Problem:
0-1 Knapsack Problem II

You have N items that you want to put them into a knapsack. Item i has value vi and weight wi.

You want to find a subset of items to put such that:

The total value of the items is as large as possible.

The items have combined weight at most W, that is capacity of the knapsack.

Find the maximum total value of items in the knapsack.

Input

N W
v1 w1
v2 w2
:
vN wN

The first line consists of the integers N and W. In the following N lines, the value and weight of the i-th item are given.

Output

Print the maximum total values of the items in a line.

Constraints

1 ≤ N ≤ 100

1 ≤ vi ≤ 100

1 ≤ wi ≤ 10,000,000

1 ≤ W ≤ 1,000,000,000

Sample Input 1

4 5
4 2
5 2
2 1
8 3

Sample Output 1

13

Sample Input 2

2 20
5 9
4 10

Sample Output 2

9

Solution in Haskell (judge verdict: Accepted)

import Control.Applicative
import qualified Data.IntMap.Strict as Map
import Data.List (sort)

main = do
  [_,capa] <- map (read :: String -> Int) . words <$> getLine
  goods <-map (map (read :: String -> Int) . words) . lines <$> getContents
  let maxValue = foldl1 (+) $ map head goods
  let ans = resolve capa maxValue (Map.fromList (zip [0..maxValue] [0,0..])) (reverse (sort goods))
  print $ if Map.null ans then 0 else fst $ Map.findMax ans

resolve capa maxValue valueMap ([v,w]:xs)
  | xs == []  = Map.filter (>0) koushin'
  | otherwise = resolve capa maxValue koushin' xs
  where
    koushin'
      | capa < w  = valueMap
      | otherwise = koushin valueMap [v,w] (maxValue-v)
    koushin valueMap [v,w] n
      | n == 0 && valueMap Map.! v > w        = Map.insert v w valueMap
      | n == 0 && oldWight == 0              = Map.insert v w valueMap
      | n == 0                                = valueMap
      | oldWight == 0                         = next
      | w + oldWight > capa                  = next
      | (w + oldWight >= newWight) && newWight /= 0 = next
      | otherwise = koushin (Map.insert (n+v) (w + oldWight) valueMap) [v,w] (n-1)
      where
        oldWight = valueMap Map.! n
        newWight =valueMap Map.! (n+v)
        next     = koushin valueMap [v,w] (n-1)