Is Minimum Total Operations easy or hard?

Minimum Total Operations is generally considered an easy problem because it relies on a straightforward greedy observation and a single linear scan. Once you recognize that each element only depends on the previous one, the implementation becomes simple and efficient.

Minimum Total Operations Python/Java solution

The Python and Java implementations both follow the same logic: iterate through the array once, track the previous valid value, and accumulate operations whenever the current value needs adjustment. Because the algorithm is language-independent, the time complexity remains O(n) with O(1) space.

How to solve Minimum Total Operations in O(n)?

Traverse the array once while maintaining the previous valid value. If the current element satisfies the constraint, continue. If it violates the rule, compute the difference required to fix it, add that difference to the total operations, and update the current value accordingly. This single-pass greedy process ensures O(n) time complexity.

What is the best approach for Minimum Total Operations?

The optimal approach is a greedy single-pass traversal of the array. Iterate from left to right and adjust elements whenever they violate the required ordering constraint with the previous element. This guarantees the minimal number of operations while running in O(n) time and O(1) extra space.

Is Minimum Total Operations asked at Google/Amazon/Meta?

Problems that require minimizing operations on arrays using greedy traversal patterns frequently appear in interviews at companies like Amazon, Google, and Meta. Variations of this pattern test whether candidates can recognize when a single-pass adjustment strategy replaces expensive repeated scans.

What data structure is used in Minimum Total Operations?

The primary data structure is a simple array. The algorithm processes it sequentially using a greedy strategy and a few tracking variables. No additional structures like heaps or hash maps are required, which keeps the space complexity constant.

What is the time complexity of Minimum Total Operations?

The optimal solution runs in O(n) time because the array is processed exactly once. Each element is checked against its predecessor and adjusted if needed. The space complexity is O(1) since only a few variables are used for tracking the previous value and operation count.

Description Hints 1 Solution Video 8:12

3353. Minimum Total Operations

Easy63.8% acceptancePremium elsewhere, free here

Given an array of integers nums, you can perform any number of operations on this array.

In each operation, you can:

Choose a prefix of the array.
Choose an integer k (which can be negative) and add k to each element in the chosen prefix.

A prefix of an array is a subarray that starts from the beginning of the array and extends to any point within it.

Return the minimum number of operations required to make all elements in arr equal.

Example 1:

Input: nums = [1,4,2]

Output: 2

Explanation:

Operation 1: Choose the prefix [1, 4] of length 2 and add -2 to each element of the prefix. The array becomes [-1, 2, 2].
Operation 2: Choose the prefix [-1] of length 1 and add 3 to it. The array becomes [2, 2, 2].
Thus, the minimum number of required operations is 2.

Example 2:

Input: nums = [10,10,10]

Output: 0

Explanation:

All elements are already equal, so no operations are needed.

Constraints:

1 <= nums.length <= 10⁵
-10⁹ <= nums[i] <= 10⁹

Topics

Array

Hints open one at a time

Hint 1

Would you ever change the last element of the array?

8:12

Still stuck?Read the written solution, or watch a walkthrough.

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1class Solution:
  def solve(self):
      pass


Starter codePython 3Spaces: 4

Examples

Case 1Case 2

Input

[1,4,2]

Input

[10,10,10]

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