Maximum Value at a Given Index in a Bounded Array — LeetCode 1802 Python Solution

The problem

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.

Example

Input

n = 4, index = 2, maxSum = 6

Output

2

Explanation

nums = [1,2,2,1] is one array that satisfies all the conditions.

Python solution

class Solution:
    def maxValue(self, n: int, index: int, maxSum: int) -> int:
        def sum(x, cnt):
            return (
                (x + x - cnt + 1) * cnt // 2 if x >= cnt else (x + 1) * x // 2 + cnt - x
            )

        left, right = 1, maxSum
        while left < right:
            mid = (left + right + 1) >> 1
            if sum(mid - 1, index) + sum(mid, n - index) <= maxSum:
                left = mid
            else:
                right = mid - 1
        return left

Complexity

Pattern: Monotonic Stack

Answer "what is the next greater element" for every position in one pass. LeetCode 1802. Maximum Value at a Given Index in a Bounded Array is filed here because the reference solution below belongs to the algorithm family this hub collects, even though its LeetCode tags point elsewhere.

The monotonic stack guide has the Python template for the pattern and the 225 LeetCode problems that use it.

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