funcprog: finished week 2, assignment 5.{1,2,3}.

funcprog/week2/ass5_1.ml

+(*
+ * Check if the given year is a leap year. This will return true if the given
+ * integer is larger than 1582, can be divided by 4, but not by 100, or it can
+ * be divided by 400. Otherwise, false is returned.
+ *)
 let isLeapYear x =
-    x >= 1582 && x mod 4 == 0 && (x mod 100 != 0 || x mod 400 == 0)
+    x > 1582 && x mod 4 == 0 && (x mod 100 != 0 || x mod 400 == 0)
 ;;
 
 let testLeapYear x =
-    Printf.printf "%4d: %b\n" x (isLeapYear x);;
+    Printf.printf "%d: %b\n" x (isLeapYear x);;
 
 (testLeapYear 1400);; (* false *)
 (testLeapYear 1582);; (* false *)

funcprog/week2/ass5_2.ml

+(*
+ * Implementation of date2str.
+ *
+ * Given a correct calendar triple (day, month, year), return a proper English
+ * date. For example: (1, 2, 2011) returns "February 1st, 2011".
+ *
+ * The suffix of the day number is not related to the actual month, so "February
+ * 31st, 2011" can be generated. However, there is no reason to implement error
+ * checking to prevent returning unvalid day/month combinations (not part of the
+ * assignment). Note: the assigment clearly states that a correct calendar
+ * triple is the input of date2str.
+ *
+ * This implementation does check for invalid day numbers or invalid month
+ * numbers. The exception Hell will be raised for these invalid integers.
+ *)
 exception Hell
 
+(*
+ * Given a day number, return the day number followed by its English suffix. For
+ * example, this will return ``1st'' for day 1, ``23rd'' for day 23 and ``12th'
+ * for day 12. If the day number is negative or the day number is not between 1
+ * and 31 (inclusive), Hell will be raised.
+ *)
 let day_with_suffix day =
     match day with
-      1 | 21 | 31     -> (string_of_int day) ^ "st"
-    | 2 | 22          -> (string_of_int day) ^ "nd"
-    | 3 | 23          -> (string_of_int day) ^ "rd"
-    | _ when day > 0  -> (string_of_int day) ^ "th"
-    | _               -> raise Hell
+      1 | 21 | 31                  -> (string_of_int day) ^ "st"
+    | 2 | 22                       -> (string_of_int day) ^ "nd"
+    | 3 | 23                       -> (string_of_int day) ^ "rd"
+    | _ when (day > 0 && day < 32) -> (string_of_int day) ^ "th"
+    | _                            -> raise Hell
 ;;
 
+(*
+ * Return the English name of a month number (a number between 1 and 12,
+ * inclusive). If the month number is not defined, Hell will be raised.
+ *)
 let month_name month =
     match month with
       1  -> "January"

funcprog/week2/ass5_3.ml

-let rec digitRoot number =
-    let result = ref 0 in
-    let current = ref number in (
-        Printf.printf "input: %d\n" !current;
+(*
+ * Calculate the digital root of a number: add up all of its digits, and do that
+ * recursively until a single digit is obtained.
+ *)
 
-        while !current > 0 do
-            result := !result + (!current mod 10);
-            Printf.printf "%d + " (!current mod 10);
-            current := !current / 10;
-        done;
-
-        Printf.printf "= %d\n" !result;
-
-        if !result > 9 then
-            (digitRoot !result)
-        else
-            !result
-    )
+let rec digitRoot ?(sum=0) number = match number with
+      _ when number < 10 -> (sum + number)
+    | _ -> (digitRoot (digitRoot ~sum:(sum + (number mod 10)) (number / 10)))
 ;;
 
 let test_digitRoot input =
@@ -23,8 +13,11 @@ let test_digitRoot input =
     Printf.printf "%d -> %d\n" input (digitRoot input)
 ;;
 
-(test_digitRoot 20);;
-(test_digitRoot 24);;
-(test_digitRoot 1234);;
-(test_digitRoot 123456789);;
-(test_digitRoot (-1));; (* what to do with negative numbers? *)
+test_digitRoot 20;;
+test_digitRoot 24;;
+test_digitRoot 1234;; (* = 1 *)
+test_digitRoot 65536;; (* = 7 *)
+test_digitRoot 12345678;; (* = 9 *)
+test_digitRoot 18273645;; (* = 9 *)
+test_digitRoot 123456789;; (* = 9 *)
+test_digitRoot 5674;; (* = 4 *)