Fastest algorithm for circle shift N sized array for M position

Question

What is the fastest algorithm for circle shifting array for M positions?
For example, [3 4 5 2 3 1 4] shift M = 2 positions should be [1 4 3 4 5 2 3

Answer 1

This algorithm runs in O(n) time and O(1) space. The idea is to trace each cyclic group in the shift (numbered by nextGroup variable).

var shiftLeft = function(list, m) {
    var from = 0;
    var val = list[from];
    var nextGroup = 1;
    for(var i = 0; i < list.length; i++) {
        var to = ((from - m) + list.length) % list.length;
        if(to == from)
            break;

        var temp = list[to];
        list[to] = val;
        from = to;
        val = temp;

        if(from < nextGroup) {
            from = nextGroup++;
            val = list[from];
        }
    }
    return list;
}