Python Program to Solve n-Queen Problem without Recursion

class QueenChessBoard:
    def __init__(self, size):
        # board has dimensions size x size
        self.size = size
        # columns[r] is a number c if a queen is placed at row r and column c.
        # columns[r] is out of range if no queen is place in row r.
        # Thus after all queens are placed, they will be at positions
        # (columns[0], 0), (columns[1], 1), ... (columns[size - 1], size - 1)
        self.columns = []
 
    def place_in_next_row(self, column):
        self.columns.append(column)
 
    def remove_in_current_row(self):
        return self.columns.pop()
 
    def is_this_column_safe_in_next_row(self, column):
        # index of next row
        row = len(self.columns)
 
        # check column
        for queen_column in self.columns:
            if column == queen_column:
                return False
 
        # check diagonal
        for queen_row, queen_column in enumerate(self.columns):
            if queen_column - queen_row == column - row:
                return False
 
        # check other diagonal
        for queen_row, queen_column in enumerate(self.columns):
            if ((self.size - queen_column) - queen_row
                == (self.size - column) - row):
                return False
 
        return True
 
    def display(self):
        for row in range(self.size):
            for column in range(self.size):
                if column == self.columns[row]:
                    print('Q', end=' ')
                else:
                    print('.', end=' ')
            print()
 
 
def solve_queen(size):
    """Display a chessboard for each possible configuration of placing n queens
    on an n x n chessboard and print the number of such configurations."""
    board = QueenChessBoard(size)
    number_of_solutions = 0
 
    row = 0
    column = 0
    # iterate over rows of board
    while True:
        # place queen in next row
        while column < size:
            if board.is_this_column_safe_in_next_row(column):
                board.place_in_next_row(column)
                row += 1
                column = 0
                break
            else:
                column += 1
 
        # if could not find column to place in or if board is full
        if (column == size or row == size):
            # if board is full, we have a solution
            if row == size:
                board.display()
                print()
                number_of_solutions += 1
 
                # small optimization:
                # In a board that already has queens placed in all rows except
                # the last, we know there can only be at most one position in
                # the last row where a queen can be placed. In this case, there
                # is a valid position in the last row. Thus we can backtrack two
                # times to reach the second last row.
                board.remove_in_current_row()
                row -= 1
 
            # now backtrack
            try:
                prev_column = board.remove_in_current_row()
            except IndexError:
                # all queens removed
                # thus no more possible configurations
                break
            # try previous row again
            row -= 1
            # start checking at column = (1 + value of column in previous row)
            column = 1 + prev_column
 
    print('Number of solutions:', number_of_solutions)
 
 
n = int(input('Enter n: '))
solve_queen(n)

Output

Enter n: 4
. Q . . 
. . . Q 
Q . . . 
. . Q . 
 
. . Q . 
Q . . . 
. . . Q 
. Q . . 
 
Number of solutions: 2