Minimize Maximum of Array
Asked at Visa
Problem
Minimize Maximum of Array lets you repeatedly move one unit from nums[i] to nums[i-1]. What is the smallest possible maximum value? Value can only flow left, so the answer is governed by prefix averages.
Asked At
| Company | Difficulty | |
|---|---|---|
| Visa | Medium | View all Visa questions → |
How to Think About It
Units only move leftward, so the first i + 1 elements can never shed their total — they can only spread it evenly among themselves.
For each prefix, the best you can do is make its maximum ceil(prefixSum / (i + 1)). So the answer is at least the largest such value over all prefixes.
Key insight: that lower bound is also achievable — you can always balance each prefix down to its ceiling average by pushing excess left.
So the answer is max over i of ceil(prefix[i] / (i + 1)).
Walkthrough for [3,7,1,6]: prefixes 3, 10, 11, 17 -> ceilings 3, 5, 4, 5 -> answer 5.
Optimal Approach
Step 1: total = 0, best = 0.
Step 2: For each index i: total += nums[i]; best = max(best, ceil(total / (i + 1))).
Step 3: Return best.
Time: O(n). Space: O(1).
What Trips People Up in Real Interviews
Simulating the moves one unit at a time — values reach 10^9.
Binary searching the answer without noticing the closed-form prefix-average bound (binary search works, but explain the monotone check).
Using floor instead of ceiling division.
Overflow of the prefix sum in C++/Java; use 64-bit.
Solution Code
def minimizeArrayValue(nums):
total = best = 0
for i, x in enumerate(nums):
total += x
best = max(best, (total + i) // (i + 1))
return bestFrequently Asked Questions
What is the Minimize Maximum of Array problem?
Minimize Maximum of Array lets you repeatedly move one unit from `nums[i]` to `nums[i-1]`. What is the smallest possible maximum value? Value can only flow left, so the answer is governed by prefix averages.
How do you solve Minimize Maximum of Array?
The optimal approach is described in detail above, including step-by-step walkthroughs, complexity analysis, and solution code in Python. Scroll up to the "Optimal Approach" section.
What companies ask Minimize Maximum of Array?
Minimize Maximum of Array is asked at Visa. It is a medium difficulty problem.
What are common mistakes on Minimize Maximum of Array?
- Simulating the moves one unit at a time — values reach `10^9`.
- Binary searching the answer without noticing the closed-form prefix-average bound (binary search works, but explain the monotone check).
- Using floor instead of ceiling division.
- Overflow of the prefix sum in C++/Java; use 64-bit.