N=4 , N-Queens Problem

4queens.py

N = 4

def print_board(board):
  for i in range(N):
    for j in range(N):
      print(board[i][j], end=" ")
    print()


def isValid(board, row, col):
  """check 3 directions if the Queen can take out any other Queens """

  # check left side
  for i in range(col):
    if board[row][i] == 1:
      return False
  
  # check the upper diagonal
  for i, j in zip(range(row, -1, -1), range(col, -1, -1)):
    if board[i][j] == 1:
      return False
  
  # check the bottom diagonal
  for i, j in zip(range(row, N, 1), range(col, -1, -1)):
    if board[i][j] == 1:
      return False
  
  return True


def solve_NQ_util(board, col):

  """ If all Queens are placed, then return True """
  if col == N:
    return True

  for i in range(N):

    if isValid(board, i, col):
      board[i][col] = 1

      if solve_NQ_util(board, col+1):
        return True
      
      board[i][col] = 0
  
  return False
      

def solve_NQ():
  board = [[0 for i in range(N)]for i in range(N)]

  if not solve_NQ_util(board,0):
    print("No Solution exist")
    return False
  
  print_board(board)
  return True

solve_NQ()