Question

Here is my code to solve the fractional knapsack problem, input to knap should be in the form

[("label 1", value, weight), ("label 2", value, weight), ...]

And output should be in the form

[("label 1", value, solution_weight), ("label 2", value, solution_weight), ...]

Code:

import Data.List {- Need for the sortBy function -}
{- Input "how much can the knapsack hole <- x" "Possible items in sack [(label, value, weight), ...] <- y" -}
{-knap x [([Char], Integer, Integer), ... ] = -}
knap x [] = []
knap x y = if length y == 1 
    then 
        if x > last3 (head y)
            then y
            else [(frst3 (head y), scnd3 (head y), x)]
    else 
        knap2 x y []
{- x is the knap max, y is the sorted frac list, z is the solution list -}
knap2 x y z = if x == 0
    then z
    else
        if thrd4 (head y) > x
            then [((frst4 (head y)), (scnd4 (head y)), x)]
            else knap2 (x-(thrd4 (head y))) (tail y) (z++[((frst4 (head y)), (scnd4 (head y)), (thrd4 (head y)))]) 

{- take a list of labels, values, and weights and return list of labels and fractions -}
fraclist :: (Fractional t1) => [(t, t1, t1)] -> [(t, t1, t1, t1)]
fraclist xs = [(x, y, z, y/z) | (x, y, z) <- xs]

{- Sort the list -}
sortList x = sortBy comparator x
    where comparator (_,_,_,d) (_,_,_,h) = if d > h then LT else GT

{- helper func to get values from tuples -}
frst3 (a,b,c) = a
scnd3 (a,b,c) = b
last3 (a,b,c) = c
frst4 (a,b,c,d) = a
scnd4 (a,b,c,d) = b
thrd4 (a,b,c,d) = c
last4 (a,b,c,d) = d

Here is the error I am getting

Couldn't match expected type `(t1, t0, t2, t3)'
            with actual type `(t1, t0, t2)'
Expected type: [(t1, t0, t2, t3)]
  Actual type: [(t1, t0, t2)]
In the second argument of `knap2', namely `y'
In the expression: knap2 x y []

I am not quite sure what else I can do. before I sit here and bang my head on the wall for an hour maybe someone could point out an obvious mistake if there are any?

Answer 1

I can’t tell how the four-tuples in knap2 and the three-tuples in knap are supposed to fit together but you’ll have a much clearer view of the matter if you pattern match and drop head, tail,thrd4, thirteenth17 etc

knap _ []        = []
knap x [(a,b,c)] = if x > c then [(a,b,c)]  else [(a, b, x)]
knap x abcs      = knap2 x abcs []

knap2 0 abcs z = z
knap2 x abcs z = undefined  -- not sure how to do this

-- but this makes sense, it seems:
knap3 0 _  zs = zs
knap3 _ [] _ = []
knap3 x ((a,b,c,d):abcds) zs =
  if c > x then [(a, b, x)]
           else knap3 (x - c) abcds (zs ++ [(a, b, c)]) 

or something like that. Instead of writing if length y == 1 you can pattern match on the singleton case; instead of using an equality test, if x == 0 you can pattern match on the 0 case, distinguishing it from other cases.