A Fortran Primer, Puzzle, and Solution

! modules are basically packages that can be used by programs
modUle testers

  ! disables a fortran feature that treats all variables starting with
  ! i, j, k, l, m, and n as integers and all other variables as reals
  ! by default
  implicit none

  ! defines a variable
  ! first argument is the data type of the variable
  ! parameter keyword specifies that this variable is a named constant
  ! selected_TYPE_kind(a) returns a kind for the specified data type that can represent all values from -10^a to 10^a
  integer, parameter :: ikind=selected_int_kind(16)
  integer, parameter :: rkind = selected_real_kind(16)

! contains blocks off the module's procedures from its global definitions
contains

  ! function definition
  ! begins with a type and kind to specify what the function will return
  ! next is the function keyword followed by the function name and its parameters
  ! optionally you can define a result variable which will inherit its type from the function
  ! the alternative to explicitly defining the result variable is to remove the result section entirely and the result 
  ! variable will default to the name of the function
  integer(16) function find_nb(m) result(n)

    ! defining the type and kind for the parameter m
    integer(ikind) :: m 
    integer(ikind) :: sum

    ! reals are a category of number that, in simple terms, can have decimals
    real(rkind) :: k

    ! Given a volume of m, return the number of cubes n where the volume
    ! of each cube is given by n^3 -> (n-1)^3 -> etc... -> 1^3 and when each
    ! cube's volume is added together you get m

    ! iterative solution
    ! n = 0
    ! sum = 0
    ! do while (sum < m)
    !   n = n + 1
    !   sum = sum + n ** 3
    ! end do
    ! if (sum /= m) then
    !   n = -1
    ! end if

    ! formulaic solution
    ! the real keyword here is used to convert the integer m into a real datatype of kind rkind
    ! the decimal tells the compiler to treat these whole numbers as reals instead of integers
    k = ((8. * (real(m, rkind)) ** (.5) + 1.) ** (.5) - 1.) / 2.
    ! merge is the ternary operator for fortran: merge(if true, if false, case)
    ! floor is the equivalent of Math.floor() in javascript
    n = merge(-1, floor(k), floor(k) /= k)

  ! end the function definition
  end function find_nb

! end the module
end module testers

! program denotes where we start the code for a file
program test

  ! gives access to the testers module defined above
  use testers
  implicit none

  ! outputs to the console in the specified format
  ! a lot to go into here, but basically the first argument to print specifies the type and spacing of the rest of the arguments
  ! A is for strings and i is for integers
  print "(A)", "Pile O' Cubes"
  print "(A, i4.0, A)", "expected: ", find_nb(9_ikind), " -> actual: 2" ! the function find_nb and the kind ikind are both provided by the cubes module
  print "(A, i4.0, A)", "expected: ", find_nb(36_ikind), " -> actual: 3"
  print "(A, i4.0, A)", "expected: ", find_nb(1071225_ikind), " -> actual: 45"
  print "(A, i4.0, A)", "expected: ", find_nb(24723578342962_ikind), " -> actual: -1"
  print "(A, i4.0, A)", "expected: ", find_nb(4183059834009_ikind), " -> actual: 2022"
  print "(A, i4.0, A)", "expected: ", find_nb(135440716410000_ikind), " -> actual: 4824"

! end the program
end program test