Sean Seibel exercises

exercises/compareTime.sml

@@ -1,4 +1,10 @@
-fun timeBefore((h1, m1, "AM"), (h2, m2, "AM")) = false;
+fun toElapsedMinutes(h1, m1, t1) =
+        h1 * 60 +
+        m1 + 
+        (if t1 = "PM" then 12*60 else 0);
+
+fun timeBefore((h1, m1, t1), (h2, m2, t2)) =
+        toElapsedMinutes(h1, m1, t1) < toElapsedMinutes(h2, m2, t2);
 
 timeBefore((1, 59, "AM"), (2, 40, "PM")) = true;
 timeBefore((1, 59, "PM"), (2, 40, "PM")) = true;

exercises/eqTri.sml

@@ -2,10 +2,27 @@ datatype shape = Point of real * real
 | Line of (real * real) * (real * real)
 | Triangle of (real * real) * (real * real) * (real * real)
 
+fun close (a:real, b:real) = (a - b) < 0.0001 andalso (a - b) > ~0.0001
+
+fun distance ((ax: real, ay: real), (bx: real, by: real)) =
+        Math.sqrt ( (ax - bx) * (ax - bx) + (ay - by) * (ay - by) );
+
+fun isEqTri (Point (_)) = false
+    | isEqTri (Line (_)) = false
+    | isEqTri (Triangle (a, b, c)) = 
+        (close (distance (a, b), distance (b, c))) andalso
+        (close (distance (a, b), distance (a, c)));
+
+
 
 fun showTriCood [] = []
-| showTriCood(Triangle(a,b,c)::ps) = (a,b,c)::showTriCood(ps)
-| showTriCood(p::ps) = showTriCood(ps)
+    | showTriCood(Triangle(a,b,c)::ps) = (a,b,c)::showTriCood(ps)
+    | showTriCood(p::ps) = showTriCood(ps)
+
+fun containsEqTri l = List.exists isEqTri l;
 
 val shapes = [Line((2.2,3.5),(4.1,5.0)), Point(4.5,2.0), Triangle((21.0, 4.5),(15.5, 21.1),(10.5, 10.2))];
-showTriCood(shapes);
+showTriCood(shapes);
+val hasEqTri = [Line((2.2,3.5),(4.1,5.0)), Point(4.5,2.0), Triangle((0.0, 0.0),(0.5, 0.866025404),(1.0, 0.0))];
+containsEqTri(shapes);
+containsEqTri(hasEqTri);

exercises/fib.sml

@@ -1,7 +1,12 @@
+fun fibt(0, n1, n2) = n1
+    | fibt(count, n1, n2) = fibt(count - 1, n1 + n2, n1);
+
 fun fib(0) = 0
-| fib(1) = 1
-| fib(n) = fib(n-2) + fib(n-1);
+    | fib(n) = fibt(n - 1, 1, 0);
+
 
 fib(10) = 55;
 fib(8) = 21;
-fib(2) = 1;
+fib(2) = 1;
+fib(50) = 12586269025;
+e

exercises/makeChange.sml

@@ -1,9 +1,10 @@
-fun allChange(coins, coinvals, 0) = [coins]
-| allChange(coins, [], amount) = []
-| allChange(coins, c::coinvals, amount) =
-    if amount < 0 then []
-    else allChange(c::coins, c::coinvals, amount-c) @
-            allChange(coins, coinvals, amount);
+fun allChange(coins, coinvals, 0, res) = coins :: res
+    | allChange(coins, [], amount, res) = res
+    | allChange(coins, c::coinvals, amount, res) =
+        if amount < 0 then res
+        else allChange(c::coins, c::coinvals, amount-c, allChange(coins, coinvals, amount, res));
 
-allChange([], [5,2], 16);
-allChange([], [25,10,2,1], 43);
+allChange([], [5,2], 16, []);
+allChange([], [25,10,2,1], 43, []);
+
+e

exercises/max.sml

@@ -1,5 +1,12 @@
-fun maxm [m] = m
-| maxm(m::n::ns) = if m > n then maxm(m::ns) else maxm(n::ns);
+fun max2 (i1, i2) = if i1 > i2 then i1 else i2;
+
+fun maxmt (sofar, []) = sofar
+    | maxmt (sofar, h::tail) = maxmt(max2(sofar, h), tail)
+
+fun maxm [] = NONE
+    | maxm (m::ns) = SOME(maxmt(m, ns));
 
 maxm([43,25,2,4,2434]);
-maxm([]);
+maxm([30, 41, 22, ~12, 0, 3]);
+maxm([]);
+e

exercises/prod.sml

@@ -1,6 +1,9 @@
 (* Make tail recursive *)
+fun prodt (total, []) = total
+    | prodt (total, h::tail) = prodt(total * h, tail);
 fun prod [] = 1
-| prod (n::ns) = n * (prod ns);
+    | prod (n::ns) = prodt(n, ns);
 
 prod([2,3,4,5]) = 120;
-prod([]) = 1;
+prod([]) = 1;
+e

exercises/treetav.sml

@@ -1,3 +1,21 @@
 datatype 'a tree = Lf | Br of 'a * 'a tree * 'a tree;
 
-val birnam = Br(1, Br(2, Lf, Br(3,Br(4,Lf,Lf), Lf)), Lf);
+fun treedepth Lf = 0
+    | treedepth (Br (_, l, r)) = 1 + Int.max(treedepth l, treedepth r);
+
+fun preorder (Lf, res) = res
+    | preorder (Br(v, t1, t2), res) = v::(preorder (t1, preorder(t2, res))); 
+
+fun inorder (Lf, res) = res
+    | inorder (Br(v, t1, t2), res) = (inorder (t1, v::inorder(t2, res))); 
+
+fun postorder (Lf, res) = res
+    | postorder (Br(v, t1, t2), res) = (postorder (t1, postorder(t2, v::res))); 
+
+val birnam = Br(1, Br(2, Lf, Br(3,Br(4,Lf,Lf), Lf)), Lf);
+treedepth(birnam);
+preorder(birnam, []);
+inorder(birnam, []);
+postorder(birnam, []);
+
+e

exercises/validateDayMonth.sml

@@ -1,2 +1,19 @@
 (* Complete the expression *)
-fun isValidDate(d, m) = true;
+fun isValidDate(d, m) = 
+  d >= 1 andalso
+    d <= (
+      case m of
+        "January" => 31
+      | "February" => 28
+      | "March" => 31
+      | "April" => 30
+      | "May" => 31
+      | "June" => 30
+      | "July" => 31
+      | "August" => 31
+      | "September" => 30
+      | "October" => 31
+      | "November" => 30
+      | "December" => 31
+      | _ => 0
+    )