sfti_ch02_exercises.sc

// 1. The signum of a number is 1 if the number is positive, -1 if it is negative, and
// 0 if it is zero. Write a function that computes this value.
  
def signum(n: Int) = {
  if (n > 0) 1
  else if (n < 0) -1
  else 0
}                                               //> signum: (n: Int)Int
  
signum(4)                                       //> res0: Int = 1
signum(0)                                       //> res1: Int = 0
signum(-20)                                     //> res2: Int = -1

// 2. What is the value of an empty block expression {}? What is its type?
val blank = {}                                  //> blank  : Unit = ()
// Value is () and type is Unit

// 3. Come up with one situation where the assignment x = y = 1 is valid in Scala.
// (Hint: Pick a suitable type for x.)
var y: Int = 0                            //> y  : Int = 0
val x: Unit = y = 1                       //> x  : Unit = ()
// x should be of type Unit

// 4. Write a Scala equivalent for the Java loop
// for (int i = 10; i >= 0; i--) System.out.println(i);
for(i <- 10 to (0, -1)) println(i)        //> 10
                                          //| 9
                                          //| 8
                                          //| 7
                                          //| 6
                                          //| 5
                                          //| 4
                                          //| 3
                                          //| 2
                                          //| 1
                                          //| 0
// 5. Write a procedure countdown(n: Int) that prints the numbers from n to 0.
def countdown(n: Int): Unit = {
 	for(i <- n to (0, -1)) println(i)
}                                         //> countdown: (n: Int)Unit
countdown(5)                              //> 5
                                          //| 4
                                          //| 3
                                          //| 2
                                          //| 1
                                          //| 0
// 6. Write a for loop for computing the product of the Unicode codes of all letters
// in a string. For example, the product of the characters in "Hello" is 9415087488.
var prod: BigInt = 1                              //> prod: BigInt = 1
for(c <- "Hello") prod *= c
prod                                      //> res3: Int = 9415087488
 
// 7. Solve the preceding exercise without writing a loop. (Hint: Look at the StringOps
// Scaladoc.)
"Hello".foldLeft(1: BigInt)((a, b) => a * b)      //> res4: BigInt = 9415087488

// 8. Write a function product(s : String) that computes the product, as described
// in the preceding exercises.
def product(s: String) = s.foldLeft(1: BigInt)((a, b) => a * b)
                                          //> product: (s: String)BigInt
product("Hello")                                //> res5: BigInt = 9415087488

// 9. Make the function of the preceding exercise a recursive function.
def productRec(s: String): BigInt = {
  if (s.length == 0) 1
  else s.head * productRec(s.tail)
}                                        //> productRec: (s: String)BigInt
productRec("Hello")                       //> res6: BigInt = 9415087488

// 10. Write a function that computes x^n, where n is an integer. Use the following
// recursive definition
// xn = y2 if n is even and positive, where y = x ^ n / 2.
// xn = x * x ^ n - 1 if n is odd and positive.
// x0 = 1
// xn = 1 / x ^ -n if n is negative.
// Don't use a return statement.
def xpown(x: BigDecimal, n: Int): BigDecimal = {
  if (n == 0) 1
  else if (n < 0) 1 / xpown(x, -n)
  else if (n % 2 == 0) {
    val i = xpown(x, n / 2)
    i * i
  }
  else x * xpown(x, n - 1)
}                               //> xpown: (x: BigDecimal, n: Int)BigDecimal
xpown(2, 1024)                  //> res7: BigDecimal = 1.797693134862315907729305190789023E+308
xpown(-2, -10)			//> res8: BigDecimal = 0.0009765625
xpown(-2, 10)			//> res9: BigDecimal = 1024

Exercise 5 should omit '=' sign as given in example in chapter 2.9 or use
def countdown(n: Int): Unit = {
...
}
signature

Thanks for pointing out the problems with the code @thayashi88 and @DonatasD. I've update the code and it should be correct now.