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:

code Ran=1, ChOut=8, IntOut=11;
def Size = 1_000_000;
int I, S, A(Size), Hi(Size), Lo(Size);
[for I:= 0 to Size-1 do A(I):= Ran(100) - 50;
S:= 0;
for I:= 0 to Size-1 do [S:= S+A(I);  Lo(I):= S];
S:= 0;
for I:= Size-1 downto 0 do [S:= S+A(I);  Hi(I):= S];
for I:= 0 to Size-1 do
    if Lo(I) = Hi(I) then [IntOut(0, I);  ChOut(0, ^ )];
]