Is Minimum Moves to Equal Array Elements easy or hard?

The problem is rated Medium because the naive interpretation leads to inefficient simulation. The challenge is recognizing the mathematical transformation that converts the operation into reducing elements toward the minimum value.

Minimum Moves to Equal Array Elements Python/Java solution

Most implementations compute the array sum and minimum value in one pass. The result is returned using the formula sum(nums) − n × min(nums). The logic is identical across Python, Java, C++, C#, and JavaScript because it relies only on basic arithmetic.

How to solve Minimum Moves to Equal Array Elements in O(n)?

Scan the array once to compute the minimum element and the total sum. Each move effectively reduces one element toward the minimum. The total moves required equals sum(nums) − n × min(nums). This formula directly calculates the result without simulation, giving O(n) time and constant space.

What is the best approach for Minimum Moves to Equal Array Elements?

The best approach is a mathematical observation that converts the operation. Incrementing n−1 elements is equivalent to decrementing one element. This means all numbers effectively move toward the minimum element. The total moves equal sum(nums) − n × min(nums), which runs in O(n) time and O(1) space.

Is Minimum Moves to Equal Array Elements asked at Google/Amazon/Meta?

Array and mathematical reasoning problems like this frequently appear in interviews at companies such as Amazon, Google, and Meta. The question tests whether you recognize the invariant that converts repeated increments into a simpler arithmetic formula.

What data structure is used in Minimum Moves to Equal Array Elements?

The problem primarily uses a basic array. No advanced data structures are required. The optimal solution only iterates through the array while tracking the minimum value and total sum.

What is the time complexity of Minimum Moves to Equal Array Elements?

The optimal solution runs in O(n) time because it requires a single pass through the array to compute the total sum and the minimum value. Space complexity is O(1) since only a few variables are used regardless of input size.

Description Solution Video 3:02

453. Minimum Moves to Equal Array Elements

Medium59.2% acceptance8 companies

Given an integer array nums of size n, return the minimum number of moves required to make all array elements equal.

In one move, you can increment n - 1 elements of the array by 1.

Example 1:

Input: nums = [1,2,3]
Output: 3
Explanation: Only three moves are needed (remember each move increments two elements):
[1,2,3]  =>  [2,3,3]  =>  [3,4,3]  =>  [4,4,4]

Example 2: