Key to CSE341 Section #1 Problems

1.      (3, 4.5)                int * real
        [4.5, 3.8]              real list
        ((3, 4), 18.5)          (int * int) * real
        [[3, 4], [7]]           int list list
        [("hello", 3)]          (string * int) list

2.      int * string * real             (3, "hello", 4.5)
        string list                     ["abc", "def", "gh"]
        int * string list               (38, ["ab", "cd"])
        (int * string) list             [(38, "ab"), (19, "cd")]
        (int * string) list list        [[(38, "ab")], [(19, "cd")]]
        (int * string list) list        [(38, ["ab", "cd"]), (7, ["foo"])]

3. One possible solution appears below.
        fun gcd(x, y) =
            if y = 0 then x
            else gcd(y, x mod y)
        fun lcm(x, y) = x * y div gcd(x, y)

4. One possible solution appears below.
        fun grade(pct) =
            if pct >= 90.0 then "A"
	    else if pct >= 80.0 then "B"
	    else if pct >= 70.0 then "C"
	    else if pct >= 60.0 then "D"
	    else "F";

5. One possible solution appears below.
        fun sum(lst) =
            if lst = [] then 0
            else hd(lst) + sum(tl(lst))
   To make it sum reals, change "0" to "0.0" in the "then" branch.

6. One possible solution appears below.
        fun toReal(lst) =
            if lst = [] then []
            else real(hd(lst))::toReal(tl(lst))

7. One possible solution appears below.
        (* helper function*)
        fun combine(first, last) = last ^ ", " ^ first;

        fun convert(lst) =
            if lst = [] then []
            else combine(hd(lst))::convert(tl(lst));

8. One possible solution appears below.
        fun switchPairs(lst) =
            if length(lst) <= 1 then lst
            else hd(tl(lst))::hd(lst)::switchPairs(tl(tl(lst)));