Lecture Notes on 9 Mar 2022

class Queens (object):
  # initialize the board
  def __init__ (self, n = 8):
    self.board = []
    self.n = n
    for i in range (self.n):
      row = []
      for j in range (self.n):
        row.append ('*')
      self.board.append (row)

  # print the board
  def print_board (self):
    for i in range (self.n):
      for j in range (self.n):
        print (self.board[i][j], end = ' ')
      print ()
    print ()

  # check if no queen captures the queen placed at (row, col)
  def is_valid (self, row, col):
    # check row and column
    for i in range (self.n):
      if (self.board[row][i] == 'Q') or (self.board[i][col] == 'Q'):
        return False

    # check along diagonals
    for i in range (self.n):
      for j in range (self.n):
        row_diff = abs (row - i)
        col_diff = abs (col - j)
        if (row_diff == col_diff) and (self.board[i][j] == 'Q'):
          return False
    return True

  # do a recursive backtracking solution
  def recursive_solve (self, col):
    if (col == self.n):
      return True
    else:
      for i in range (self.n):
        if (self.is_valid(i, col)):
          self.board[i][col] = 'Q'
          if (self.recursive_solve (col + 1)):
            return True
          self.board[i][col] = '*'
      return False

  # if the problem has a solution print the board
  def solve (self):
    for i in range (self.n):
      if (self.recursive_solve(i)):
        self.print_board()

def main():
  # create a chess board
  game = Queens (8)

  # place the queens on the board
  game.solve()

main()