Minimum Rotation: O(N)

min_rotation.cpp

int min_rotation(string s) {
    int a = 0, N = s.size();
    s += s;
    for (int b = 0; b < N; b++)
        for (int i = 0; i < N; i++) {
            if (a + i == b || s[a + i] < s[b + i]) {
                b += max(0, i - 1);
                break;
            }
            if (s[a + i] > s[b + i]) {
                a = b;
                break;
            }
        }
    return a;
}