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

from random import randint

# Quick select solution.
class Solution(object):
    def minMoves2(self, nums):
        """
        :type nums: List[int]
        :rtype: int
        """
        def kthElement(nums, k):
            def PartitionAroundPivot(left, right, pivot_idx, nums):
                pivot_value = nums[pivot_idx]
                new_pivot_idx = left
                nums[pivot_idx], nums[right] = nums[right], nums[pivot_idx]
                for i in xrange(left, right):
                    if nums[i] > pivot_value:
                        nums[i], nums[new_pivot_idx] = nums[new_pivot_idx], nums[i]
                        new_pivot_idx += 1

                nums[right], nums[new_pivot_idx] = nums[new_pivot_idx], nums[right]
                return new_pivot_idx

            left, right = 0, len(nums) - 1
            while left <= right:
                pivot_idx = randint(left, right)
                new_pivot_idx = PartitionAroundPivot(left, right, pivot_idx, nums)
                if new_pivot_idx == k - 1:
                    return nums[new_pivot_idx]
                elif new_pivot_idx > k - 1:
                    right = new_pivot_idx - 1
                else:  # new_pivot_idx < k - 1.
                    left = new_pivot_idx + 1

        median = kthElement(nums, len(nums)/2 + 1)
        return sum(abs(num - median) for num in nums)

    def minMoves22(self, nums):
        """
        :type nums: List[int]
        :rtype: int
        """
        median = sorted(nums)[len(nums) / 2]
        return sum(abs(num - median) for num in nums)