Find the Smallest Divisor Given a Threshold in Python

Problem: 

Given an array of integers nums and an integer threshold, we will choose a positive integer divisor and divide all the array by it and sum the result of the division. Find the smallest divisor such that the result mentioned above is less than or equal to threshold.

Each result of division is rounded to the nearest integer greater than or equal to that element. (For example: 7/3 = 3 and 10/2 = 5).

It is guaranteed that there will be an answer.

Example:

Input: nums = [1,2,5,9], threshold = 6
Output: 5
Explanation: We can get a sum to 17 (1+2+5+9) if the divisor is 1. If the divisor is 4 we can get a sum to 7 (1+1+2+3) and if the divisor is 5 the sum will be 5 (1+1+1+2).

Constraints:

1 <= nums.length <= 5 * 10^4
1 <= nums[i] <= 10^6
nums.length <= threshold <= 10^6

Solution:

class Solution:
  def smallestDivisor(nums, threshold):
    def getSum(divisor, xs):
      return sum([x // divisor + 1 if x % divisor else x // divisor for x in xs])

    left, right = 1, 10 ** 6
    while left + 1 < right:
      mid = (left + right) // 2
      if getSum(mid, nums) > threshold:
        left = mid
      else: right = mid
    return left if getSum(left, nums) <= threshold else right

nums = [1,2,5,9]
threshold = 6
print(Solution.smallestDivisor(nums, threshold))

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