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. E.g. 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.
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.
