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2195. Append K Integers With Minimal Sum

Difficulty Topics

Description

You are given an integer array nums and an integer k. Append k unique positive integers that do not appear in nums to nums such that the resulting total sum is minimum.

Return the sum of the k integers appended to nums.

 

Example 1:

Input: nums = [1,4,25,10,25], k = 2
Output: 5
Explanation: The two unique positive integers that do not appear in nums which we append are 2 and 3.
The resulting sum of nums is 1 + 4 + 25 + 10 + 25 + 2 + 3 = 70, which is the minimum.
The sum of the two integers appended is 2 + 3 = 5, so we return 5.

Example 2:

Input: nums = [5,6], k = 6
Output: 25
Explanation: The six unique positive integers that do not appear in nums which we append are 1, 2, 3, 4, 7, and 8.
The resulting sum of nums is 5 + 6 + 1 + 2 + 3 + 4 + 7 + 8 = 36, which is the minimum. 
The sum of the six integers appended is 1 + 2 + 3 + 4 + 7 + 8 = 25, so we return 25.

 

Constraints:

  • 1 <= nums.length <= 105
  • 1 <= nums[i] <= 109
  • 1 <= k <= 108

Solution

append-k-integers-with-minimal-sum.py
class Solution:
    def minimalKSum(self, nums: List[int], k: int) -> int:
        nums = sorted(list(set(nums)))
        n = len(nums)

        if nums[-1] <= k + n:
            return (k + n) * (k + n + 1) // 2 - sum(nums)

        left, right = 0, n - 1

        while left < right:
            mid = left + (right - left) // 2

            if nums[mid] - mid > k:
                right = mid
            else:
                left = mid + 1

        return (left + k) * (left + k + 1) // 2 - sum(nums[:left])