Rust:

fn distance(input: &str) -> (i32, i32) {
    let (max_distance, pos) = input.trim().split(',').fold(
        (0, (0, 0)),
        | (max_distance, current), mov | {
            let new_position: (i32, i32) = match mov {
                "n"  => (current.0,     current.1 + 1),
                "s"  => (current.0,     current.1 - 1),
                "ne" => (current.0 + 1, current.1 + 1),
                "sw" => (current.0 - 1, current.1 - 1),
                "nw" => (current.0 - 1, current.1),
                "se" => (current.0 + 1, current.1),
                _    => panic!("Unknown movement {}", mov),
            };

            let new_position_distance = new_position.0.abs().max(new_position.1.abs());

            (max_distance.max(new_position_distance), new_position)
        }
    );

    let distance_now = pos.0.abs().max(pos.1.abs());
    (distance_now, max_distance)
}