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POScheme, N-queens optimization stragegies SICP chapter 2
 

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    <p>SICP contains an partially complete example of the n-queens solutions, by walking a tree of every possible queen placement in the last row, generating more possible positions in the next row to combine the results so far, filtering the possibilities to keep only ones where the newest queen is safe, and repeating recursively. </p> <p>This strategy blows up after about n=11 with a maximum recursion error.</p> <p>I've implemented an alternate strategy that does a smarter tree-walk from the first column, generating possible positions from a list of unused rows, consing each position-list onto an updated list of yet-unused rows. Filtering those pairs considered safe, and recursively mapping over these pairs for the next column. This doesn't blow up (so far) but n=12 takes a minute and n=13 takes about 10 minutes to solve.</p> <pre><code>(define (queens board-size) (let loop ((k 1) (pp-pair (cons '() (enumerate-interval 1 board-size)))) (let ((position (car pp-pair)) (potential-rows (cdr pp-pair))) (if (&gt; k board-size) (list position) (flatmap (lambda (pp-pair) (loop (++ k) pp-pair)) (filter (lambda (pp-pair) (safe? k (car pp-pair))) ;keep only safe (map (lambda (new-row) (cons (adjoin-position new-row k position) (remove-row new-row potential-rows))) ;make pp-pair potential-rows))))))) ;auxiliary functions not listed </code></pre> <p>Not really looking for code, but a simple explanation of a strategy or two that's less naive and that clicks well with a functional approach. </p>
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    1. COWhat do you mean by 'blows up'? If it is that the Scheme implementation fails, what implementation are you using?
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    2. COHere: http://stackoverflow.com/q/2595132/1286639
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    3. CO@GoZoner,The maximum recursion error kicks in at n 11 or greater, but not for n 10 or less. Using Mit-scheme,
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