solution2.5.2.11.scala provided (#79)

Signed-off-by: Andreas Roehler <[email protected]>

chapter02/worksheets/solution2.5.2.11.scala

@@ -0,0 +1,113 @@
+/** 
+  Exercise 2.5.2.11
+  (a) For a given integer interval [𝑛1 , 𝑛2], find the largest integer
+      𝑘 ∈ [𝑛1 , 𝑛2] such that the decimal representation of 𝑘 does
+      not contain any of the digits 3, 5, or 7.
+
+  The required type signature and a sample test:
+
+  def largestNotThreeFiveSeven(a: Long, b: Long): Long = ??? 
+
+  scala> largestNotThreeFiveSeven(19, 97)
+  res0: Long = 96
+  
+  (b) For a given integer interval [𝑛1 , 𝑛2], find the integer 𝑘 ∈ [𝑛1 , 𝑛2] with the
+      largest sum of decimal digits.
+
+  (c) A positive integer 𝑛 is called a perfect number if it is equal to the sum of
+      its divisors (integers 𝑘 such that 1 ≤ 𝑘 < 𝑛 and 𝑘 divides 𝑛).
+      For example, 6 is a perfect number because its divisors are 1, 2,
+      and 3, and 1 + 2 + 3 = 6, while 8 is not a perfect number because
+      its divisors are 1, 2, and 4, and 1 + 2 + 4 = 7 ≠ 8. 
+
+      Write a function that determines whether a given number 𝑛 is perfect.
+      Determine all perfect numbers up to one million.
+  */
+
+def largestNotThreeFiveSeven(a: Long=19, b: Long = 97): Long = {
+  val xs = (a to b).toList
+  val ys =  xs.map(x => x.toString).map(_.toString).filter(! _.contains("3")).filter(! _.contains("5")).filter(! _.contains("7")).last
+  ys.toLong
+}
+
+def largestSumDezDigitsIntern(xs: List[Long], res: Long = 0, thisNumber: Long = 0): Long = {
+  if (xs.isEmpty) thisNumber
+  else {
+    val a =  xs.head.toString.toList.map(_.asDigit).sum
+    if (res < a) {
+      largestSumDezDigitsIntern(xs.tail, a, xs.head)
+    }
+    else
+    {
+      largestSumDezDigitsIntern(xs.tail, res, thisNumber)
+    }
+  }
+}
+
+def largestSumDezDigits(a: Long = 9, b: Long = 101): Long = {
+  val xs = (a to b).toList
+  largestSumDezDigitsIntern(xs)
+}
+
+def allNeededDivisors(n: Int = 99): List[Int] = {
+  (1 to (n - 1)).toList.filter(n % _ == 0)
+}
+
+def isPerfect(n: Int = 28): Boolean = {
+  val a: Int =  allNeededDivisors(n).sum
+  allNeededDivisors(n).sum ==  n
+}
+
+def perfectNumbersUpToN(n: Int): List[Int] = {
+  (1 to n).toList.filter(isPerfect(_))
+}
+
+val result = largestNotThreeFiveSeven()
+val expected: Long = 96
+assert(result == expected) 
+
+val result2 =  largestSumDezDigits()
+val expected2: Long = 99
+assert(result2 == expected2) 
+
+val result3 = isPerfect(8)
+val expected3 =  false
+assert(result3 == expected3) 
+
+val result4 = isPerfect(6)
+val expected4 =  true
+assert(result4 == expected4) 
+
+val result5 = isPerfect(28)
+val expected5 =  true
+assert(result5 == expected5) 
+
+val result6 = isPerfect(33)
+val expected6 =  false
+assert(result6 == expected6) 
+
+val result7 = perfectNumbersUpToN(10000)
+val expected7: List[Int] = List(6, 28, 496, 8128)
+assert(result7 == expected7) 
+
+// :load solution2.5.2.11.scala
+// def largestNotThreeFiveSeven(a: Long, b: Long): Long
+// def largestSumDezDigitsIntern(xs: List[Long], res: Long, thisNumber: Long): Long
+// def largestSumDezDigits(a: Long, b: Long): Long
+// def allNeededDivisors(n: Int): List[Int]
+// def isPerfect(n: Int): Boolean
+// def perfectNumbersUpToN(n: Int): List[Int]
+// val result: Long = 96
+// val expected: Long = 96
+// val result2: Long = 99
+// val expected2: Long = 99
+// val result3: Boolean = false
+// val expected3: Boolean = false
+// val result4: Boolean = true
+// val expected4: Boolean = true
+// val result5: Boolean = true
+// val expected5: Boolean = true
+// val result6: Boolean = false
+// val expected6: Boolean = false
+// val result7: List[Int] = List(6, 28, 496, 8128)
+// val expected7: List[Int] = List(6, 28, 496, 8128)