Maximum Value at a Given Index in a Bounded Array
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 == nnums[i]is a positive integer where0 <= i < n.abs(nums[i] - nums[i+1]) <= 1where0 <= i < n - 1.- The sum of all the elements of
numsdoes not exceedmaxSum. 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 = 6Output
2nums = [1, 2, 2, 1] satisfies all the conditions, and no valid array can have nums[2] == 3.Example 2
Input
n = 6, index = 1, maxSum = 10Output
3The maximum possible value at index
1 while satisfying all conditions is 3.Constraints
- 1 <= n <= maxSum <= 10^9
- 0 <= index < n