2439. Minimize Maximum of Array
Description
You are given a 0-indexed array nums
comprising of n
non-negative integers.
In one operation, you must:
- Choose an integer
i
such that1 <= i < n
andnums[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
Solutions
Solution 1: Binary Search
To minimize the maximum value of the array, it is intuitive to use binary search. We binary search for the maximum value $mx$ of the array, and find the smallest $mx$ that satisfies the problem requirements.
The time complexity is $O(n \times \log M)$, where $n$ is the length of the array, and $M$ is the maximum value in the array.
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