Array Equilibrium

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 = 7 elements:

A[0] = -7   A[1] =  1   A[2] = 5
A[3] =  2   A[4] = -4   A[5] = 3
A[6] =  0

P = 3 is an equilibrium index of this array, because:

•A[0] + A[1] + A[2] = A[4] + A[5] + A[6]

P = 6 is also an equilibrium index, because:

•A[0] + A[1] + A[2] + A[3] + A[4] + A[5] = 0

and there are no elements with indices greater than 6.

P = 7 is not an equilibrium index, because it does not fulfill the condition 0 ≤ P < N.

Questions related to the array Equilibrium problem;

• What is the complexity of your code (Big O Notation)
• Could the implementation be optimized to linear time