Leetcode #2439: Minimize Maximum of Array
In this guide, we solve Leetcode #2439 Minimize Maximum of Array in Python and focus on the core idea that makes the solution efficient.
You will see the intuition, the step-by-step method, and a clean Python implementation you can use in interviews.
Problem Statement
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.
Quick Facts
- Difficulty: Medium
- Premium: No
- Tags: Greedy, Array, Binary Search, Dynamic Programming, Prefix Sum
Intuition
The problem structure suggests a monotonic decision, which makes binary search a natural fit.
By halving the search space each step, we reach the answer efficiently.
Approach
Search either directly on a sorted array or on the answer space using a check function.
Each check is fast, and the logarithmic search keeps the overall runtime low.
Steps:
- Define the search bounds.
- Check the mid point condition.
- Narrow the bounds until convergence.
Example
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.
Python Solution
class Solution:
def minimizeArrayValue(self, nums: List[int]) -> int:
def check(mx):
d = 0
for x in nums[:0:-1]:
d = max(0, d + x - mx)
return nums[0] + d <= mx
left, right = 0, max(nums)
while left < right:
mid = (left + right) >> 1
if check(mid):
right = mid
else:
left = mid + 1
return left
Complexity
The time complexity is , where is the length of the array, and is the maximum value in the array. The space complexity is O(1).
Edge Cases and Pitfalls
Watch for boundary values, empty inputs, and duplicate values where applicable. If the problem involves ordering or constraints, confirm the invariant is preserved at every step.
Summary
This Python solution focuses on the essential structure of the problem and keeps the implementation interview-friendly while meeting the constraints.