Problem Statement

An equilibrium index of a sequence is an index into the sequence such that the sum of elements at lower indices is equal to the sum of elements at higher indices.

For example, in a sequence

A

{\displaystyle A}

: 3   is an equilibrium index, because: 6   is also an equilibrium index, because: (sum of zero elements is zero) 7   is not an equilibrium index, because it is not a valid index of sequence

A

{\displaystyle A}

.

Write a function that, given a sequence, returns its equilibrium indices (if any). Assume that the sequence may be very long.

Let's start with the solution:

program Equilibrium
  implicit none
  
  integer :: array(7) = (/ -7, 1, 5, 2, -4, 3, 0 /)
 
  call equil_index(array)
 
contains

subroutine equil_index(a)
  integer, intent(in) :: a(:)
  integer :: i

  do i = 1, size(a)
    if(sum(a(1:i-1)) == sum(a(i+1:size(a)))) write(*,*) i
  end do

end subroutine
end program