Search⌘ K
Home
Courses
Learn Scala

Learning by Example: Summation

Explore how to apply higher order functions in Scala to perform summation tasks. Learn to create recursive functions that calculate sums of integers, cubes, and factorials between given values, and understand how to abstract common patterns for reusable, flexible code.

We'll cover the following...

Let’s look at an example where we will learn how to implement higher-order functions and also understand the type of scenarios in which they should be used.

Below, we are going to define a set of recursive functions which all perform some sort of summation.

1. Sum of integers between ‘a’ and ‘b’

Scala
def sumOfInts(a: Int, b: Int): Int ={
  if(a>b) 0
  else a + sumOfInts(a+1,b)
}
println(sumOfInts(1,5))

2. Sum of the cubes of all the integers between ‘a’ and ‘b’

Scala
def cube(x: Int): Int ={
  x * x * x
}
def sumOfCubes(a: Int, b: Int): Int ={
  if(a>b) 0
  else cube(a) + sumOfCubes(a+1,b)
}
println(sumOfCubes(1,5))

3. Sum of the factorials of all the integers between ‘a’ and ‘b’

Scala
def factorial(x: Int): Int = {
  if(x==0) 1
  else x * factorial(x-1)
}
def sumOfFactorials(a: Int, b: Int): Int ={
  if(a>b) 0
  else factorial(a) + sumOfFactorials(a+1,b)
}
println(sumOfFactorials(1,5))

You might have noticed that all the functions we have defined above are different cases of:

∑n=abf(n)\sum_{n=a}^b f(n)

With ff being any of the functions above.

Can we factor out the common pattern into a single function rather than have three separate functions?

In the next lesson, we will try to solve the above problem using higher-order functions.