minimize_maximum_of_array.py

"""
You are given a 0-indexed array nums comprising of n non-negative integers.

In one operation, you must:

Choose an integer i such that 1 <= i < n and nums[i] > 0.
Decrease nums[i] by 1.
Increase nums[i - 1] by 1.
Return the minimum possible value of the maximum integer of nums after performing any number of operations.

 

Example 1:

Input: nums = [3,7,1,6]
Output: 5
Explanation:
One set of optimal operations is as follows:
1. Choose i = 1, and nums becomes [4,6,1,6].
2. Choose i = 3, and nums becomes [4,6,2,5].
3. Choose i = 1, and nums becomes [5,5,2,5].
The maximum integer of nums is 5. It can be shown that the maximum number cannot be less than 5.
Therefore, we return 5.
Example 2:

Input: nums = [10,1]
Output: 10
Explanation:
It is optimal to leave nums as is, and since 10 is the maximum value, we return 10.
 

Constraints:

n == nums.length
2 <= n <= 105
0 <= nums[i] <= 109

"""

class Solution:
    def minimizeArrayValue(self, nums: List[int]) -> int:
        total_sum = 0
        result = 0

        for index in range(len(nums)):
            total_sum = total_sum + nums[index]
            result = max(result, (total_sum + index) // (index + 1))
        
        return int(result)