This Python program uses a recursive approach to solve the n-Queens problem. It explores all possible combinations of queen placements on the chessboard while ensuring that queens do not attack each other. The N-Queen problem is a classic puzzle that asks you to place N chess queens on an N×N chessboard so that no two queens threaten each other. In other words, no two queens can share the same row, column, or diagonal.

## Problem Statement

Write a Python program to find all possible solutions to the N-Queen problem for a given board size N.

## Python Program to Solve n-Queen Problem with Recursion

def is_safe(board, row, col, N): # Check if there is a queen in the same column for i in range(row): if board[i][col] == 1: return False # Check upper-left diagonal for i, j in zip(range(row, -1, -1), range(col, -1, -1)): if board[i][j] == 1: return False # Check upper-right diagonal for i, j in zip(range(row, -1, -1), range(col, N)): if board[i][j] == 1: return False return True def solve_n_queens(N): def solve(board, row): if row == N: solutions.append(["".join(["Q" if x == 1 else "." for x in row]) for row in board]) return for col in range(N): if is_safe(board, row, col, N): board[row][col] = 1 solve(board, row + 1) board[row][col] = 0 solutions = [] chessboard = [[0] * N for _ in range(N)] solve(chessboard, 0) return solutions def print_solutions(solutions): for i, solution in enumerate(solutions): print(f"Solution {i + 1}:") for row in solution: print(row) print() if __name__ == "__main__": N = int(input("Enter the size of the chessboard (N): ")) solutions = solve_n_queens(N) print_solutions(solutions)

## How it Works

- The
`is_safe`

function checks whether it is safe to place a queen at a specific position on the chessboard by examining the column and diagonal positions. - The
`solve_n_queens`

function uses recursion to find all possible solutions to the N-Queen problem. It initializes an empty chessboard and starts the solving process with the first row. - The
`print_solutions`

function prints all the solutions found.

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