leetcode 1802 maximum value at a given index in a bounded array

sure! let's discuss leetcode problem 1802, titled "maximum value at a given index in a bounded array." this problem requires you to find the maximum value that can be placed at a specific index in an array while adhering to specific constraints.

problem statement

given three integers `n`, `index`, and `maxsum`, you need to construct an array of length `n` such that:
- the value at position `index` is maximized.
- each element in the array must be at least `1`.
- the sum of all elements in the array must be less than or equal to `maxsum`.

additionally, the value at each index must not exceed its neighboring values by more than one, which means if you have a value at `index`, the values directly adjacent to it (both left and right) must be equal to or less than `value` and can at most increase by `1` from `value` to the next element.

approach

to solve this problem, you can use a binary search approach to efficiently find the maximum value that can be placed at the specified `index`.

1. **binary search**: the idea is to set boundaries for the maximum value at `index`. the lower bound can start from `1`, and the upper bound can be `maxsum`.

2. **check feasibility**: for a mid-value during the binary search, you need a function to check whether it is possible to achieve this mid-value while satisfying the constraints. this involves calculating the total sum of the array formed by the value at `index` and its neighbors.

3. **sum calculation**: you can calculate the sum of the elements on the left and right side of the `index` based on how far they can go while respecting the constraints defined by the `mid` value.

code example

here’s a python implementation of the above approach:

explanation of the code

1. **function `canplacevalue(value)`**: this helper function checks if you can place the specified `value` at the `index` such that the total sum of the array does not exceed `maxsum`.

2. **binary search**: the main function `maxvalue` performs binar ...

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Leetcode
maximum value
bounded array
index
dynamic programming
constraints
array manipulation
optimization problem
algorithm
problem-solving
value calculation
sliding window
prefix sum
greedy approach
input limits