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3774. Absolute Difference Between Maximum and Minimum K Elements

Description

You are given an integer array nums and an integer k.

Find the absolute difference between:

  • the sum of the k largest elements in the array; and
  • the sum of the k smallest elements in the array.

Return an integer denoting this difference.

 

Example 1:

Input: nums = [5,2,2,4], k = 2

Output: 5

Explanation:

  • The k = 2 largest elements are 4 and 5. Their sum is 4 + 5 = 9.
  • The k = 2 smallest elements are 2 and 2. Their sum is 2 + 2 = 4.
  • The absolute difference is abs(9 - 4) = 5.

Example 2:

Input: nums = [100], k = 1

Output: 0

Explanation:

  • The largest element is 100.
  • The smallest element is 100.
  • The absolute difference is abs(100 - 100) = 0.

 

Constraints:

  • 1 <= n == nums.length <= 100
  • 1 <= nums[i] <= 100
  • 1 <= k <= n

Solutions

Solution 1: Sorting

We first sort the array $\textit{nums}$. Then we calculate the sum of the first $k$ elements and the sum of the last $k$ elements in the array, and finally return the difference between them.

The time complexity is $O(n \times \log n)$, and the space complexity is $O(\log n)$, where $n$ is the length of the array $\textit{nums}$.

  • class Solution {
    public int absDifference(int[] nums, int k) {
        Arrays.sort(nums);
        int ans = 0;
        int n = nums.length;
        for (int i = 0; i < k; ++i) {
            ans += nums[n - i - 1] - nums[i];
        }
        return ans;
    }
}


  • class Solution {
public:
    int absDifference(vector<int>& nums, int k) {
        ranges::sort(nums);
        int n = nums.size();
        int ans = 0;
        for (int i = 0; i < k; ++i) {
            ans += nums[n - i - 1] - nums[i];
        }
        return ans;
    }
};


  • class Solution:
    def absDifference(self, nums: List[int], k: int) -> int:
        nums.sort()
        return sum(nums[-k:]) - sum(nums[:k])


  • func absDifference(nums []int, k int) (ans int) {
	slices.Sort(nums)
	for i := 0; i < k; i++ {
		ans += nums[len(nums)-i-1] - nums[i]
	}
	return
}


  • function absDifference(nums: number[], k: number): number {
    nums.sort((a, b) => a - b);
    let ans = 0;
    for (let i = 0; i < k; ++i) {
        ans += nums.at(-i - 1)! - nums[i];
    }
    return ans;
}

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