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CHAPTER 9 ■ MAGIC METHODS, PROPERTIES, AND ITERATORS 199 What results do you expect from the recursive call? You want the positions of all the lower queens, right? Let’s say they are returned as a tuple. In that case you probably have to change your base case to return a tuple as well (of length one)—but I get to that later. So, you’re supplied with one tuple of positions from “above,” and for each legal position of the current queen, you are supplied with a tuple of positions from “below.” All you have to do to keep things flowing is to yield the result from below with your own position added to the front: ... else: for pos in range(num): if not conflict(state, pos): for result in queens(num, state + (pos,)): yield (pos,) + result The for pos and if not conflict parts of this are identical to what you had before so you can rewrite this a bit to simplify the code. Let’s add some default arguments as well: def queens(num=8, state=()): for pos in range(num): if not conflict(state, pos): if len(state) == num-1: yield (pos,) else: for result in queens(num, state + (pos,)): yield (pos,) + result If you find the code hard to understand, you might find it helpful to formulate what it does in your own words. (And, you do remember that the comma in (pos,) is necessary to make it a tuple, and not simply a parenthesized value?) The queens generator gives you all the solutions (that is, all the legal ways of placing the queens): >>> list(queens(3)) [] >>> list(queens(4)) [(1, 3, 0, 2), (2, 0, 3, 1)] >>> for solution in queens(8): ... print solution ... (0, 4, 7, 5, 2, 6, 1, 3) (0, 5, 7, 2, 6, 3, 1, 4) ... (7, 2, 0, 5, 1, 4, 6, 3) (7, 3, 0, 2, 5, 1, 6, 4) >>> If you run queens with eight queens, you see a lot of solutions flashing by. Let’s find out how many:
200 CHAPTER 9 ■ MAGIC METHODS, PROPERTIES, AND ITERATORS >>> len(list(queens(8))) 92 Wrapping It Up Before leaving the queens, let’s make the output a bit more understandable. Clear output is always a good thing because it makes it easier to spot bugs, among other things. def prettyprint(solution): def line(pos, length=len(solution)): return '. ' * (pos) + 'X ' + '. ' * (length-pos-1) for pos in solution: print line(pos) Note that I’ve made a little helper function inside prettyprint. I put it there because I assumed I wouldn’t need it anywhere outside. In the following, I print out a random solution to satisfy myself that it is correct: >>> import random >>> prettyprint(random.choice(list(queens(8)))) . . . . . X . . . X . . . . . . . . . . . . X . X . . . . . . . . . . X . . . . . . . . . . . X . . . . X . . . . . X . . . . . This “drawing” corresponds to the diagram in Figure 9-2. Fun to play with Python, isn’t it? Figure 9-2. One of many possible solutions to the Eight Queens problem
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572 APPENDIX C ■ ONLINE RESOURCES
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Index ■Symbols - operator 558 !=
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■INDEX 585 finding conflicts 197
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■INDEX 601 TestCase class methods
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