An O(n) way to cycle a list. Inspired by Jon Bentley's 'Programming Pearls' in Chapter 2, 'Aha! Algorithms', section 2.3, 'Power of Primitives'. Less efficient than the three rotate method by a constant factor, but still interesting.

juggling.py

from fractions import gcd

def rotate(vector, k):
    ''' rotate the vector to the left '''
    n = len(vector)
    for i in range(gcd(k,n)):
        temp = vector[i]
        j = i
        while True:
            p = j + k
            if p >= n: p = p-n
            if p == i: break
            vector[j] = vector[p]
            j = p
        vector[j] = temp
    return vector

# vec = ['a','b','c','d','e']
# rotate(vec, 3) # output: ['d', 'e', 'a', 'b', 'c']

if __name__ == '__main__':
    vec = ['a','b','c','d','e']
    print ",".join(vec) + " -> rotate(vec, 3) -> " + ",".join(rotate(vec, 3))