Is Minimum Operations to Make Array Equal easy or hard?

The problem is rated Medium because the optimal solution requires recognizing a mathematical pattern rather than performing direct simulation. Once the symmetry of the array is understood, the solution reduces to a simple formula.

Minimum Operations to Make Array Equal Python/Java solution

In Python or Java, the optimal solution computes floor(n*n/4). For even n the result is (n/2)*(n/2), and for odd n it is (n//2)*(n//2 + 1). This constant-time calculation avoids building the array or simulating operations.

How to solve Minimum Operations to Make Array Equal in O(n)?

Iterate through the first half of the array where arr[i] = 2*i + 1. For each element, calculate how far it is from the target value n and accumulate the difference n - (2*i + 1). Each unit difference corresponds to one operation transferred from the right side. Summing these values produces the total operations in O(n) time and O(1) space.

What is the best approach for Minimum Operations to Make Array Equal?

The best approach uses a mathematical observation about the symmetric array [1,3,5,...]. Every value must become the mean, which equals n. By summing the deficits of the left half of the array, the total operations simplify to floor(n^2 / 4). This gives an O(1) time and O(1) space solution.

Is Minimum Operations to Make Array Equal asked at Google/Amazon/Meta?

Problems based on mathematical observations and array balancing appear frequently in interviews at companies like Google, Amazon, and Meta. While this exact question may vary, the core idea of identifying symmetry and deriving a formula is a common interview pattern.

What data structure is used in Minimum Operations to Make Array Equal?

The problem primarily relies on mathematical reasoning rather than advanced data structures. The array structure arr[i] = 2*i + 1 is analyzed directly, and the optimal solution uses arithmetic properties and symmetry instead of additional storage.

What is the time complexity of Minimum Operations to Make Array Equal?

The optimal mathematical solution runs in O(1) time because the result can be computed directly using the formula floor(n^2 / 4). A more explanatory approach that sums differences across half the array runs in O(n). A brute force simulation can degrade to O(n^2).

Description Hints 2 Solution Video 6:02

1551. Minimum Operations to Make Array Equal

Medium82.8% acceptance2 companies

You have an array arr of length n where arr[i] = (2 * i) + 1 for all valid values of i (i.e., 0 <= i < n).

In one operation, you can select two indices x and y where 0 <= x, y < n and subtract 1 from arr[x] and add 1 to arr[y] (i.e., perform arr[x] -=1 and arr[y] += 1). The goal is to make all the elements of the array equal. It is guaranteed that all the elements of the array can be made equal using some operations.

Given an integer n, the length of the array, return the minimum number of operations needed to make all the elements of arr equal.

Example 1:

Input: n = 3
Output: 2
Explanation: arr = [1, 3, 5]
First operation choose x = 2 and y = 0, this leads arr to be [2, 3, 4]
In the second operation choose x = 2 and y = 0 again, thus arr = [3, 3, 3].

Example 2:

Input: n = 6
Output: 9

Constraints:

1 <= n <= 10⁴

Asked at 2 companies

Brillio Amazon

Topics

Math

Hints open one at a time

Hint 1

Build the array arr using the given formula, define target = sum(arr) / n

Hint 2

What is the number of operations needed to convert arr so that all elements equal target ?

6:02

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