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:

function array_sum(t)
   assert(type(t) == "table", "t must be a table!")
   local sum = 0
   for i=1, #t do sum = sum + t[i] end
   return sum
end

function equilibrium_index(t)
   assert(type(t) == "table", "t must be a table!")
   local left, right, ret = 0, array_sum(t), -1
   for i,j in pairs(t) do
      right = right - j
      if left == right then
	 ret = i
	 break
      end
      left = left + j
   end
   return ret
end

print(equilibrium_index({-7, 1, 5, 2, -4, 3, 0}))