1802. Maximum Value at a Given Index in a Bounded Array

https://leetcode.com/problems/maximum-value-at-a-given-index-in-a-bounded-array

Description

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

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