public class Solution
extends Object
1802 - Maximum Value at a Given Index in a Bounded Array\.
Medium
You are given three positive integers: `n`, `index`, and `maxSum`. You want to construct an array `nums` ( **0-indexed** ) that satisfies the following conditions:
* `nums.length == n`
* `nums[i]` is a **positive** integer where `0 <= i < n`.
* `abs(nums[i] - nums[i+1]) <= 1` where `0 <= i < n-1`.
* The sum of all the elements of `nums` does not exceed `maxSum`.
* `nums[index]` is **maximized**.
Return `nums[index]` _of the constructed array_.
Note that `abs(x)` equals `x` if `x >= 0`, and `-x` otherwise.
**Example 1:**
**Input:** n = 4, index = 2, maxSum = 6
**Output:** 2
**Explanation:** nums = [1,2, **2** ,1] is one array that satisfies all the conditions. There are no arrays that satisfy all the conditions and have nums[2] == 3, so 2 is the maximum nums[2].
**Example 2:**
**Input:** n = 6, index = 1, maxSum = 10
**Output:** 3
**Constraints:**
* 1 <= n <= maxSum <= 109
* `0 <= index < n`