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 nums2 == 3, so 2 is the maximum nums2.

Example 2:

Input: n = 6, index = 1, maxSum = 10

Output: 3

Constraints:

• <code>1 <= n <= maxSum <= 10⁹</code>

• 0 <= index < n