Equilibrium index of an array of large numbers, how to prevent overflow?

Question

Problem statement:
An equilibrium index of an array is an index into the array such that the sum of elements at lower indices is equal to the sum o

Answer 1

Yes it is possible. Notice that if data[0] < data[len - 1], then data[1] shall belong to the "left" part; similarly if data[0] > data[len-1] then data[len-2] belongs to the "right" part. This observation allows an inductive proof of correctness of the following algorithm:

left_weight = 0; right_weight = 0
left_index = 0; right_index = 0

while left_index < right_index
    if left_weight < right_weight
        left_weight += data[left_index++];
    else
        right_weight += data[--right_index]

Still there is an accumulation, but it is easy to deal with by keeping track of imbalance and a boolean indicator of which side is heavier:

while left_index < right_index
    if heavier_side == right
        weight = data[left_index++]
    else
        weight = data[--right_index]

    if weight < imbalance
        imbalance = imbalance - weight
    else
        heavier_side = !heavier_side
        imbalance = weight - imbalance

At least for unsigned data there is no possibility of overflow. Some tinkering might be required for signed values.