How to Write a Program to Solve the N Queens Problem in Python

Discover the intricacies of solving the N Queens problem using Python through our comprehensive step-by-step guide. This classic puzzle challenges your strategic thinking as you aim to delicately position N chess queens on an N×N chessboard, ensuring that no two queens pose a threat to each other. Embark on this intellectual journey with confidence as we present a detailed Python program, leveraging the powerful backtracking technique, to conquer this enthralling challenge. Unravel the complexities, understand the algorithms, and witness elegant solutions unfold.

Create Your Python N Queens Solution

Explore the step-by-step process of solving the N Queens problem using Python on our comprehensive guide. Learn how to strategically position chess queens on an N×N board and gain insights into algorithmic problem-solving. Let us help you solve your Python assignment with this insightful resource. Whether you're a beginner or an experienced programmer, our guide will equip you with the tools to tackle complex challenges and enhance your coding skills.

Problem Overview

The N Queens problem involves:

• Placing N queens on an N×N chessboard, ensuring they can't attack each other.
• Achieving a solution by placing one queen in each row, with no shared column, row, or diagonal.

Python Program

```python # Define function to check if it's safe to place a queen def is_safe(board, row, col, N): # Check the left side of the current row for i in range(col): if board[row][i] == 1: return False # Check upper diagonal on left side for i, j in zip(range(row, -1, -1), range(col, -1, -1)): if board[i][j] == 1: return False # Check lower diagonal on left side for i, j in zip(range(row, N, 1), range(col, -1, -1)): if board[i][j] == 1: return False return True # Define recursive utility function to solve N Queens def solve_n_queens_util(board, col, N): if col >= N: return True for i in range(N): if is_safe(board, i, col, N): board[i][col] = 1 if solve_n_queens_util(board, col + 1, N): return True board[i][col] = 0 return False # Define main function to solve N Queens and print solution def solve_n_queens(N): board = [[0 for _ in range(N)] for _ in range(N)] if not solve_n_queens_util(board, 0, N): print("Solution does not exist") return False # Print the solution for row in board: print(" ".join(map(str, row))) return True # Driver code N = int(input("Enter the value of N: ")) solve_n_queens(N) ```

Explanation

• is_safe: This function verifies the safety of placing a queen at a particular spot. It examines the left side of the current row, upper diagonal, and lower diagonal on the left side to ensure no other queens are threatened.
• solve_n_queens_util: A recursive utility function that seeks to solve the N Queens problem. It cycles through each row in the given column, placing a queen if it's deemed safe, and then advances to the next column. When a solution is found, it returns True.
• solve_n_queens: The central function that initializes the chessboard, calls the utility function, and displays the solution.
• Driver code: Takes input for N (the board's size), calls the solve_n_queens function, and presents the solution.

Conclusion

In this guide, we've taken you through the process of solving the N Queens problem using Python's backtracking technique. By immersing yourself in this classic challenge and implementing our Python solution, you'll not only gain invaluable insights into the art of algorithmic problem-solving but also strengthen your ability to devise elegant solutions to intricate puzzles. As you continue to explore the depths of backtracking algorithms, don't hesitate to experiment with varying board sizes and further refine your skills.