Code Complexity Classes: Math vs. Reality

Had an enjoyable first day of my computer science classes yesterday.  In my Computer Organization and Assembly Language class, the teacher went over some examples of different C code, then we'd look at the Assembly for the code to see what was really going on.  One example he showed used large arrays.

In the example, the scenario he gave was that students are given a large array, and they need to write code to copy the array to another array.  In this scenario, two students have very similar implementations, but with one key difference.

Note: I redid the code in Java so I could add a few tweaks, C and other languages to come later.

Code for the first student:

static void copyij(){
  for( int i = 0; i < size; i++){
   for( int j = 0; j < size; j++){
    B[i][j] = A[i][j];
   }
  }
 }

Code for the second student:

static void copyji(){
  for( int j = 0; j < size; j++){
   for( int i = 0; i < size; i++){
    B[i][j] = A[i][j];
   }
  }
 }

Just in case you missed it, or didn't feel like looking at the code, the difference is in the order they copied the elements of the array. Both students' code will compile and run without error. The first student copied all elements row by row, as opposed to the second student who went column by column.

Looking just at the complexity class of each piece of code, we see that both have a complexity of O(n²). Since this is often how we measure the efficiency of code, most people wouldn't look into it any further. The real world doesn't always work out so perfectly though. Running both segments of code and logging the time of each copy shows that the second student's code runs significantly slower than the first.

How much slower? Over 10 runs, the first student's code averaged 16ms, whereas the second student's code averaged 71ms. On my netbook, the difference was even more profound, with the first code being, on average, ~10 times faster than the second.

These times are in milliseconds though, and are so small as to be negligible. Without running benchmarks like this, you wouldn't even notice this in your program. What happens when your array has 10 times the amount of data as the one used here? Well, wait until tomorrow where we cover the same topic using C code and you can find out.

Edit: forgot to add the complete code so you can run it for yourself.  The complete code can be found here.  Happy coding!