StackOverflow2013

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2013-06-01T15:30:54.423
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2013-06-01T15:30:54.423
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2017-05-23T10:25:52.980
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Body
I agree with <a href="https://stackoverflow.com/users/98117/hammar">hammar</a>, <a href="https://stackoverflow.com/questions/16870683/avoid-pattern-matching-in-recursion#comment24338245_16870930"><code>unfoldr</code> is the way to go here</a>. You can also get rid of the pattern matching in <code>diagNums</code>: <pre><code>diagNums = go skips 2 where go (s:skips) x = let x' = x+s in x':go skips (x'+1) </code></pre> The recursion makes it a little difficult to tell what's going on here, so let's examine it in depth. Suppose <code>skips = s0 : s1 : s2 : s3 : ...</code>, then we have: <pre><code>diagNums = go skips 2 = go (s0 : s1 : s2 : s3 : ...) 2 = s0+2 : go (s1 : s2 : s3 : ... ) (s0+3) = s0+2 : s0+s1+3 : go (s2 : s3 : ... ) (s0+s1+4) = s0+2 : s0+s1+3 : s0+s1+s2+4 : go (s3 : ... ) (s0+s1+s2+5) = s0+2 : s0+s1+3 : s0+s1+s2+4 : s0+s1+s2+s3+5 : go (...) (s0+s1+s2+s3+6) </code></pre> This makes it much clearer what's going on, we've got the sum of two sequences, which is easy to compute using <code>zipWith (+)</code>: <pre><code>diagNums = zipWith (+) [2,3,4,5,...] [s0, s0+s1, s0+s1+s2, s0+s1+s2+s3,...] </code></pre> So now we just need to find a better way to compute the partial sums of <code>skips</code>, which is a great use for <a href="http://hackage.haskell.org/packages/archive/base/latest/doc/html/Prelude.html#v:scanl1" rel="nofollow noreferrer"><code>scanl1</code></a>: <pre><code>scanl1 (+) skips = s0 : s0+s1 : s0+s1+s2 : s0+s1+s2+s3 : ... </code></pre> Leaving a (IMO) much easier to understand definition for <code>diagNums</code>: <pre><code>diagNums = zipWith (+) [2..] $ scanl1 (+) skips </code></pre>
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