1846 - Maximum Element After Decreasing and Rearranging.

Medium

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 be 1.

• 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 each i where 1 <= i < arr.length ( 0-indexed ). abs(x) is the absolute value of x.

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:

• Rearrange arr so it becomes [1,100,1000].

• Decrease the value of the second element to 2.

• 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:

• <code>1 <= arr.length <= 10⁵</code>

• <code>1 <= arri<= 10⁹</code>