Python Homework Help - Python Logical Puzzles, Games, and Algorithms: 8 queens problem

Python Homework Help

Python Homework Question

Python Logical Puzzles, Games, and Algorithms: 8 Queens problem

Python Homework Solution

The 8 Queens Problem is a classic chess puzzle where the objective is to place eight queens on a standard 8x8 chessboard in such a way that no two queens threaten each other. That is, no two queens can occupy the same row, column, or diagonal.
Here's a Python program that uses the backtracking algorithm to solve the 8 Queens Problem:

def solve_queens(n):
    board = [[0 for _ in range(n)] for _ in range(n)]
    solutions = []

    def place_queen(row):
        if row == n:
            solutions.append([board[i][:] for i in range(n)])
            return

        for col in range(n):
            if is_valid_move(row, col):
                board[row][col] = 1
                place_queen(row+1)
                board[row][col] = 0

    def is_valid_move(row, col):
        for i in range(row):
            if board[i][col] == 1:
                return False

        for i, j in zip(range(row-1, -1, -1), range(col-1, -1, -1)):
            if board[i][j] == 1:
                return False

        for i, j in zip(range(row-1, -1, -1), range(col+1, n)):
            if board[i][j] == 1:
                return False

        return True

    place_queen(0)

    return solutions

# example usage
solutions = solve_queens(8)
print(f"Number of solutions: {len(solutions)}")
for i, solution in enumerate(solutions):
    print(f"Solution {i+1}:")
    for row in solution:
        print(" ".join(str(col) for col in row))
The solve_queens function takes an integer n as input, representing the size of the chessboard. It initializes an empty n x n board, then uses a recursive place_queen function to try placing a queen on each row of the board. The is_valid_move function is used to check if a queen can be safely placed at a given row and column.
The function returns a list of all valid solutions. For each solution, it prints the board in a human-readable format.