2439. Minimize Maximum of Array

Problem Link

Description

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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

Solution

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Python3

class Solution:
    def minimizeArrayValue(self, nums: List[int]) -> int:
        N = len(nums)
        left, right = min(nums), max(nums)
 
        def good(k):
            A = nums[:]
 
            for i in range(N - 1, 0, -1):
                if A[i] <= k: continue
 
                deduct = A[i] - k
                A[i] -= deduct
                A[i - 1] += deduct
 
            return max(A) <= k
 
        while left < right:
            mid = left + (right - left) // 2
 
            if good(mid):
                right = mid
            else:
                left = mid + 1
        
        return left