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}

:

   




A

0


=
−
7


{\displaystyle A_{0}=-7}


   




A

1


=
1


{\displaystyle A_{1}=1}


   




A

2


=
5


{\displaystyle A_{2}=5}


   




A

3


=
2


{\displaystyle A_{3}=2}


   




A

4


=
−
4


{\displaystyle A_{4}=-4}


   




A

5


=
3


{\displaystyle A_{5}=3}


   




A

6


=
0


{\displaystyle A_{6}=0}


3   is an equilibrium index, because:

   




A

0


+

A

1


+

A

2


=

A

4


+

A

5


+

A

6




{\displaystyle A_{0}+A_{1}+A_{2}=A_{4}+A_{5}+A_{6}}


6   is also an equilibrium index, because:

   




A

0


+

A

1


+

A

2


+

A

3


+

A

4


+

A

5


=
0


{\displaystyle A_{0}+A_{1}+A_{2}+A_{3}+A_{4}+A_{5}=0}


(sum of zero elements is zero)

7   is not an equilibrium index, because it is not a valid index of sequence 



A


{\displaystyle A}

.



Task;
Write a function that, given a sequence, returns its equilibrium indices (if any).

Assume that the sequence may be very long.




 
extern crate num;
 
use num::traits::Zero;
 
fn equilibrium_indices(v: &[i32]) -> Vec<usize> {
    let mut right = v.iter().sum();
    let mut left = i32::zero();
 
    v.iter().enumerate().fold(vec![], |mut out, (i, &el)| {
        right -= el;
        if left == right {
            out.push(i);
        }
        left += el;
 
        out
    })
}
 
fn main() {
    let v = [-7i32, 1, 5, 2, -4, 3, 0];
    let indices = equilibrium_indices(&v);
    println!("Equilibrium indices for {:?} are: {:?}", v, indices);
}
 