kth smallest element

class :
    """
    @param n: An integer
    @param nums: An array
    @return: the Kth largest element
    """
    def kthLargestElement(self, k, A):
        if not A or k < 1 or k > len(A):
            return None
        return self.partition(A, 0, len(A) - 1, len(A) - k)
        
    def partition(self, nums, start, end, k):
        """
        During the process, it's guaranteed start <= k <= end
        """
        if start == end:
            return nums[k]
            
        left, right = start, end
        pivot = nums[(start + end) // 2]
        while left <= right:
            while left <= right and nums[left] < pivot:
                left += 1
            while left <= right and nums[right] > pivot:
                right -= 1
            if left <= right:
                nums[left], nums[right] = nums[right], nums[left]
                left, right = left + 1, right - 1
        
        if k <= right:
            return self.partition(nums, start, right, k)
        if k >= left:
            return self.partition(nums, left, end, k)
        
        return nums[k]