added lesson 2

src/Assignment2/Ex2.sc

@@ -0,0 +1,12 @@
+import scala.annotation.tailrec
+
+def sum(f: Int => Double, a: Int, b: Int) = {
+    @tailrec
+    def iter(a: Int, acc: Double): Double = {
+        if (a > b) acc
+        else iter(a + 1, acc + f(a))
+    }
+    iter(a, 0)
+}
+
+sum(x => x * x, 3, 5)

src/Assignment2/Ex3.sc

@@ -0,0 +1,37 @@
+import scala.annotation.tailrec
+
+// 3.1
+def product(f: Int => Double)(a: Int)(b: Int): Double = {
+  @tailrec
+  def iter(i: Int, prod: Double): Double =
+    if (i > b) prod
+    else iter(i + 1, prod * f(i))
+
+  iter(a, 1)
+}
+
+product(x => x)(3)(5)
+
+// 3.2
+def factorial(n: Int): Double = product(i => if (i == 0) {1} else {i})(0)(n)
+
+factorial(5)
+
+
+// 3.3
+def mapReduce(red: (Double, Double) => Double)(v0: Double)(f: Int => Double)(a: Int)(b: Int) = {
+  @tailrec
+  def iter(i: Int, acc: Double): Double =
+    if (i > b) acc
+    else iter(i + 1, red(acc, f(i)))
+
+  iter(a, v0)
+}
+
+val sum = mapReduce((a, b) => a + b)(0) _
+val prod = mapReduce((a, b) => a * b)(1) _
+
+sum(i => i)(1)(5)
+prod(i => i)(1)(5)
+
+mapReduce((a, b) => a + b)(0)(i => 2 * i + 1)(1)(5)

src/Lesson2/Curryfication.sc

@@ -0,0 +1,6 @@
+def mul(x: Int, y: Int): Int = x * y
+
+def mulCurry(x: Int) = (y :Int) => x * y
+
+def mulCurryScala(x: Int)(y: Int): Int = x * y
+

src/Lesson2/SumInts.sc

@@ -0,0 +1,20 @@
+def sumInts(a: Int, b: Int): Double =
+  if (a > b) 0 else a + sumInts(a + 1, b)
+
+def sumCubes(a: Int, b: Int): Double =
+  if (a > b) 0 else a * a * a + sumCubes(a + 1, b)
+
+def sumRec(a: Int, b: Int): Double =
+  if (a > b) 0 else 1.0 / a + sumRec(a + 1, b)
+
+def mapReduce(f: Int => Double, a: Int, b: Int): Double =
+  if (a > b) 0 else f(a) + mapReduce(f, a + 1, b)
+
+sumInts(3, 5)
+sumCubes(1, 3)
+sumRec(1, 3)
+
+mapReduce(i => i, 3, 5)
+mapReduce(i => i*i*i, 1, 3)
+mapReduce(i => 1.0/i, 1, 3)
+