funclang series3: made challenge code more compact and fixed isSublist.

funclang-taddeus/series3/ass7.ml

@@ -2,6 +2,7 @@ open List
 
 (* 1 *)
 let rec nth l n =
+    (*  *)
     match n with
     | 0 -> hd l
     | i when i > 0 && i < (length l) -> nth (tl l) (i - 1)
@@ -13,14 +14,20 @@ let heads l = map hd l;;
 
 (* 3 *)
 let zip l m =
+    (* Cut off a list l at length e *)
     let rec cut l e = if e = (length l) then l else cut (rev (tl (rev l))) e in
+    (* Get the minimum of two integers *)
     let min a b = if a > b then b else a in
+    (* Get the length of the shortest list *)
     let len = min (length l) (length m) in
+    (* Cut off both lists at the length of the shortest list to equal their
+     * lengts, then use the native 'combine' function *)
     combine (cut l len) (cut m len)
 ;;
 
 (* 4 *)
 let rec map f l =
+    (* Apply f to the head, then map it to the tail recursively *)
     match l with
     | [] -> []
     | h::t -> f h::map f t
@@ -28,6 +35,7 @@ let rec map f l =
 
 (* 5 *)
 let rec reduce f z l =
+    (* Apply f to the head, and the reducement of the tail *)
     match l with
     | [] -> z
     | h::t -> f z (reduce f h t)
@@ -35,13 +43,21 @@ let rec reduce f z l =
 
 (* 6 *)
 let rec isSublist l s =
-    match s with
-    | [] -> true
-    | h::t -> h = (hd l) && isSublist (tl l) t
+    (* Check if l starts with s, otherwise chech the tail recursively *)
+    let rec startsWith l s =
+        (length s) <= (length l) && match s with
+        | [] -> true
+        | h::t -> h = (hd l) && startsWith (tl l) t
+    in
+    match l with
+    | [] -> false
+    | _::t -> (startsWith l s) || (isSublist t s)
 ;;
 
 (* 7 *)
 let rec lookup l key =
+    (* Math key to the first tuple and return the value-side of the tuple if
+    * matched. Otherwise, lookup in the rest of the tuples *)
     match l with
     | [] -> raise (Failure "lookup")
     | h::t -> let k, v = h in if k = key then v else lookup t key
@@ -49,13 +65,11 @@ let rec lookup l key =
 
 (* Challenge *)
 let rec coin_permutation l n =
-    let perms coin l =
-        match coin with
-        | i when i < n -> 1 + (coin_permutation l (n - coin))
-        | i when i = n -> 1
-        | _ -> 0
-    in
+    (* Reduce the list using the fact that the the total number of coin
+     * permutations is equal to the number of permutations given a single coin,
+     * added to the number of permutations without that coin *)
     match l with
     | [] -> 0
-    | h::t -> (perms h t) + (coin_permutation t n)
+    | h::t -> (if h > n then 0 else 1 + (coin_permutation t (n - h)))
+        + (coin_permutation t n)
 ;;