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POEuler 43 - is there a monad to help write this list comprehension?
 

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  1. POEuler 43 - is there a monad to help write this list comprehension?
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    <p>Here is a way to solve Euler problem 43 (please let me know if this doesn't give the correct answer). Is there a monad or some other syntatic sugar which could assist with keeping track of the <code>notElem</code> conditions?</p> <pre><code>toNum xs = foldl (\s d -&gt; s*10+d) 0 xs numTest xs m = (toNum xs) `mod` m == 0 pandigitals = [ [d0,d1,d2,d3,d4,d5,d6,d7,d8,d9] | d7 &lt;- [0..9], d8 &lt;- [0..9], d8 `notElem` [d7], d9 &lt;- [0..9], d9 `notElem` [d8,d7], numTest [d7,d8,d9] 17, d5 &lt;- [0,5], d5 `notElem` [d9,d8,d7], d3 &lt;- [0,2,4,6,8], d3 `notElem` [d5,d9,d8,d7], d6 &lt;- [0..9], d6 `notElem` [d3,d5,d9,d8,d7], numTest [d6,d7,d8] 13, numTest [d5,d6,d7] 11, d4 &lt;- [0..9], d4 `notElem` [d6,d3,d5,d9,d8,d7], numTest [d4,d5,d6] 7, d2 &lt;- [0..9], d2 `notElem` [d4,d6,d3,d5,d9,d8,d7], numTest [d2,d3,d4] 3, d1 &lt;- [0..9], d1 `notElem` [d2,d4,d6,d3,d5,d9,d8,d7], d0 &lt;- [1..9], d0 `notElem` [d1,d2,d4,d6,d3,d5,d9,d8,d7] ] main = do let nums = map toNum pandigitals print $ nums putStrLn "" print $ sum nums </code></pre> <p>For instance, in this case the assignment to <code>d3</code> is not optimal - it really should be moved to just before the <code>numTest [d2,d3,d4] 3</code> test. Doing that, however, would mean changing some of the <code>notElem</code> tests to remove <code>d3</code> from the list being checked. Since the successive <code>notElem</code> lists are obtained by just consing the last chosen value to the previous list, it seems like this should be doable - somehow.</p> <p>UPDATE: Here is the above program re-written with Louis' <code>UniqueSel</code> monad below:</p> <pre><code>toNum xs = foldl (\s d -&gt; s*10+d) 0 xs numTest xs m = (toNum xs) `mod` m == 0 pandigitalUS = do d7 &lt;- choose d8 &lt;- choose d9 &lt;- choose guard $ numTest [d7,d8,d9] 17 d6 &lt;- choose guard $ numTest [d6,d7,d8] 13 d5 &lt;- choose guard $ d5 == 0 || d5 == 5 guard $ numTest [d5,d6,d7] 11 d4 &lt;- choose guard $ numTest [d4,d5,d6] 7 d3 &lt;- choose d2 &lt;- choose guard $ numTest [d2,d3,d4] 3 d1 &lt;- choose guard $ numTest [d1,d2,d3] 2 d0 &lt;- choose guard $ d0 /= 0 return [d0,d1,d2,d3,d4,d5,d6,d7,d8,d9] pandigitals = map snd $ runUS pandigitalUS [0..9] main = do print $ pandigitals </code></pre>
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