Problem 76

76.hs

@@ -0,0 +1,25 @@
+import qualified Data.IntMap.Strict as M
+
+filterSum :: Int -> M.IntMap Int -> Int
+filterSum n subMap = 
+    let filterMap = M.filterWithKey (\k _ -> k <= n) subMap
+    in M.foldr (+) 0 filterMap
+
+getSubmap :: Int -> M.IntMap (M.IntMap Int) -> M.IntMap Int
+getSubmap k numMap = M.findWithDefault undefined k numMap
+
+insertSubmap :: Int -> M.IntMap (M.IntMap Int) -> M.IntMap (M.IntMap Int)
+insertSubmap n numMap = 
+    let getFilterSumInsert k subMap = M.insert k (filterSum k (getSubmap (n-k) numMap)) subMap
+        subMap = foldr getFilterSumInsert M.empty [n, n-1..1]
+    in M.insert n subMap numMap
+
+createNummap :: Int -> M.IntMap (M.IntMap Int)
+createNummap bound = 
+    let initialMap = M.fromList [(0, M.fromList [(0, 1)])]
+    in foldr insertSubmap initialMap [bound, bound-1..1]
+
+main = print $ 
+    let bound = 100
+        ways = filterSum bound $ M.findWithDefault undefined bound $ createNummap bound
+    in ways - 1