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:

to equilibrium.iter :i :before :after :tail :ret
  if equal? :before :after [make "ret lput :i :ret]
  if empty? butfirst :tail [output :ret]
  output equilibrium.iter :i+1 (:before+first :tail) (:after-first butfirst :tail) (butfirst :tail) :ret
end
to equilibrium.index :list
  output equilibrium.iter 1 0 (apply "sum butfirst :list) :list []
end

show equilibrium_index [-7 1 5 2 -4 3 0]    ; [4 7]