Here is my solution for this problem.
Basically the time complexity is O(n). For each item in the input list, the comparison between the value of index and 0 is conducted. If it is zero, first we shift all the element after it to the end of the list 1 index ahead, then we put 0 to the very end. If it is not zero, shift the index to the next element.
class Solution(object): def moveZeroes(self, nums): """ :type nums: List[int] :rtype: void Do not return anything, modify nums in-place instead. """ idx = 0 for i in range(len(nums)): if nums[idx] == 0: nums[idx:-1] = nums[(idx+1):] nums[-1] = 0 else: idx +=1