Minimum Operations to Sort a Permutation — Python

# Time:  O(n)
# Space: O(1)

# array
class Solution(object):
    def minOperations(self, nums):
        """
        :type nums: List[int]
        :rtype: int
        """
        def check(i, d):
            return all(nums[(i+j*d)%len(nums)] == j for j in xrange(len(nums)))

        idx = nums.index(0)
        return min(idx, 1+(len(nums)-idx)+1) if check(idx, +1) else min((idx+1)+1, 1+(len(nums)-(idx+1))) if check(idx, -1) else -1


# Time:  O(n)
# Space: O(1)
# array
class Solution2(object):
    def minOperations(self, nums):
        """
        :type nums: List[int]
        :rtype: int
        """
        def check(compare):
            return sum(not compare(nums[i], nums[(i+1)%len(nums)]) for i in xrange(len(nums))) <= 1

        idx = nums.index(0)
        return min(idx, 1+(len(nums)-idx)+1) if check(lambda a, b: a <= b) else min((idx+1)+1, 1+(len(nums)-(idx+1))) if check(lambda a, b: a >= b) else -1