8-Queen Problem:

The 8-Queen Problem is a classic puzzle that challenges you to place eight queens on an 8×8 chessboard in a way that no two queens can attack each other. In chess, queens can move horizontally, vertically, and diagonally, which means no two queens can share a row, column, or diagonal.

The best strategy to solve the 8-Queen Problem is to use a backtracking algorithm. Solution using Backtracking:

 

1. Start in the First Row: Begin in the first row of the chessboard, and in the first column.

2. Place a Queen: Place a queen in the current column if it doesn't conflict with any previously placed queens.

3. Move to the Next Row: Move to the next row and try to place a queen in the first column.

4. Backtracking: If you find a row where you can't place a queen without violating the constraints (i.e., no two queens threaten each other), backtrack to the previous row and move the previous queen to a different column. Keep repeating this process until you find a valid configuration or exhaust all possibilities.

5. Continue Backtracking:

Keep backtracking until you have explored all possible configurations.

6. Solution Found: If you find a configuration where all eight queens can be placed without conflicts, you've found a solution to the problem.

7. Optimizations: Implement optimizations like pruning to avoid exploring branches that are known to lead to invalid solutions, improving the algorithm's efficiency.

 

Backtracking is a robust strategy for solving complex combinatorial puzzles like the 8-Queen Problem. The problem complexity increases with larger boards (N-Queens) and can be computationally intensive. Finding solutions for large N can be time-consuming and resource-intensive.