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Quiz 1.8: Functions

Q1: Function comparison

Given the following code snippet:

function foo(x)
  list = []
  for i in 2:x
    cond = true
    for j in list
      if i%j == 0
        cond = false
      end
    end
    if cond push!(list,i); end
  end
  return list
end

function foo2(x)
  if x == 1 return []; end
  ns = foo2(x-1)
  cond = true
  for i in ns
    if x%i == 0
      cond = false
    end
  end
  if cond push!(ns,x); end
  return ns
end

Which of the following sentences are correct ?

RESOLUTION

The two functions compute the list of prime numbers up to x, with the second one being recursive. While often recursive functions are slow, here the computations to derive the prime numbers are roughly the same in the two cases with a O(x²) complexity bound, and there isn't a version that is definitely slower. Note that much more efficient approaches to find prime number exist.

The correct answers are:

  • "None of the (other) sentences is correct"

Q2: Function optimisation (1)

Given the following code snippet:

function foo(x)
  list = XXXX[]
  for i in 2:x
    cond = true
    for j in list 
      if i%j == 0
        cond = false
      end        
    end
    if cond push!(list,i); end
  end
  return list
end

To what XXXX should be replaced to make the function more efficient?


RESOLUTION

The function can be made orders of magnitude more efficient by simply specifying that the list is an array of integers rather than "any" values.

The correct answer is: "Int64"

Q3: Function optimisation (2)

Given the following code snippet:

function foo(x)
  list = []
  for i in 2:x
    cond = true
    for j in list 
      if i%j == 0
        cond = false
        XXXX
      end        
    end
    if cond push!(list,i); end
  end
  return list
end

To what XXXX should be replaced to make the function more efficient?


RESOLUTION

The function can be made many times more efficient by breaking the loop for that specific item once the first condition leading to cond=false has been found.

The correct answer is: break

Q4: Call by sharing

Given the following code snippet:

a = ([1,2,3],4)
function foo(x)
  x[1][1] = 10
  x[2]    = 40
end
foo(a)

Which of the following sentences are correct ?

RESOLUTION

a is a Tuple, that is an immutable type. The attempt to modify it in the command x[2] = 40 raises an error during the JIT compilation. The first modification, however (x[1][1] = 10), had already taken place.

The correct answers are:

  • An error is raised during compilation/running
  • a is now ([10,2,3],4)

Q5: Call by sharing 2

Given the following code snippet:

a = ([1,2,3],4)
function foo(x)
  x[1][1] = 10
  x       = ([10,20,30],40)
end
foo(a)

Which of the following sentences are true ?

RESOLUTION

a is a Tuple, that is an immutable type. The first command doesn't mutate it but mutates an object contained in it (that being an Array is mutable and doesn't create a problem). The second statement in the foo function rebinds x to a new object, without influencing the original object. Note that as the function mutates its parameter a more appropriate name would have been foo!. Append the function name with an exclamation mark for mutating functions is however only a convention.

The correct answers are:

  • a is now ([10,2,3],4)