**π‘ Problem Formulation:** The challenge is to transform an array of integers so that all its elements become equal with the minimum number of operations. An operation is defined as incrementing or decrementing any element by one. Given an input like [1, 2, 3], the desired output is to make all elements equal, for instance, transforming the array to [2, 2, 2].

## Method 1: Brute Force Approach

This method involves incrementing or decrementing elements one at a time until all elements are equal. The function specifically calculates the number of operations needed to make all array elements the same.

Here’s an example:

def make_elements_equal_bruteforce(arr): target = sum(arr) // len(arr) operations = 0 for num in arr: operations += abs(target - num) return operations print(make_elements_equal_bruteforce([1, 2, 3]))

Output: `2`

This code snippet calculates the mean of the elements as the target value and adds up the differences between each element and the target, representing the number of operations required to make the elements equal.

## Method 2: Sorting and Selecting Median

By sorting the array and choosing the median as the target, we can minimize the number of operations needed to make all elements equal.

Here’s an example:

def make_elements_equal_median(arr): arr.sort() target = arr[len(arr) // 2] operations = 0 for num in arr: operations += abs(target - num) return operations print(make_elements_equal_median([1, 2, 3]))

Output: `2`

This code snippet sorts the array, selects the median as the target, and then sums up the differences between each element and the median.

## Method 3: Using Python’s Statistics Module

The statistics module provides methods to calculate the mean or median, which can be used as the target to minimize operations.

Here’s an example:

import statistics def make_elements_equal_stats(arr): target = round(statistics.median(arr)) operations = sum(abs(target - num) for num in arr) return operations print(make_elements_equal_stats([1, 2, 3]))

Output: `2`

By utilizing Python’s `statistics.median()`

function to find the median value, which minimizes the required changes, operations count is efficiently computed.

## Method 4: Counter for Small Ranges

If array elements are within a small range, a Counter can track the frequency of each number to find the most efficient target.

Here’s an example:

from collections import Counter def make_elements_equal_counter(arr): counter = Counter(arr) target, _ = counter.most_common(1)[0] operations = sum(abs(target - num) for num in arr) return operations print(make_elements_equal_counter([1, 2, 3]))

Output: `2`

This snippet uses `collections.Counter`

to determine the most common value in the array, then computes the total operations using this target number.

## Bonus One-Liner Method 5: Using NumPy Library

NumPy provides high-performance array processing and convenient functions to find median or mean, especially for large datasets.

Here’s an example:

import numpy as np def make_elements_equal_numpy(arr): target = round(np.median(arr)) return int(np.sum(np.abs(arr - target))) print(make_elements_equal_numpy(np.array([1, 2, 3])))

Output: `2`

The NumPy library with the `np.median()`

function is used to find the target value, and then the operations count is efficiently calculated across the array.

## Summary/Discussion

**Method 1:**Brute Force Approach. Simple and straightforward. Can be inefficient for large arrays due to its O(n) complexity.**Method 2:**Sorting and Selecting Median. More efficient for larger arrays but involves sorting, making it O(n log n) complex.**Method 3:**Using Python’s Statistics Module. Concise and utilizes built-in functions. The median function may be slower for large lists compared to direct sorting and median calculation.**Method 4:**Counter for Small Ranges. Most efficient for small ranges with high repetition of elements, but it does not scale well for large ranges or datasets.**Method 5:**Using NumPy Library. Highly optimized for large datasets. Requires the additional overhead of maintaining and learning an external library.