35 * 35 * 35 
68 * 68 * 68 

def cube(n: Int) = n * n * n 
cube(35) 
cube(68)

def cube(n: Int) = n * n * n 
 def sumCube(a: Int, b: Int): Int = 
   if (a > b) 0 else cube(a) + sumCube(a + 1, b) 
 
sumCube(1, 10)

def cube(n: Int) = n * n * n 
def id(n: Int) = n 
def square(n : Int) = n * n 
def fact(n: Int): Int = 
  if (n == 0) 1 else n * fact(n - 1) 
 
def sumCube(a: Int, b: Int): Int = 
  if (a > b) 0 else cube(a) + sumCube(a + 1, b) 
 
def sumSquare(a: Int, b: Int): Int = 
  if(a > b) 0 else square(a) + sumSquare(a + 1, b) 
  
def sumFact(a: Int, b: Int): Int = 
  if (a > b) 0 else fact(a) + sumFact(a + 1, b) 
 
def sumInt(a: Int, b: Int): Int = 
  if(a > b) 0 else id(a) + sumInt(a + 1, b)  
 
 sumCube(1, 10) 
 sumInt(1, 10) 
 sumSquare(1, 10) 
 sumFact(1, 10)

def cube(n: Int) = n * n * n 
def id(n: Int) = n 
def square(n : Int) = n * n 
def fact(n: Int): Int = 
  if (n == 0) 1 else n * fact(n - 1) 
//高阶函数
def sum(f: Int=>Int, a:Int, b:Int): Int = 
  if(a>b) 0 else f(a)+sum(f, a+1, b)
// 使用高阶函数重新定义求和函数
def sumCube(a: Int, b: Int): Int = sum(cube, a, b) 
def sumSquare(a: Int, b: Int): Int = sum(square, a, b) 
def sumFact(a: Int, b: Int): Int = sum(fact, a, b) 
def sumInt(a: Int, b: Int): Int = sum(id, a, b) 
 
 sumCube(1, 10) 
 sumInt(1, 10) 
 sumSquare(1, 10) 
 sumFact(1, 10)

//保留逻辑较为复杂的函数
def fact(n: Int): Int = 
if (n == 0) 1 else n * fact(n - 1) 
 
def sum(f: Int => Int, a: Int, b: Int): Int = 
  if (a > b) 0 else f(a) + sum(f, a + 1, b) 
 
// 使用高阶函数重新定义求和函数
def sumCube(a: Int, b: Int): Int = sum(x => x * x * x, a, b) 
def sumSquare(a: Int, b: Int): Int = sum(x => x * x, a, b) 
def sumFact(a: Int, b: Int): Int = sum(fact, a, b) 
def sumInt(a: Int, b: Int): Int = sum(x => x, a, b) 
 

sumCube(1, 10) 
sumInt(1, 10) 
sumSquare(1, 10) 
sumFact(1, 10)

def fact(n: Int): Int = 
if (n == 0) 1 else n * fact(n - 1) 
 
// 高阶函数
def sum(f: Int => Int): (Int, Int) => Int = { 
  def sumF(a: Int, b: Int): Int = 
   if (a > b) 0 else f(a) + sumF(a + 1, b) 
 
  sumF 
} 
// 使用高阶函数重新定义求和函数
def sumCube: Int = sum(x => x * x * x) 
def sumSquare: Int = sum(x => x * x) 
def sumFact: Int = sum(fact) 
def sumInt: Int = sum(x => x) 
 
// 这些函数使用起来还和原来一样 ! 
sumCube(1, 10) 
sumInt(1, 10) 
sumSquare(1, 10) 
sumFact(1, 10)

def fact(n: Int): Int = 
  if (n == 0) 1 else n * fact(n - 1) 
 
// 高阶函数
def sum(f: Int => Int): (Int, Int) => Int = { 
  def sumF(a: Int, b: Int): Int = 
   if (a > b) 0 else f(a) + sumF(a + 1, b) 
  sumF 
}

// 直接调用高阶函数 ! 
sum(x => x * x * x) (1, 10) //=> sumCube(1, 10) 
sum(x => x) (1, 10)      //=> sumInt(1, 10) 
sum(x => x * x) (1, 10)   //=> sumSquare(1, 10) 
sum(fact) (1, 10)       //=> sumFact(1, 10)

// 没使用语法糖的 sum 函数
 def sum(f: Int => Int): (Int, Int): Int = { 
 def sumF(a: Int, b: Int): Int = 
  if (a > b) 0 else f(a) + sumF(a + 1, b) 
 
 sumF 
} 
// 使用语法糖后的 sum 函数
 def sum(f: Int => Int)(a: Int, b: Int): Int = 
 if (a > b) 0 else f(a) + sum(f)(a + 1, b)

// 柯里化后的 sum 函数
 def sum(f: Int => Int)(a: Int) (b: Int): Int = 
if (a > b) 0 else f(a) + sum(f)(a + 1)(b) 
 
// 使用柯里化后的高阶函数 ! 
 sum(x => x * x * x)(1)(10) //=> sumCube(1, 10) 
 sum(x => x)(1)(10)      //=> sumInt(1, 10)