Beginning Python - From Novice to Professional

198 CHAPTER 9 ■ MAGIC METHODS, PROPERTIES, AND ITERATORS
def queens(num, state):
if len(state) == num-1:
for pos in range(num):
if not conflict(state, pos):
yield pos
In human-speak this means the following: If all but one queen have been placed, go through
all possible positions for the last one, and return the ones that don’t give rise to any conflicts.
The num parameter is the number of queens in total, and the state parameter is the tuple of
positions for the previous queens. For example, let’s say you have four queens, and that the
first three have been given the positions 1, 3, and 0, respectively, as shown in Figure 9-1. (Pay
no attention to the white queen at this point.)
Figure 9-1. Placing four queens on a 4×4 board
As you can see in the figure, each queen gets a (horizontal) row, and their positions are
numbered across the top (beginning with zero, as is normal in Python):
>>> list(queens(4, (1,3,0)))
[2]
It works like a charm. Using list simply forces the generator to yield all of its values. In this
case, only one position qualifies. The white queen has been put in this position in Figure 9-1.
(Note that color has no special significance and is not part of the program.)
The Recursive Case
Now, let’s turn to the recursive part of the solution. When you have your base case covered, the
recursive case may correctly assume (by induction) that all results from lower levels (the queens
with higher numbers) are correct. So what you have to do is add an else clause to the if statement
in the previous implementation of the queens function.