How does the N-Queens problem work with backtracking?

Can you explain the N-Queens problem and how backtracking is used to solve it?

The N-Queens problem involves placing N queens on an N×N chessboard so that no two queens threaten each other. Backtracking is a method used to find all possible arrangements by placing queens one by one in different columns and checking for conflicts.

What are the main steps in the backtracking algorithm for this problem?

The main steps include: 1) Place a queen in a column, 2) Check for conflicts with already placed queens, 3) If no conflict, move to the next column, 4) If a conflict occurs, backtrack and try the next row in the current column.

Can you give me a simple example of how this works?

Sure! For a 4x4 board, you start by placing a queen in the first row of the first column. Then, you try to place the next queen in the second column, checking for conflicts. If you can't place it, you backtrack to the first queen and move it to the next row.

What is the time complexity of the backtracking solution?

The time complexity of the backtracking solution for the N-Queens problem is O(N!), as it explores all possible arrangements of queens.