eight queens problem hacker rank

eightqueen.py

from typing import Tuple


class InvalidGame(Exception):
    def __init__(self, message):
        super().__init__(message)


class Board:
    """N x N chessboard"""

    N = 8

    def __init__(self):
        """get the party started"""
        # queen_col[x] = y means a queen is at (x, y)
        self.queen_col = [-1] * (Board.N + 1)
        # track column occupancy
        self.columns = [False] * (Board.N + 1)
        # x + y ranges 2..16 → we index 0..16
        self.diag1 = [False] * (Board.N * 2 + 1)
        # x - y ranges -7..+7 → shift by (N−1)=7 to index 0..14
        self.diag2 = [False] * (Board.N * 2)

    def _place_queen_recursive(self, n_queen: int, row: int) -> bool:
        if row > n_queen:
            return True
        for col in range(1, Board.N + 1):
            if self.check_queen((row, col)):
                self.set_queen((row, col))
                if self._place_queen_recursive(n_queen, row + 1):
                    return True
                self.clear_queen((row, col))
        return False

    def place_queens(self, n_queen: int) -> bool:
        if n_queen > Board.N:
            raise InvalidGame(f"Can not place {n_queen} queens on a board of {Board.N}")
        return self._place_queen_recursive(n_queen, 1)

    def set_queen(self, position: Tuple[int, int]) -> None:
        x, y = position
        self.queen_col[x] = y
        self.columns[y] = True
        self.diag1[x + y] = True
        self.diag2[x - y + Board.N - 1] = True

    def check_queen(self, position: Tuple[int, int]) -> bool:
        x, y = position
        if self.columns[y]:
            return False
        if self.diag1[x + y]:
            return False
        if self.diag2[x - y + Board.N - 1]:
            return False
        return True

    def clear_queen(self, position: Tuple[int, int]) -> None:
        x, y = position
        self.queen_col[x] = -1
        self.columns[y] = False
        self.diag1[x + y] = False
        self.diag2[x - y + Board.N - 1] = False

    @staticmethod
    def is_valid_placement(position: Tuple[int, int]) -> bool:
        x, y = position
        return 0 < x <= Board.N and 0 < y <= Board.N


if __name__ == "__main__":
    board = Board()
    if board.place_queens(8):
        print("Found a valid configuration:\n")
        for r in range(1, Board.N + 1):
            row_str = ""
            c = board.queen_col[r]
            for col in range(1, Board.N + 1):
                row_str += "Q " if col == c else ". "
            print(row_str.strip())
    else:
        print("No solution found.")