3075. Maximize Happiness of Selected Children
Medium
You are given an array happiness
of length n
, and a positive integer k
.
There are n
children standing in a queue, where the i^{th}
child has happiness value happiness[i].
You want to select k
children from these n
children in k
turns.
In each turn, when you select a child, the happiness value of all the children that have not been selected till now decreases by 1
. Note that the happiness value cannot become negative and gets decremented only if it is positive.
Return the maximum sum of the happiness values of the selected children you can achieve by selecting k
children.
Example 1:

Input:
happiness = [1,2,3], k = 2

Output:
4

Explanation: We can pick
2
children in the following way: Pick the child with the happiness
value == 3
. The happiness value of the remaining children becomes[0,1]
.  Pick the child with the happiness
value == 1
. The happiness value of the remaining child becomes[0]
. Note that the happiness value cannot become less than0
.\ The sum of the happiness values of the selected children is3 + 1 = 4
.
 Pick the child with the happiness
Example 2:

Input: happiness =
[1,1,1,1], k = 2

Output:
1

Explanation: We can pick
2
children in the following way: Pick any child with the happiness
value == 1
. The happiness value of the remaining children becomes[0,0,0]
.  Pick the child with the happiness
value == 0
. The happiness value of the remaining child becomes[0,0]
.\ The sum of the happiness values of the selected children is1 + 0 = 1
.
 Pick any child with the happiness
Example 3:

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

Output:
5

Explanation: We can pick
1
child in the following way: Pick the child with the happiness
value == 5
. The happiness value of the remaining children becomes[1,2,3]
.\ The sum of the happiness values of the selected children is5
.
 Pick the child with the happiness
Constraints:
1 <= n == happiness.length <= 2 * 10^{5}
1 <= happiness[i] <= 10^{8}
1 <= k <= n
Solution:
class Solution {
/**
* @param Integer[] $happiness
* @param Integer $k
* @return Integer
*/
function maximumHappinessSum($happiness, $k) {
$ans = 0;
$decremented = 0;
sort($happiness);
rsort($happiness);
for ($i = 0; $i < $k; ++$i) {
$ans += max(0, $happiness[$i]  $decremented);
++$decremented;
}
return $ans;
}
}
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