C/C++ Implementations of Merge Sort

Question

So I was learning Merge Sort, and trying to implement it on using C++. Here is the code given by GeeksforGeeks:

/* C program for Merge Sort */
#include<stdlib.h> 
#include<stdio.h> 

// Merges two subarrays of arr[]. 
// First subarray is arr[l..m] 
// Second subarray is arr[m+1..r] 
void merge(int arr[], int l, int m, int r) 
{ 
    int i, j, k; 
    int n1 = m - l + 1; 
    int n2 =  r - m; 

    /* create temp arrays */
    int L[n1], R[n2]; 

    /* Copy data to temp arrays L[] and R[] */
    for (i = 0; i < n1; i++) 
        L[i] = arr[l + i]; 
    for (j = 0; j < n2; j++) 
        R[j] = arr[m + 1+ j]; 

    /* Merge the temp arrays back into arr[l..r]*/
    i = 0; // Initial index of first subarray 
    j = 0; // Initial index of second subarray 
    k = l; // Initial index of merged subarray 
    while (i < n1 && j < n2) 
    { 
        if (L[i] <= R[j]) 
        { 
            arr[k] = L[i]; 
            i++; 
        } 
        else
        { 
            arr[k] = R[j]; 
            j++; 
        } 
        k++; 
    } 

    /* Copy the remaining elements of L[], if there 
       are any */
    while (i < n1) 
    { 
        arr[k] = L[i]; 
        i++; 
        k++; 
    } 

    /* Copy the remaining elements of R[], if there 
       are any */
    while (j < n2) 
    { 
        arr[k] = R[j]; 
        j++; 
        k++; 
    } 
} 

/* l is for left index and r is right index of the 
   sub-array of arr to be sorted */
void mergeSort(int arr[], int l, int r) 
{ 
    if (l < r) 
    { 
        // Same as (l+r)/2, but avoids overflow for 
        // large l and h 
        int m = l+(r-l)/2; 

        // Sort first and second halves 
        mergeSort(arr, l, m); 
        mergeSort(arr, m+1, r); 

        merge(arr, l, m, r); 
    } 
} 

/* UTILITY FUNCTIONS */
/* Function to print an array */
void printArray(int A[], int size) 
{ 
    int i; 
    for (i=0; i < size; i++) 
        printf("%d ", A[i]); 
    printf("\n"); 
} 

/* Driver program to test above functions */
int main() 
{ 
    int arr[] = {12, 11, 13, 5, 6, 7}; 
    int arr_size = sizeof(arr)/sizeof(arr[0]); 

    printf("Given array is \n"); 
    printArray(arr, arr_size); 

    mergeSort(arr, 0, arr_size - 1); 

    printf("\nSorted array is \n"); 
    printArray(arr, arr_size); 
    return 0; 
}

However, there are some lines of code I can't seem to understand:

1.

// Same as (l+r)/2, but avoids overflow for 
// large l and h 
int m = l+(r-l)/2; 

I don't find any (l + r)/2 = l+(r - 1)/2 though, since they obviously have a difference of 1. Also, using l+(r - 1)/2 won't really work for arrays with even number of elements. Eg an array with 4 elements, m = 0 + (3 - 1)/2 = 1, which is not the correct middle index. I assume it to be 2. Also, I can't figure out what it means to "avoid overflow for large l and h". Suppose h is a typo that is meant to be l and r, I still don't figure out why does (l + r)/2 results in overflow while l+(r - 1)/2 doesn't.

2. k = l; // Initial index of merged subarray

That's weird. Why did the initial index of merged subarray starts with 1 instead of 0?

3.

/* Copy the remaining elements of L[], if there 
are any */
while (i < n1) 
{ 
    arr[k] = L[i]; 
    i++; 
    k++; 
} 

So I kind of figured out how the sorting works, but say

L = {0, 9, 1}, R = {1, 2, 3}
So here is what happens:
arr[1] = L[0] (0 < 1)
arr[2] = R[0] (1 < 9)
arr[3] = R[1] (2 < 9)
arr[4] = R[2] (3 < 9)
So now we have 9 and 1 remaining in L, hence
arr[5] = 9
arr[6] = 1

Well, arr is still not sorted... Could anyone explain the problems above to me? Or you can explain what the code does to achieve Merge Sort, in a nutshell. Any help is greatly appreciated, thanks.

Answer 1

I managed to figure everything out.

1. I'm tired. l and 1 are two different characters.
2. I'm tired. l and 1 are two different characters. I managed to figure out the reason k is not 0 though.
3. Figured this one out when I'm bathing.

Answer 2

Well, the answer for your first question is that, the code to find the mid " int m = l+(rl)/2; " is correct, even if the number of elements are 4 then the indexes will be " 0 1 2 3 " and here we can see the mid is index 1 (not 2). and if you find it from the code " int m = 0+(3-0)/2 = 3/2 = 1;