Problem
You are given an array of positive integers arr
. Perform some operations (possibly none) on arr
so that it satisfies these conditions:
The value of the first element in
arr
must be1
.The absolute difference between any 2 adjacent elements must be **less than or equal to **
1
. In other words,abs(arr[i] - arr[i - 1]) <= 1
for eachi
where1 <= i < arr.length
(0-indexed).abs(x)
is the absolute value ofx
.
There are 2 types of operations that you can perform any number of times:
Decrease the value of any element of
arr
to a smaller positive integer.Rearrange the elements of
arr
to be in any order.
Return **the *maximum* possible value of an element in arr
after performing the operations to satisfy the conditions**.
Example 1:
Input: arr = [2,2,1,2,1]
Output: 2
Explanation:
We can satisfy the conditions by rearranging arr so it becomes [1,2,2,2,1].
The largest element in arr is 2.
Example 2:
Input: arr = [100,1,1000]
Output: 3
Explanation:
One possible way to satisfy the conditions is by doing the following:
1. Rearrange arr so it becomes [1,100,1000].
2. Decrease the value of the second element to 2.
3. Decrease the value of the third element to 3.
Now arr = [1,2,3], which satisfies the conditions.
The largest element in arr is 3.
Example 3:
Input: arr = [1,2,3,4,5]
Output: 5
Explanation: The array already satisfies the conditions, and the largest element is 5.
Constraints:
1 <= arr.length <= 105
1 <= arr[i] <= 109
Solution
/**
* @param {number[]} arr
* @return {number}
*/
var maximumElementAfterDecrementingAndRearranging = function(arr) {
arr.sort((a, b) => a - b);
arr[0] = 1;
for (var i = 1 ; i < arr.length; i++) {
if (arr[i] - arr[i - 1] <= 1) continue;
arr[i] = arr[i - 1] + 1;
}
return arr[arr.length - 1];
};
Explain:
nope.
Complexity:
- Time complexity : O(n * log(n)).
- Space complexity : O(1).