Given three positive integers, n, index, and maxSum, output the nums[index] by constructing an array of nums with the length of n, which satisfies the following conditions:
The length of the array nums is equal to n.
Each element nums[i] is a positive integer, where i n.
The absolute difference between two consecutive elements, nums[i] and nums[i+1], is at most
The sum of all elements in nums does not exceed maxSum.
The element at nums[index] contains the maximum value.
Constraints:
n maxSum
index n
The solution to maximizing the value at a given index in a bounded array involves using a binary search approach combined with mathematical calculations of arithmetic sequences. To achieve this, we need to ensure that the values on both sides of nums[index] decrease by at most
The algorithm to solve this problem is as follows:
Initialization
Initialize two variables, left and right, with the values maxSum, respectively. We can assign a minimum value of maxSum.
Start a loop and Iterate until left is less than right, and calculate the sum of left and right elements as listed below:
Calculate mid
Calculate mid as
Determine values on the left side
If mid is greater than index, there will be a sequence starting from mid to the
Given three positive integers, n, index, and maxSum, output the nums[index] by constructing an array of nums with the length of n, which satisfies the following conditions:
The length of the array nums is equal to n.
Each element nums[i] is a positive integer, where i n.
The absolute difference between two consecutive elements, nums[i] and nums[i+1], is at most
The sum of all elements in nums does not exceed maxSum.
The element at nums[index] contains the maximum value.
Constraints:
n maxSum
index n
The solution to maximizing the value at a given index in a bounded array involves using a binary search approach combined with mathematical calculations of arithmetic sequences. To achieve this, we need to ensure that the values on both sides of nums[index] decrease by at most
The algorithm to solve this problem is as follows:
Initialization
Initialize two variables, left and right, with the values maxSum, respectively. We can assign a minimum value of maxSum.
Start a loop and Iterate until left is less than right, and calculate the sum of left and right elements as listed below:
Calculate mid
Calculate mid as
Determine values on the left side
If mid is greater than index, there will be a sequence starting from mid to the