Lecture Notes on 24 Feb 2014

This is the classic 8 Queens problem - how to place
8 Queens on a chess board such that no two Queens
can capture each other.

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)

  # check if no queen captures another
  def is_valid (self, row, col):
    for i in range (self.n):
      if (self.board[row][i] == 'Q' or self.board[i][col] == 'Q'):
        return False
    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 solve on the problem
  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

  # solve the problem
  def solve (self):
    for i in range (self.n):
      if (self.recursive_solve (i)):
        self.print_board()

  # 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 ()

def main ():
  # create object and solve
  queens = Queens (8)
  queens.solve()

main()

* Modify the program so that it prints 'No valid solution'
  where there is none, like a 3 x 3 board.

* Modify the program so that it prints all possible solutions.
  (There are 92 such solutions.)

* Modify the program so that it prints all unique solutions.
  (There are 12 unique solutions.)

* What is the maximum number of queens that can be placed on 
  a chess board such that all squares are under the influence
  of one or more queens? Show the placement of the queens.

* On a 8 x 8 board place 32 knights, 14 bishops, 16 kings, or
  8 rooks so that no two pieces attack each other.