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POHaskell Knapsack
 

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    <p>I've written an answer to the bounded knapsack problem with one of each item in Scala, and tried transposing it to Haskell with the following result:</p> <pre><code>knapsack :: [ ( Int, Int ) ] -&gt; [ ( Int, Int ) ] -&gt; Int -&gt; [ ( Int, Int ) ] knapsack xs [] _ = xs knapsack xs ys max = foldr (maxOf) [ ] [ knapsack ( y : xs ) ( filter (y /=) ys ) max | y &lt;- ys , weightOf( y : xs ) &lt;= max ] maxOf :: [ ( Int, Int ) ] -&gt; [ ( Int, Int ) ] -&gt; [ ( Int, Int ) ] maxOf a b = if valueOf a &gt; valueOf b then a else b valueOf :: [ ( Int, Int ) ] -&gt; Int valueOf [ ] = 0 valueOf ( x : xs ) = fst x + valueOf xs weightOf :: [ ( Int, Int ) ] -&gt; Int weightOf [ ] = 0 weightOf ( x : xs ) = snd x + weightOf xs </code></pre> <p>I'm not looking for tips on how to clean up the code, just to get it working. To my knowledge it should be doing the following:</p> <ul> <li>For each tuple option (in ys) <ul> <li>if the weight of the current tuple (y) and the running total (xs) combined is less than the capacity</li> <li>get the optimal knapsack that contains the current tuple and the current total (xs), using the available tuples (in ys) less the current tuple</li> </ul></li> <li>Finally, get the most valuable of these results and return it</li> </ul> <p>*<em>Edit: *</em> Sorry, forgot to say what's wrong... So it compiles alright, but it gives the wrong answer. For the following inputs, what I expect and what it produces:</p> <pre><code>knapsack [] [(1,1),(2,2)] 5 Expect: [(1,1),(2,2)] Produces: [(1,1),(2,2)] knapsack [] [(1,1),(2,2),(3,3)] 5 Expect: [(2,2),(3,3)] Produces: [] knapsack [] [(2,1),(3,2),(4,3),(6,4)] 5 Expect: [(2,1),(6,4)] Produces: [] </code></pre> <p>So I was wondering what could be the cause of the discrepancy?</p> <p>The solution, thanks to sepp2k:</p> <pre><code>ks = knapsack [] knapsack :: [ ( Int, Int ) ] -&gt; [ ( Int, Int ) ] -&gt; Int -&gt; [ ( Int, Int ) ] knapsack xs [] _ = xs knapsack xs ys max = foldr (maxOf) [ ] ( xs : [ knapsack ( y : xs ) ( ys #- y ) max | y &lt;- ys, weightOf( y : xs ) &lt;= max ] ) (#-) :: [ ( Int, Int ) ] -&gt; ( Int, Int ) -&gt; [ ( Int, Int ) ] [ ] #- _ = [ ] ( x : xs ) #- y = if x == y then xs else x : ( xs #- y ) maxOf :: [ ( Int, Int ) ] -&gt; [ ( Int, Int ) ] -&gt; [ ( Int, Int ) ] maxOf a b = if valueOf a &gt; valueOf b then a else b valueOf :: [ ( Int, Int ) ] -&gt; Int valueOf [ ] = 0 valueOf ( x : xs ) = fst x + valueOf xs weightOf :: [ ( Int, Int ) ] -&gt; Int weightOf [ ] = 0 weightOf ( x : xs ) = snd x + weightOf xs </code></pre> <p>Which returns the expected results, above.</p>
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