Equilibrium Interpolation

gistfile1.txt

import scala.collection.JavaConverters._

object Solution {
  def solution(a: Array[Int]): Int = {
    var sum = 0
    for (i <- 0 to (a.length - 1)) {
      sum += a(i)
    }
    
    var sum_left = 0
    for (i <- 0 to (a.length - 1)) {
      var sum_right = sum - sum_left - a(i)
      if (sum_left == sum_right)
        return i
      sum_left += a(i)
    }
    
    return -1
  }
}

gistfile2.txt

A zero-indexed array A consisting of N integers is given. An equilibrium index of this array is any integer P such that 0 ≤ P < N and the sum of elements of lower indices is equal to the sum of elements of higher indices, i.e. 
A[0] + A[1] + ... + A[P−1] = A[P+1] + ... + A[N−2] + A[N−1].
Sum of zero elements is assumed to be equal to 0. This can happen if P = 0 or if P = N−1.

For example, consider the following array A consisting of N = 8 elements:

  A[0] = -1
  A[1] =  3
  A[2] = -4
  A[3] =  5
  A[4] =  1
  A[5] = -6
  A[6] =  2
  A[7] =  1
P = 1 is an equilibrium index of this array, because:

A[0] = −1 = A[2] + A[3] + A[4] + A[5] + A[6] + A[7]
P = 3 is an equilibrium index of this array, because:

A[0] + A[1] + A[2] = −2 = A[4] + A[5] + A[6] + A[7]
P = 7 is also an equilibrium index, because:

A[0] + A[1] + A[2] + A[3] + A[4] + A[5] + A[6] = 0
and there are no elements with indices greater than 7.

P = 8 is not an equilibrium index, because it does not fulfill the condition 0 ≤ P < N.

Write a function:

object Solution { def solution(a: Array[Int]): Int }

that, given a zero-indexed array A consisting of N integers, returns any of its equilibrium indices. The function should return −1 if no equilibrium index exists.

For example, given array A shown above, the function may return 1, 3 or 7, as explained above.

Assume that:

N is an integer within the range [0..100,000];
each element of array A is an integer within the range [−2,147,483,648..2,147,483,647].
Complexity:

expected worst-case time complexity is O(N);
expected worst-case space complexity is O(N), beyond input storage (not counting the storage required for input arguments).
Elements of input arrays can be modified.