course-2002-02.scala

JAVA 语言的函数式编程扩展

      if (a > b) result
      else iter(a + 1, result + f(a))
    }
    iter(a, 0)
  }

  def product(f: Int => Double)(a: Int, b: Int): Double = {
    def iter(a: Int, result: Double): Double = {
      if (a > b) result
      else iter(a + 1, result * f(a))
    }
    iter(a, 1)
  }

  def factorial(n: Int) = product(x => x)(1 , n)

  Console.println(
      "1 + 2 + .. + 5 = " + sum(x => x)(1, 5));
  Console.println(
      "1 * 2 * .. * 5 = " + product(x => x)(1, 5));
  Console.println;

  Console.println(
      "1^2 + 2^2 + .. + 5^2 = " + sum(x => x*x)(1, 5));
  Console.println(
      "1^2 * 2^2 * .. * 5^2 = " + product(x => x*x)(1, 5));
  Console.println;

  Console.println(
      "factorial(0) = " + factorial(0))
  Console.println(
      "factorial(1) = " + factorial(1))
  Console.println(
      "factorial(2) = " + factorial(2))
  Console.println(
      "factorial(3) = " + factorial(3))
  Console.println(
      "factorial(4) = " + factorial(4))
  Console.println(
      "factorial(5) = " + factorial(5))
  Console.println
}

//############################################################################

object MD {
  def reduce(op: (Double,Double) => Double, zero:Double)(f: Int => Double)(a: Int,b: Int): Double = {
    def iter(a: Int, result: Double): Double = {
      if (a > b) result
      else iter(a + 1, op(result, f(a)))
    }
    iter(a, zero)
  }

  def plus (x:Double,y:Double) = x+y; 
  val sum: (Int => Double) => (Int, Int) => Double = reduce(plus , 0);
  def times(x:Double,y:Double) = x*y; 
  val product: (Int => Double) => (Int, Int) => Double = reduce(times, 1);

  def factorial(n: Int) = product(x => x)(1 , n)

  Console.println(
      "1 + 2 + .. + 5 = " + sum(x => x)(1, 5))
  Console.println(
      "1 * 2 * .. * 5 = " + product(x => x)(1, 5))
  Console.println;

  Console.println(
      "1^2 + 2^2 + .. + 5^2 = " + sum(x => x*x)(1, 5))
  Console.println(
      "1^2 * 2^2 * .. * 5^2 = " + product(x => x*x)(1, 5))
  Console.println;

  Console.println(
      "factorial(0) = " + factorial(0))
  Console.println(
      "factorial(1) = " + factorial(1))
  Console.println(
      "factorial(2) = " + factorial(2))
  Console.println(
      "factorial(3) = " + factorial(3))
  Console.println(
      "factorial(4) = " + factorial(4))
  Console.println(
      "factorial(5) = " + factorial(5))
  Console.println
}

//############################################################################

object ME {
  def reduce(op: (Double,Double) => Double, zero:Double)(f: Int => Double)(a: Int,b: Int): Double = {
    def iter(a: Int, result: Double): Double = {
      if (a > b) result
      else iter(a + 1, op(result, f(a)))
    }
    iter(a, zero)
  }

  def sum: (Int => Double) => (Int, Int) => Double     = reduce((x,y) => x + y, 0);
  def product: (Int => Double) => (Int, Int) => Double = reduce((x,y) => x * y, 1);

  def factorial(n: Int) = product(x => x)(1 , n)

  Console.println(
      "1 + 2 + .. + 5 = " + sum(x => x)(1, 5))
  Console.println(
      "1 * 2 * .. * 5 = " + product(x => x)(1, 5))
  Console.println;

  Console.println(
      "1^2 + 2^2 + .. + 5^2 = " + sum(x => x*x)(1, 5))
  Console.println(
      "1^2 * 2^2 * .. * 5^2 = " + product(x => x*x)(1, 5))
  Console.println;

  Console.println(
      "factorial(0) = " + factorial(0))
  Console.println(
      "factorial(1) = " + factorial(1))
  Console.println(
      "factorial(2) = " + factorial(2))
  Console.println(
      "factorial(3) = " + factorial(3))
  Console.println(
      "factorial(4) = " + factorial(4))
  Console.println(
      "factorial(5) = " + factorial(5))
  Console.println
}

//############################################################################

object MF {
  def fib(x: Int): Int =
    if (x <= 1) x
    else fib(x - 2) + fib(x - 1)

  Console.println("fib(0) = " + fib(0))
  Console.println("fib(1) = " + fib(1))
  Console.println("fib(2) = " + fib(2))
  Console.println("fib(3) = " + fib(3))
  Console.println("fib(4) = " + fib(4))
  Console.println("fib(5) = " + fib(5))
  Console.println("fib(6) = " + fib(6))
  Console.println("fib(7) = " + fib(7))
  Console.println("fib(8) = " + fib(8))
  Console.println("fib(9) = " + fib(9))
}

//############################################################################

object MG {
  def fib(x: Int) = {
    def loop(n: Int, prev: Int, fibn: Int): Int =
      if (n == x) fibn
      else loop(n + 1, fibn, fibn + prev)
    if (x == 0) 0 else loop(1, 0, 1)
  }

  Console.println("fib(0) = " + fib(0))
  Console.println("fib(1) = " + fib(1))
  Console.println("fib(2) = " + fib(2))
  Console.println("fib(3) = " + fib(3))
  Console.println("fib(4) = " + fib(4))
  Console.println("fib(5) = " + fib(5))
  Console.println("fib(6) = " + fib(6))
  Console.println("fib(7) = " + fib(7))
  Console.println("fib(8) = " + fib(8))
  Console.println("fib(9) = " + fib(9))
}

//############################################################################

object MH {
  def power(x: Double, y: Int): Double =
    if (y <= 0) 1
    else if (y % 2 == 0) power(x * x, y / 2)
    else x * power(x, y - 1);


  Console.println("power(0,0) = " + power(0,0))
  Console.println("power(0,1) = " + power(0,1))
  Console.println("power(0,2) = " + power(0,2))
  Console.println("power(0,3) = " + power(0,3))
  Console.println("power(0,4) = " + power(0,4))
  Console.println("power(0,5) = " + power(0,5))
  Console.println("power(0,6) = " + power(0,6))
  Console.println("power(0,7) = " + power(0,7))
  Console.println("power(0,8) = " + power(0,8))
  Console.println

  Console.println("power(1,0) = " + power(1,0))
  Console.println("power(1,1) = " + power(1,1))
  Console.println("power(1,2) = " + power(1,2))
  Console.println("power(1,3) = " + power(1,3))
  Console.println("power(1,4) = " + power(1,4))
  Console.println("power(1,5) = " + power(1,5))
  Console.println("power(1,6) = " + power(1,6))
  Console.println("power(1,7) = " + power(1,7))
  Console.println("power(1,8) = " + power(1,8))
  Console.println

  Console.println("power(2,0) = " + power(2,0))
  Console.println("power(2,1) = " + power(2,1))
  Console.println("power(2,2) = " + power(2,2))
  Console.println("power(2,3) = " + power(2,3))
  Console.println("power(2,4) = " + power(2,4))
  Console.println("power(2,5) = " + power(2,5))
  Console.println("power(2,6) = " + power(2,6))
  Console.println("power(2,7) = " + power(2,7))
  Console.println("power(2,8) = " + power(2,8))
  Console.println

  Console.println("power(3,0) = " + power(3,0))
  Console.println("power(3,1) = " + power(3,1))
  Console.println("power(3,2) = " + power(3,2))
  Console.println("power(3,3) = " + power(3,3))
  Console.println("power(3,4) = " + power(3,4))
  Console.println("power(3,5) = " + power(3,5))
  Console.println("power(3,6) = " + power(3,6))
  Console.println("power(3,7) = " + power(3,7))
  Console.println("power(3,8) = " + power(3,8))
  Console.println

  Console.println("power(4,0) = " + power(4,0))
  Console.println("power(4,1) = " + power(4,1))
  Console.println("power(4,2) = " + power(4,2))
  Console.println("power(4,3) = " + power(4,3))
  Console.println("power(4,4) = " + power(4,4))
  Console.println("power(4,5) = " + power(4,5))
  Console.println("power(4,6) = " + power(4,6))
  Console.println("power(4,7) = " + power(4,7))
  Console.println("power(4,8) = " + power(4,8))
  Console.println

  Console.println("power(5,0) = " + power(5,0))
  Console.println("power(5,1) = " + power(5,1))
  Console.println("power(5,2) = " + power(5,2))
  Console.println("power(5,3) = " + power(5,3))
  Console.println("power(5,4) = " + power(5,4))
  Console.println("power(5,5) = " + power(5,5))
  Console.println("power(5,6) = " + power(5,6))
  Console.println("power(5,7) = " + power(5,7))
  Console.println("power(5,8) = " + power(5,8))
  Console.println
}

//############################################################################

object Test {
  def main(args: Array[String]): Unit = {
    M0
    M1
    M2
    M3
    M4
    M5
    M6
    M7
    M8
    M9
    MA
    MB
    MC
    MD
    ME
    MF
    MG
    MH
    ()
  }
}

//############################################################################