In place merging is still O(n) ?

#include <iostream>
#include <vector>

void merge(std::vector<int>& arr, int l, int m, int r) {
    int n1 = m - l + 1;
    int n2 = r - m;

    std::vector<int> L(n1);
    std::vector<int> R(n2);

    for (int i = 0; i < n1; i++)
        L[i] = arr[l + i];
    for (int j = 0; j < n2; j++)
        R[j] = arr[m + 1 + j];

    int i = 0, j = 0, k = l;

    while (i < n1 && j < n2) {
        if (L[i] <= R[j]) {
            arr[k] = L[i];
            i++;
        } else {
            arr[k] = R[j];
            j++;
        }
        k++;
    }

    while (i < n1) {
        arr[k] = L[i];
        i++;
        k++;
    }

    while (j < n2) {
        arr[k] = R[j];
        j++;
        k++;
    }
}

void mergeSort(std::vector<int>& arr, int l, int r) {
    if (l < r) {
        int m = l + (r - l) / 2;
        mergeSort(arr, l, m);
        mergeSort(arr, m + 1, r);
        merge(arr, l, m, r);
    }
}

int main() {
    std::vector<int> arr = {12, 11, 13, 5, 6, 7};
    int arr_size = arr.size();

    mergeSort(arr, 0, arr_size - 1);

    for (int i = 0; i < arr_size; i++)
        std::cout << arr[i] << " ";
    std::cout << std::endl;

    return 0;
}






// In place merging 

#include <iostream>
#include <vector>

void inPlaceMerge(std::vector<int>& arr, int l, int m, int r) {
    int i = l;      // Current index in the first subarray
    int j = m + 1;  // Current index in the second subarray

    while (i <= m && j <= r) {
        if (arr[i] <= arr[j]) {
            i++;
        } else {
            int value = arr[j];
            int index = j;

            while (index > i) {
                arr[index] = arr[index - 1];
                index--;
            }

            arr[i] = value;

            i++;
            m++;
            j++;
        }
    }
}

void mergeSort(std::vector<int>& arr, int l, int r) {
    if (l < r) {
        int m = l + (r - l) / 2;
        mergeSort(arr, l, m);
        mergeSort(arr, m + 1, r);
        inPlaceMerge(arr, l, m, r);
    }
}

int main() {
    std::vector<int> arr = {12, 11, 13, 5, 6, 7};
    int arr_size = arr.size();

    mergeSort(arr, 0, arr_size - 1);

    for (int i = 0; i < arr_size; i++)
        std::cout << arr[i] << " ";
    std::cout << std::endl;

    return 0;
}