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"""

The nqueens problem is of placing N queens on a N * N

chess board such that no queen can attack any other queens placed

on that chess board.

This means that one queen cannot have any other queen on its horizontal, vertical and

diagonal lines.

"""

from __future__ import annotations

solution = []

def isSafe(board: list[list[int]], row: int, column: int) -> bool:

"""

This function returns a boolean value True if it is safe to place a queen there

considering the current state of the board.

Parameters :

board(2D matrix) : board

row ,column : coordinates of the cell on a board

Returns :

Boolean Value

"""

for i in range(len(board)):

if board[row][i] == 1:

return False

for i in range(len(board)):

if board[i][column] == 1:

return False

for i, j in zip(range(row, -1, -1), range(column, -1, -1)):

if board[i][j] == 1:

return False

for i, j in zip(range(row, -1, -1), range(column, len(board))):

if board[i][j] == 1:

return False

return True

def solve(board: list[list[int]], row: int) -> bool:

"""

It creates a state space tree and calls the safe function until it receives a

False Boolean and terminates that branch and backtracks to the next

possible solution branch.

"""

if row >= len(board):

"""

If the row number exceeds N we have board with a successful combination

and that combination is appended to the solution list and the board is printed.

"""

solution.append(board)

printboard(board)

print()

return True

for i in range(len(board)):

"""

For every row it iterates through each column to check if it is feasible to

place a queen there.

If all the combinations for that particular branch are successful the board is

reinitialized for the next possible combination.

"""

if isSafe(board, row, i):

board[row][i] = 1

solve(board, row + 1)

board[row][i] = 0

return False

def printboard(board: list[list[int]]) -> None:

"""

Prints the boards that have a successful combination.

"""

for i in range(len(board)):

for j in range(len(board)):

if board[i][j] == 1:

print("Q", end=" ")

else:

print(".", end=" ")

print()

# n=int(input("The no. of queens"))

n = 8

board = [[0 for i in range(n)] for j in range(n)]

solve(board, 0)

print("The total no. of solutions are :", len(solution))

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