Understand Quicksort with DDD

Sorting is one of the most common functions performed by a computer, and Quicksort is one of the most efficient ways to do it. This article demonstrates the usefulness of a graphical debugger for learning how Quicksort works.

DDD (Data Display Debugger) is a free, visual front end that can control many popular debuggers. This article uses DDD to work through a simple C implementation of Quicksort.

First, find a copy of DDD and install it. Binary and source packages are available for RPM-based distributions at rpmfind.net, and Debian packages are available at debian.org. This article was written using DDD version 3.3.1 on Red Hat 7.3. This article also makes the following assumptions: 1) you have a GNU/Linux-enhanced computer and it is plugged in; 2) you know basic C concepts including arrays, loops and recursion; and 3) you have a capable C compiler, such as GNU's GCC. Even if you don't know anything about programming, try stepping through the code anyway. It's good for you.

CAR Hoare described the Quicksort algorithm in a much-cited 1962 paper, and it is still in common use 40 years later. The divide-and-conquer approach of Quicksort is probably where it got the prefix quick; by segregating smaller elements from larger elements it eliminates the need for many comparisons. In contrast, a selection sort compares every element to every other element. This is not to say that Quicksort is always faster or that it's the best way to sort; it's simply cool to know. The implementation in this article is not an optimized or extensible quicksort. It only works on integer arrays.

This code was largely borrowed from The Practice of Programming by Brian W. Kernighan and Rob Pike:

#include <stdio.h>
#include <stdlib.h>
#include <time.h>
/* from: The Practice of Programming (pp: 32-34)
 *   by: Brian W. Kernighan and Rob Pike
 */
/* swap: interchange v[i] and v[j] */
void swap( int v[], int i, int j )
{
  int tmp;
  tmp = v[i];
  v[i] = v[j];
  v[j] = tmp;
}
/* quicksort: sort v[0]..v[n-1] into increasing
 * order
 */
void quicksort( int v[], int n )
{
  int i = 0, last = 0;
  if ( n <= 1 )              /* nothing to do */
    return;
  swap( v, 0, rand() % n );  /* move pivot elem
                                to v[0] */
  for ( i = 1; i < n; i++ )  /* partition */
    if ( v[i] < v[0] )
      swap( v, ++last, i );
  swap( v, 0, last );        /* restore pivot */
  quicksort( v, last );      /* sort smaller
                                values */
  quicksort( v+last+1, n-last-1 );  /* sort larger
                                       values */
}
void print_array( const int array[], int elems )
{
  int i;
  printf("{ ");
  for ( i = 0; i < elems; i++ )
    printf( "%d ", array[i] );
  printf("}\n");
}
#define NUM 9
int main( void )
{
  int arr[NUM] = { 6, 12, 4, 18, 3,
                  27, 16, 15, 19 };
  /* commented out to aid in predictability
   * srand( (unsigned int) time(NULL) ); */
  print_array(arr, NUM);
  quicksort(arr, NUM);
  print_array(arr, NUM);
  return EXIT_SUCCESS;
}

Save the code to a file called easy_qsort.c. Next, compile the code:

$ gcc -Wall -pedantic -ansi -o qsortof -g \
easy_qsort.c

The most important argument to GCC is notably -g, which adds debugging symbols to the code.

Try running the program to make sure everything is kosher:

$ ./qsortof
{ 6 12 4 18 3 27 16 15 19 }
{ 3 4 6 12 15 16 18 19 27 }

The first line of output is the unsorted array, the second line is the array after running through the quicksort function.

So how does it work? Let's turn to our new friend DDD:

$ ddd qsortof

This should bring up DDD. Close any Tips and About:Help windows that pop up, and you should see something like Figure 1.

Figure 1. Freshly Started DDD

It would be a good idea to turn on line numbering now. Click the check box next to Display Source Line Numbers in the Edit-->Preferences-->Source menu. Now we can add a breakpoint and start debugging.

First, select the nothing to do line by clicking on its line number in the margin. Then, click the Set/Delete Breakpoint at () button, and click the Run button in the floating command tool.

At this point you should see a red stop sign at the line with the breakpoint and a green arrow on the same line (the code that is about to execute). Let's use DDD to display some inside information.

To begin, select Data-->Display Local Variables. Next, select Data-->Display Arguments, and then select Status-->Backtrace. Finally, type graph display v[0]@n into the console window, and press Enter. This displays elements 0 through n of the v[] array (see Figure 2).

Figure 2. Break at if (n <= 1)