmic problem where the goal is to place N queens on an N×N chessboard so that no two queens threaten each other. This means that no two queens can share the same row, column, or diagonal.

What are some common algorithms used to solve the N-Queens problem?

Common algorithms include backtracking, constraint satisfaction, and genetic algorithms. Backtracking is the most straightforward approach.

Can you explain how the backtracking algorithm works for this problem?

Sure! The backtracking algorithm places queens one by one in different columns, starting from the leftmost column. It checks for safety before placing a queen and backtracks if it finds a conflict.

Are there any optimizations that can be applied to the backtracking approach?

Yes, optimizations like using bitwise operations to track columns and diagonals can significantly reduce the search space and improve performance.