Minimize Rounding Error to Meet Target — Python

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

import math
import random


class Solution(object):
    def minimizeError(self, prices, target):
        """
        :type prices: List[str]
        :type target: int
        :rtype: str
        """
        def kthElement(nums, k, compare=lambda a, b: a < b):
            def PartitionAroundPivot(left, right, pivot_idx, nums, compare):
                new_pivot_idx = left
                nums[pivot_idx], nums[right] = nums[right], nums[pivot_idx]
                for i in xrange(left, right):
                    if compare(nums[i], nums[right]):
                        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 = random.randint(left, right)
                new_pivot_idx = PartitionAroundPivot(left, right, pivot_idx, nums, compare)
                if new_pivot_idx == k:
                    return
                elif new_pivot_idx > k:
                    right = new_pivot_idx - 1
                else:  # new_pivot_idx < k.
                    left = new_pivot_idx + 1
        
        errors = []
        lower, upper = 0, 0
        for i, p in enumerate(map(float, prices)):
            lower += int(math.floor(p))
            upper += int(math.ceil(p))
            if p != math.floor(p):
                errors.append(p-math.floor(p))
        if not lower <= target <= upper:
            return "-1"

        lower_round_count = upper-target
        kthElement(errors, lower_round_count)
        result = 0.0
        for i in xrange(len(errors)):
            if i < lower_round_count:
                result += errors[i]
            else:
                result += 1.0-errors[i]
        return "{:.3f}".format(result)