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

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

The N-Queens problem is a classic algorithmic problem in computer science 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 algorithms are commonly used to solve the N-Queens problem?

Common algorithms include backtracking, constraint satisfaction, and even genetic algorithms. Backtracking is the most straightforward approach, where you place queens one by one and backtrack when a conflict arises.

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

Sure! The backtracking algorithm places a queen in a column and then recursively attempts to place queens in subsequent columns. If a placement leads to a conflict, it backtracks and tries the next position until all queens are placed or all options are exhausted.

Are there any optimizations for the backtracking approach?

Yes, optimizations include using bitwise operations to track threats more efficiently, and pruning the search space by avoiding placements that are known to lead to conflicts.