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# Time:  O(n)
# Space: O(1)
# Rotate an array of n elements to the right by k steps.
# For example, with n = 7 and k = 3, the array [1,2,3,4,5,6,7] is rotated to [5,6,7,1,2,3,4].
# Try to come up as many solutions as you can, there are at least 3 different ways to solve this problem.
class Solution:
    :type nums: List[int]
    :type k: int
    :rtype: void Do not return anything, modify nums in-place instead.
    def rotate(self, nums, k):
        k %= len(nums)
        self.reverse(nums, 0, len(nums))
        self.reverse(nums, 0, k)
        self.reverse(nums, k, len(nums))
    def reverse(self, nums, start, end):
        while start < end:
            nums[start], nums[end - 1] = nums[end - 1], nums[start]
            start += 1
            end -= 1
    def rotate2(self, nums, k):
        """
        :type nums: List[int]
        :type k: int
        :rtype: void Do not return anything, modify nums in-place instead.
        """
        nums[:] = nums[len(nums) - k:] + nums[:len(nums) - k]
from fractions import gcd
class Solution2:
    :type nums: List[int]
    :type k: int
    :rtype: void Do not return anything, modify nums in-place instead.
    def rotate(self, nums, k):
        k %= len(nums)
        num_cycles = gcd(len(nums), k)
        cycle_len = len(nums) / num_cycles
        for i in xrange(num_cycles):
            self.apply_cycle_permutation(k, i, cycle_len, nums)
    def apply_cycle_permutation(self, k, offset, cycle_len, nums):
        tmp = nums[offset]
        for i in xrange(1, cycle_len):
            nums[(offset + i * k) % len(nums)], tmp = tmp, nums[(offset + i * k) % len(nums)]
        nums[offset] = tmp
class Solution3:
    :type nums: List[int]
    :type k: int
    :rtype: void Do not return anything, modify nums in-place instead.
    def rotate(self, nums, k):
        count = 0
        start = 0
        while count < len(nums):
            curr = start
            prev = nums[curr]
            while True:
                idx = (curr + k) % len(nums)
                nums[idx], prev = prev, nums[idx]
                curr = idx
                count += 1
                if start == curr:
            start += 1
if __name__ == '__main__':
    nums = [1, 2, 3, 4, 5, 6, 7]
    Solution().rotate(nums, 3)
    print nums

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