Code Golf: Shortest code to find a weighted median?

Question

My try at code golfing.

The problem of finding the minimum value of ∑W_i*|X-X_i| reduces to finding the weighted median of a list of x[i] with weights <

Answer 1

Haskell code, ungolfed: trying for a reasonable functional solution.

import Data.List (zip4)
import Data.Maybe (listToMaybe)

mid :: (Num a, Ord a) => [a] -> (Int, Bool)
mid w = (i, total == part && maybe False (l ==) r) where
    (i, l, r, part):_ = dropWhile less . zip4 [0..] w v $ map (2*) sums
    _:sums = scanl (+) 0 w; total = last sums; less (_,_,_,x) = x < total
    v = map Just w ++ repeat Nothing

wmedian :: (Num a, Ord a) => [a] -> [a] -> (a, Maybe a)
wmedian w x = (left, if rem then listToMaybe rest else Nothing) where
    (i, rem) = mid w; left:rest = drop i x

> wmedian [1,1,1,1] [1,2,3,4]
(2,Just 3)
> wmedian [1,1,2,1] [1,2,3,4]
(3,Nothing)
> wmedian [1,2,2,5] [1,2,3,4]
(3,Just 4)
> wmedian [1,2,2,6] [1,2,3,4]
(4,Nothing)

> wmedian [1..10] [0..9]
(6,Nothing)
> wmedian ([1..6]++[6..8]) [1..9]
(6,Just 7)

---

My original J solution was a straightforward translation of the above Haskell code.

Here's a Haskell translation of the current J code:

{-# LANGUAGE ParallelListComp #-}
import Data.List (find); import Data.Maybe (fromJust)
w&x=foldr((+).fst.fromJust.find((>=sum w).snd))0[f.g(+)0$map
    (2*)w|f<-[zip x.tail,reverse.zip x]|g<-[scanl,scanr]]/2

Yeah… please don't write code like this.

> [1,1,1,1]&[1,2,3,4]
2.5
> [1,1,2,1]&[1,2,3,4]
3
> [1,2,2,5]&[1,2,3,4]
3.5
> [1,2,2,6]&[1,2,3,4]
4
> [1..10]&[0..9]
6
> ([1..6]++[6..8])&[1..9]
6.5