# counting number of comparisons in merge sort

• May 26th, 2012, 11:47 AM
mia_tech
counting number of comparisons in merge sort
guys, I have the following merge sort algorithm, and I'm trying to count the number of comparison that is has to do in order to sort the whole array. I know the formula, I just don't know where to put the counter since it is a recursive algorithm... could someone shed some light on this. Thanks

Code :

```//sorting array using merge sort static void mergeSort(int[] a) { if(a.length > 2) { int mid = a.length / 2; int[] first = new int[mid]; int[] second = new int[a.length - mid];   for(int i = 0; i < first.length; i++) { first[i] = a[i]; } for(int i = 0; i < second.length; i++) { second[i] = a[mid+i]; } mergeSort(first); mergeSort(second); merge(first, second, a); } }   //merging first and second halfs of mergeSort array static void merge(int[] first, int[] second, int[] a) { int iFirst = 0; int iSecond = 0; int i = 0; //moving the smaller element into a while(iFirst < first.length && iSecond < second.length) { if(first[iFirst] < second[iSecond]) { a[i] = first[iFirst]; iFirst++; } else { a[i] = second[iSecond]; iSecond++; } i++; mergeCounter += i; } //copying the remaning of the first array while(iFirst < first.length) { a[i] = first[iFirst]; iFirst++; i++; } //copying the remaining of second array while(iSecond < second.length) { a[i] = second[iSecond]; iSecond++; i++; } }```
• May 26th, 2012, 12:34 PM
andreas90
Re: counting number of comparisons in merge sort
Hello mia_tech!
If I'm getting it right you are trying to count how many times executes the first while loop of merge. If you want to count it every time that merge is called you can have a local variable inside the method that does this. For example
Code :

```static void merge(int[] first, int[] second, int[] a){ int mergeCounter = 0;   while(...){ i++; } mergeCounter += i; //you have to increment the variable AFTER the loop has exit }```
If you want to count it in a whole mergesort proccess then you should declare mergeCounter as a global variable. For example
Code :

```  class MergeSort{   static int mergeCounter = 0;   static void mergeSort(int[] a){   }   static void merge(int[] first, int[] second, int[] a){ while(...){ i++; } mergeCounter += i; //you have to increment the variable AFTER the loop has exit } }```
Hope this helps.
• May 26th, 2012, 01:47 PM
mia_tech
Re: counting number of comparisons in merge sort
yeah, that's exactly what I did... well, kind of, my mergeSorter is inside the while loop, in other words everytime loops is comparing, but yours is outsid the while loop, which gives a different number. Lets take for example an array of 10 numbers with merge sort according to your example it takes 12 comparisons, but if you do it like my code which is inside the while loop it takes 26 comparisons
• May 26th, 2012, 04:02 PM
andreas90
Re: counting number of comparisons in merge sort
Cannot test the code right now but I think the problem with your code is that you add i to the counter in every iteration. See the following example:
1st iteration: i = 1 , counter = 1;
2nd iteration: i = 2 , counter = 3 (1+2)
3rd iteration: i = 3 , counter = 6 (3+3).
So, in three iterations (which is what you want to count) the counter is six when actually the comparisons are 3.
The actual number of the comparisons is i. Therefore you should add i after the loop (when it has its last value).
Hope I was clear.
• May 26th, 2012, 04:34 PM
mia_tech
Re: counting number of comparisons in merge sort
Quote:

Originally Posted by andreas90
Cannot test the code right now but I think the problem with your code is that you add i to the counter in every iteration. See the following example:
1st iteration: i = 1 , counter = 1;
2nd iteration: i = 2 , counter = 3 (1+2)
3rd iteration: i = 3 , counter = 6 (3+3).
So, in three iterations (which is what you want to count) the counter is six when actually the comparisons are 3.
The actual number of the comparisons is i. Therefore you should add i after the loop (when it has its last value).
Hope I was clear.

if you take a look at mergeSort method it has two recursive calls in it, so every time merge is called it reset i = 0, so you need some sort of class variable to keep track of total i's
• May 26th, 2012, 04:43 PM
andreas90
Re: counting number of comparisons in merge sort
Quote:

Originally Posted by mia_tech
if you take a look at mergeSort method it has two recursive calls in it, so every time merge is called it reset i = 0, so you need some sort of class variable to keep track of total i's

Exactly, this is what I suggested you with the second code of post#2. Did you try it?
In post#4 I only explained why you need to put the mergeCounter += i; statement after the while loop and not inside it.
• May 26th, 2012, 04:49 PM
mia_tech
Re: counting number of comparisons in merge sort
I think you might be right ;0)
• May 26th, 2012, 07:14 PM
mia_tech
Re: counting number of comparisons in merge sort
so, how many comparison does it take using merge sort to sort an array of 10 numbers?... I got 26, what do you get?
by doing like you told me gives me only 12 comparison, and I know is more than that, something is wrong....
• May 26th, 2012, 08:05 PM
mia_tech
Re: counting number of comparisons in merge sort
ok, I forgot that 25 is worst case scenario in which you need to compare all numbers, but here are the numbers I'm comparing. could you tell me what's the number of comparison you get

45 62 98 89 47 59 72 82 45 18

Thanks
• May 27th, 2012, 12:54 AM
mia_tech
Re: counting number of comparisons in merge sort
Quote:

Originally Posted by mia_tech
ok, I forgot that 25 is worst case scenario in which you need to compare all numbers, but here are the numbers I'm comparing. could you tell me what's the number of comparison you get

45 62 98 89 47 59 72 82 45 18

Thanks

the answer is 23 for this array