Learning by Example: Summation

In this lesson, we will write a summation program using the methods we have learned so far.

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’

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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’

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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’

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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.