[TOC]
** 声明**
该系列文章来自：http://aperiodic.net/phil/scala/s-99/
大部分内容和原文相同,加入了部分自己的代码。
如有侵权，请及时联系本人。本人将立即删除相关内容。
在接下来的章节，我们将采取不同的策略。声明了一个类-S99Int,和一个隐式转化器，用来从传统的Int转换到S99Int.
下面是该类的最初声明：
package arithmetic {
class S99Int(val start: Int) {
import S99Int._
}
object S99Int {
implicit def int2S99Int(i: Int): S99Int = new S99Int(i)
}
}
并且在每个问题中将给该类添加相关的功能。最终将得到一个完整的S99Int类。
P31 (**) Determine whether a given integer number is prime.
要求
Example:
scala> 7.isPrime
res0: Boolean = true
代码
class S99Int(val start: Int) {
import S99Int._
def isPrime: Boolean =
(start > 1) && (primes.takeWhile(_ <= Math.sqrt(start)).forall(start % _ != 0))
}
object S99Int {
implicit def int2S99Int(i: Int): S99Int = new S99Int(i)
val primes = Stream.cons(2, Stream.from(3, 2) filter { _.isPrime })
}
P32 (**) Determine the greatest common divisor of two positive integer numbers.
要求
Use Euclid's algorithm.
scala> gcd(36, 63)
res0: Int = 9
代码
object S99Int {
def gcd(m: Int, n: Int): Int = if (n == 0) m else gcd(n, m % n)
}
P33 (*) Determine whether two positive integer numbers are coprime.
要求
Two numbers are coprime if their greatest common divisor equals 1.
scala> 35.isCoprimeTo(64)
res0: Boolean = true
代码
class S99Int(val start: Int) {
import S99Int._
def isCoprimeTo(x: Int): Boolean = gcd(start, x) == 1
}
P34 (**) Calculate Euler's totient function phi(m).
要求
Euler's so-called totient function phi(m) is defined as the number of positive integers r (1 <= r <= m) that are coprime to m.
scala> 10.totient
res0: Int = 4
代码
class S99Int(val start: Int) {
import S99Int._
def totient: Int = (1 to start).filter(start.isCoprimeTo(_)).length
}
P35 (**) Determine the prime factors of a given positive integer.
要求
Construct a flat list containing the prime factors in ascending order.
scala> 315.primeFactors
res0: List[Int] = List(3, 3, 5, 7)
代码
class S99Int(val start: Int) {
import S99Int._
def primeFactors: List[Int] = {
def primeFactorsR(x: Int, ps: Stream[Int]): List[Int] = {
x match {
//本身就是素数
case n if n.isPrime => List(n)
//能分解为n*ps.head
case n if (n % ps.head) == 0 => ps.head :: primeFactorsR(n / ps.head, ps)
//其他
case n => primeFactorsR(n, ps.tail)
}
}
return primeFactorsR(start, primes)
}
}
