Make K-Subarray Sums Equal solution and explanation

def make_k_subarray_sums_equal(arr, k):
    from statistics import median
    n = len(arr)
    changes = 0
    for start in range(k):
        values = [arr[i] for i in range(start, n, k)]
        med = median(values)
        changes += sum(abs(val - med) for val in values)
    return int(changes)

# Example usage
print(make_k_subarray_sums_equal([1, 4, 1, 3], 2))  # Output: 1
print(make_k_subarray_sums_equal([2, 5, 5, 7], 3))  # Output: 5

import java.util.*;
public class KSubarraySumsEqual {
    public static int makeKSubarraySumsEqual(int[] arr, int k) {
        int n = arr.length;
        int changes = 0;
        for (int start = 0; start < k; start++) {
            List<Integer> values = new ArrayList<>();
            for (int i = start; i < n; i += k) {
                values.add(arr[i]);
            }
            Collections.sort(values);
            int med = values.get(values.size() / 2);
            for (int val : values) {
                changes += Math.abs(val - med);
            }
        }
        return changes;
    }

    public static void main(String[] args) {
        System.out.println(makeKSubarraySumsEqual(new int[]{1, 4, 1, 3}, 2)); // Output: 1
        System.out.println(makeKSubarraySumsEqual(new int[]{2, 5, 5, 7}, 3)); // Output: 5
    }
}

#include <iostream>
#include <vector>
#include <algorithm>
#include <cmath>

using namespace std;

int makeKSubarraySumsEqual(vector<int>& arr, int k) {
    int n = arr.size();
    int changes = 0;
    for (int start = 0; start < k; ++start) {
        vector<int> values;
        for (int i = start; i < n; i += k) {
            values.push_back(arr[i]);
        }
        sort(values.begin(), values.end());
        int med = values[values.size() / 2];
        for (int val : values) {
            changes += abs(val - med);
        }
    }
    return changes;
}

int main() {
    vector<int> arr1 = {1, 4, 1, 3};
    cout << makeKSubarraySumsEqual(arr1, 2) << endl; // Output: 1

    vector<int> arr2 = {2, 5, 5, 7};
    cout << makeKSubarraySumsEqual(arr2, 3) << endl; // Output: 5
    
    return 0;
}

function makeSubKSumEqual(arr: number[], k: number): number {
    const n = arr.length;
    const g = gcd(n, k);
    let ans = 0;
    for (let i = 0; i < g; ++i) {
        const t: number[] = [];
        for (let j = i; j < n; j += g) {
            t.push(arr[j]);
        }
        t.sort((a, b) => a - b);
        const mid = t[t.length >> 1];
        for (const x of t) {
            ans += Math.abs(x - mid);
        }
    }
    return ans;
}

function gcd(a: number, b: number): number {
    if (b === 0) {
        return a;
    }
    return gcd(b, a % b);
}

func makeSubKSumEqual(arr []int, k int) (ans int64) {
	n := len(arr)
	g := gcd(n, k)
	for i := 0; i < g; i++ {
		t := []int{}
		for j := i; j < n; j += g {
			t = append(t, arr[j])
		}
		sort.Ints(t)
		mid := t[len(t)/2]
		for _, x := range t {
			ans += int64(abs(x - mid))
		}
	}
	return
}

func abs(x int) int {
	if x < 0 {
		return -x
	}
	return x
}

func gcd(a, b int) int {
	if b == 0 {
		return a
	}
	return gcd(b, a%b)
}