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    <p>As <a href="https://stackoverflow.com/questions/1672074/selection-sort-in-functional-scala/1672190#1672190">starblue already said</a>, you need a function that calculates the minimum of a list and returns the list with that element removed. Here is my tail recursive implementation of something similar (as I believe <code>foldl</code> is tail recursive in the standard library), and I tried to make it as functional as possible :). It returns a list that contains all the elements of the original list (but kindof reversed - see the explanation below) with the minimum as a head.</p> <pre><code>def minimum(xs: List[Int]): List[Int] = (List(xs.head) /: xs.tail) { (ys, x) =&gt; if(x &lt; ys.head) (x :: ys) else (ys.head :: x :: ys.tail) } </code></pre> <p>This basically does a fold, starting with a list containing of the first element of <code>xs</code> If the first element of <code>xs</code> is smaller than the head of that list, we pre-append it to the list <code>ys</code>. Otherwise, we add it to the list <code>ys</code> as the second element. And so on recursively, we've folded our list into a new list containing the minimum element as a head and a list containing all the elements of <code>xs</code> (not necessarily in the same order) with the minimum removed, as a tail. Note that this function does not remove duplicates.</p> <p>After creating this helper function, it's now easy to implement selection sort.</p> <pre><code>def selectionSort(xs: List[Int]): List[Int] = if(xs.isEmpty) List() else { val ys = minimum(xs) if(ys.tail.isEmpty) ys else ys.head :: selectionSort(ys.tail) } </code></pre> <p>Unfortunately this implementation is <em>not</em> tail recursive, so it will blow up the stack for large lists. Anyway, you shouldn't use a O(n^2) sort for large lists, but still... it would be nice if the implementation was tail recursive. I'll try to think of something... I think it will look like the implementation of a fold.</p> <p><strong>Tail Recursive!</strong></p> <p>To make it tail recursive, I use quite a common pattern in functional programming - an accumulator. It works a bit backward, as now I need a function called <code>maximum</code>, which basically does the same as <code>minimum</code>, but with the maximum element - its implementation is exact as minimum, but using <code>&gt;</code> instead of <code>&lt;</code>.</p> <pre><code>def selectionSort(xs: List[Int]) = { def selectionSortHelper(xs: List[Int], accumulator: List[Int]): List[Int] = if(xs.isEmpty) accumulator else { val ys = maximum(xs) selectionSortHelper(ys.tail, ys.head :: accumulator) } selectionSortHelper(xs, Nil) } </code></pre> <p><strong>EDIT</strong>: Changed the answer to have the helper function as a subfunction of the selection sort function.</p> <p>It basically accumulates the maxima to a list, which it eventually returns as the base case. You can also see that it is tail recursive by replacing <code>accumulator</code> by <code>throw new NullPointerException</code> - and then inspect the stack trace.</p> <p>Here's a step by step sorting using an accumulator. The left hand side shows the list <code>xs</code> while the right hand side shows the <code>accumulator</code>. The maximum is indicated at each step by a star.</p> <pre><code>64* 25 12 22 11 ------- Nil 11 22 12 25* ------- 64 22* 12 11 ------- 25 64 11 12* ------- 22 25 64 11* ------- 12 22 25 64 Nil ------- 11 12 22 25 64 </code></pre> <p>The following shows a step by step folding to calculate the maximum:</p> <pre><code>maximum(25 12 64 22 11) 25 :: Nil /: 12 64 22 11 -- 25 &gt; 12, so it stays as head 25 :: 12 /: 64 22 11 -- same as above 64 :: 25 12 /: 22 11 -- 25 &lt; 64, so the new head is 64 64 :: 22 25 12 /: 11 -- and stays so 64 :: 11 22 25 12 /: Nil -- until the end 64 11 22 25 12 </code></pre>
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    1. COI recommend making the tail-recursive function a subfunction of the main one. Otherwise you have to be concerned about things like the class or method being final to ensure the optimization can be applied.
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    2. COYeah, that's a good idea, thanks. I'll edit my answer to have it as a subfunction.
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    3. COThat is awesomely helpful not only in my specific question, but just as furthering my understanding of FP as well. Thanks, Flaviu!
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