Find Equilibrium Index of an Array

Equilibrium index of an array is an index such that the sum of elements at lower indexes is equal to the sum of elements at higher indexes. For example, in an array A:

(A[0] + A[1] + ... + A[i-1]) = (A[i+1] + A[i+2] + ... + A[n-1])

where 0 < i < n - 1

Given an array of integers, find the list of equilibrium indexes in it.

Example Solution

Let array arr equal to [ 0, -3, 5, -4, -2, 3, 1, 0 ]. The equilibrium index found at index 0, 3 and 7:

• Index 0: 0 = (-3) + 5 + (-4) + (-2) + 3 + 1 + 0
• Index 3: (-3) = (-4) + (-2) + 3 + 1 + 0
• Index 7: 0 + (-3) + 5 + (-4) + (-2) + 3 + 1 = 0

Therefore the solution should return [ 0, 3, 7 ].