LeetCode 2656. Maximum Sum With Exactly K Elements

You are given a 0-indexed integer array nums and an integer k. Your task is to perform the following operation exactly k times in order to maximize your score:

1. Select an element m from nums.

2. Remove the selected element m from the array.

3. Add a new element with a value of m + 1 to the array.

4. Increase your score by m.

Return the maximum score you can achieve after performing the operation exactly k times.

Example 1:

Input: nums = [1,2,3,4,5], k = 3

Output: 18

Explanation: 

We need to choose exactly 3 elements from nums to maximize the sum. 

For the first iteration, we choose 5. Then sum is 5 and nums = [1,2,3,4,6] 

For the second iteration, we choose 6. Then sum is 5 + 6 and nums = [1,2,3,4,7] 

For the third iteration, we choose 7. Then sum is 5 + 6 + 7 = 18 and nums = [1,2,3,4,8] 

So, we will return 18. It can be proven, 

that 18 is the maximum answer that we can achieve.

Example 2:

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

Output: 11

Explanation: We need to choose exactly 2 elements from nums to maximize the sum. 

For the first iteration, we choose 5. Then sum is 5 and nums = [5,5,6] 

For the second iteration, we choose 6. Then sum is 5 + 6 = 11 and nums = [5,5,7]

So, we will return 11. 

It can be proven, that 11 is the maximum answer that we can achieve.

Constraints:

• 1 <= nums.length <= 100

• 1 <= nums[i] <= 100

• 1 <= k <= 100

 easy题目，不多解释，就是先找到最大值，然后根据等差数列求和的公式计算出结果，

返回即可；

Runtime: 7 ms, faster than 56.91% of Java online submissions for Maximum Sum With Exactly K Elements .

Memory Usage: 42.5 MB, less than 92.06% of Java online submissions for Maximum Sum With Exactly K Elements .