Improving the Quick sort

Question

If possible, how can I improve the following quick sort(performance wise). Any suggestions?

void main()
    {
      quick(a,0,n-1);
    }

    void quick(i         


        

Answer 1

completely dumb answer, but... compile your code in release mode and turn on optimizations !

Answer 2

The first thing to do is benchmark it. And benchmark it against the standard qsort, and against the c++ std::sort and std::stable_sort.

Your results, should your data-set be big enough, will show that the std::sort is superior to qsort in all cases except those where the std::stable_sort is superior. This is because the std::sort is templated, and therefore the comparision can be inlined.

Your code inlines the comparison because its not generic. If your code is slower than qsort, you have a problem right there.

The faster sort would be to sort parts in parallel, e.g. openmp, and then merge them back together.

Answer 3

Sorting small blocks (<5 elements) with a loopless algorithm may improve performance. I found only one example how to write a loopless sorting algorithm for 5 elements: http://wiki.tcl.tk/4118

The idea can be used to generate loopless sorting algorithms for 2,3,4,5 elements in C.

EDIT: i tried it on one set of data, and i measured 87% running time compared to the code in the question. Using insertion sort on <20 blocks resulted 92% on the same data set. This measurement is not representative but may show that this is a way how can You improve Your quicksort code.

EDIT: this example code write out loopless sorting functions for 2-6 elements:

#include <stdio.h>

#define OUT(i,fmt,...)  printf("%*.s"fmt"\n",i,"",##__VA_ARGS__);

#define IF( a,b, i, block1, block2 ) \
  OUT(i,"if(t[%i]>t[%i]){",a,b) block1 OUT(i,"}else{") block2 OUT(i,"}")

#define AB2(i,a,b)         IF(a,b,i,P2(i+2,b,a),P2(i+2,a,b))
#define  P2(i,a,b)         print_perm(i,2,(int[2]){a,b});

#define AB3(i,a,b,c)       IF(a,b,i,BC3(i+2,b,a,c),BC3(i+2,a,b,c))
#define AC3(i,a,b,c)       IF(a,c,i, P3(i+2,c,a,b), P3(i+2,a,c,b))
#define BC3(i,a,b,c)       IF(b,c,i,AC3(i+2,a,b,c), P3(i+2,a,b,c))
#define  P3(i,a,b,c)       print_perm(i,3,(int[3]){a,b,c});

#define AB4(i,a,b,c,d)     IF(a,b,i,CD4(i+2,b,a,c,d),CD4(i+2,a,b,c,d))
#define AC4(i,a,b,c,d)     IF(a,c,i, P4(i+2,c,a,b,d), P4(i+2,a,c,b,d))
#define BC4(i,a,b,c,d)     IF(b,c,i,AC4(i+2,a,b,c,d), P4(i+2,a,b,c,d))
#define BD4(i,a,b,c,d)     IF(b,d,i,BC4(i+2,c,d,a,b),BC4(i+2,a,b,c,d))
#define CD4(i,a,b,c,d)     IF(c,d,i,BD4(i+2,a,b,d,c),BD4(i+2,a,b,c,d))
#define  P4(i,a,b,c,d)     print_perm(i,4,(int[4]){a,b,c,d});

#define AB5(i,a,b,c,d,e)   IF(a,b,i,CD5(i+2,b,a,c,d,e),CD5(i+2,a,b,c,d,e))
#define AC5(i,a,b,c,d,e)   IF(a,c,i, P5(i+2,c,a,b,d,e), P5(i+2,a,c,b,d,e))
#define AE5(i,a,b,c,d,e)   IF(a,e,i,CB5(i+2,e,a,c,b,d),CB5(i+2,a,e,c,b,d))
#define BE5(i,a,b,c,d,e)   IF(b,e,i,AE5(i+2,a,b,c,d,e),DE5(i+2,a,b,c,d,e))
#define BD5(i,a,b,c,d,e)   IF(b,d,i,BE5(i+2,c,d,a,b,e),BE5(i+2,a,b,c,d,e))
#define CB5(i,a,b,c,d,e)   IF(c,b,i,DC5(i+2,a,b,c,d,e),AC5(i+2,a,b,c,d,e))
#define CD5(i,a,b,c,d,e)   IF(c,d,i,BD5(i+2,a,b,d,c,e),BD5(i+2,a,b,c,d,e))
#define DC5(i,a,b,c,d,e)   IF(d,c,i, P5(i+2,a,b,c,d,e), P5(i+2,a,b,d,c,e))
#define DE5(i,a,b,c,d,e)   IF(d,e,i,CB5(i+2,a,b,c,e,d),CB5(i+2,a,b,c,d,e))
#define  P5(i,a,b,c,d,e)   print_perm(i,5,(int[5]){a,b,c,d,e});

#define AB6(i,a,b,c,d,e,f) IF(a,b,i,CD6(i+2,b,a,c,d,e,f),CD6(i+2,a,b,c,d,e,f))
#define AC6(i,a,b,c,d,e,f) IF(a,c,i, P6(i+2,c,a,b,d,e,f), P6(i+2,a,c,b,d,e,f))
#define AE6(i,a,b,c,d,e,f) IF(a,e,i,CB6(i+2,e,a,c,b,d,f),CB6(i+2,a,e,c,b,d,f))
#define BD6(i,a,b,c,d,e,f) IF(b,d,i,DF6(i+2,c,d,a,b,e,f),DF6(i+2,a,b,c,d,e,f))
#define BE6(i,a,b,c,d,e,f) IF(b,e,i,AE6(i+2,a,b,c,d,e,f),DE6(i+2,a,b,c,d,e,f))
#define CB6(i,a,b,c,d,e,f) IF(c,b,i,DC6(i+2,a,b,c,d,e,f),AC6(i+2,a,b,c,d,e,f))
#define CD6(i,a,b,c,d,e,f) IF(c,d,i,EF6(i+2,a,b,d,c,e,f),EF6(i+2,a,b,c,d,e,f))
#define DB6(i,a,b,c,d,e,f) IF(d,b,i,BE6(i+2,a,b,c,d,e,f),BE6(i+2,c,d,a,b,e,f))
#define DC6(i,a,b,c,d,e,f) IF(d,c,i, P6(i+2,a,b,c,d,e,f), P6(i+2,a,b,d,c,e,f))
#define DE6(i,a,b,c,d,e,f) IF(d,e,i,CB6(i+2,a,b,c,e,d,f),CB6(i+2,a,b,c,d,e,f))
#define DF6(i,a,b,c,d,e,f) IF(d,f,i,DB6(i+2,a,b,e,f,c,d),BE6(i+2,a,b,c,d,e,f))
#define EF6(i,a,b,c,d,e,f) IF(e,f,i,BD6(i+2,a,b,c,d,f,e),BD6(i+2,a,b,c,d,e,f))
#define  P6(i,a,b,c,d,e,f) print_perm(i,6,(int[6]){a,b,c,d,e,f});

#define SORT(ABn,n,...) \
  OUT( 0, ""); \
  OUT( 0, "inline void sort" #n "( int t[" #n "] ){" ) \
  OUT( 2, "int tmp;" ) \
  ABn( 2, __VA_ARGS__ ) \
  OUT( 0, "}" )

void print_perm( int ind, int n, int t[n] ){
  printf("%*.s", ind-1, "");
  for( int i=0; i<n; i++ )
    if( i != t[i] ){
      printf(" tmp=t[%i]; t[%i]=",i,i);
      for( int j=t[i],k; j!=i; k=j,j=t[j],t[k]=k)
        printf("t[%i]; t[%i]=",j,j);
      printf("tmp;");
    }
  printf("\n");
}

int main( void ){
  SORT( AB2, 2, 0,1 )
  SORT( AB3, 3, 0,1,2 )
  SORT( AB4, 4, 0,1,2,3 )
  SORT( AB5, 5, 0,1,2,3,4 )
  SORT( AB6, 6, 0,1,2,3,4,5 )
}

The generated code 3718 lines long:

sort2():    8
sort3():   24
sort4():   96
sort5():  512
sort6(): 3072

Answer 4

1. Choose a better pivot: eg. in median-of-three you pick 3 (random) elements and choose the pivot as the median element
2. When length(a[]) < M (in practice choose M = 9) stop sorting. After qsort() finished apply insert sort which would take roughly M * N = O(N). This avoids many function calls close to leaf of the divide-et-impera recursion tree.

Answer 5

Currently the most advanced quicksort widely used is implemented in Java's DualPivotQuicksort.java So you can simply follow that approach and you will see a nice performance improvement:

• Use Insertion sort for small arrays (47 is the number used in Java)
• Use that dual-pivot quicksort choosing the 2nd and 4th elements of 5 as the two pivots
• Consider using mergesort for arrays with runs of sorted numbers

Or if you want to add a bit more complexity then code a 3-pivot quicksort.

Answer 6

If this is not just for learning use qsort from stdlib.h