1846. Maximum Element After Decreasing and Rearranging

https://leetcode.com/problems/maximum-element-after-decreasing-and-rearranging

Description

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:
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

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