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When to use merge sort and when to use quick sort?

Quick Sort Vs Merge Sort

Wikipedia

http://en.wikipedia.org/wiki/Merge_sort

http://en.wikipedia.org/wiki/Quicksort

quick_sort is suppose to have worst case O(n^2) but merge_sort is suppose to not have a worst case and always be O (n*log N). I thought that it was dependent upon the ordering of the data set – reverse order, forward order, or random, but when I a run test…quick_sort is always faster. The code I used is below:

/*
Needs a reszie function added
*/
#include "c_arclib.cpp"
template <class T> class dynamic_array
  {
  private:
    T* array;
    T* scratch;
  public:
    int size;
    dynamic_array(int sizein)
      {
      size=sizein;
      array = new T[size]();
      }
    void print_array()
      {
      for (int i = 0; i < size; i++) cout << array[i] << endl;
      }
    void merge_recurse(int left, int right)
      {
      if(right == left + 1)
        {
        return;
        }
      else
        {
        int i = 0;
        int length = right - left;
        int midpoint_distance = length/2;
        int l = left, r = left + midpoint_distance;
        merge_recurse(left, left + midpoint_distance);
        merge_recurse(left + midpoint_distance, right);
        for(i = 0; i < length; i++)
          {
          if((l < (left + midpoint_distance)) && (r == right || array[l] > array[r]))
            {
            scratch[i] = array[l];
            l++;
            }
          else
            {
            scratch[i] = array[r];
            r++;
            }
          }
        for(i = left; i < right; i++)
          {
          array[i] = scratch[i - left];
          }
        }
      }
    int merge_sort()
      {
      scratch = new T[size]();
      if(scratch != NULL)
        {
        merge_recurse(0, size);
        return 1;
        }
      else
        {
        return 0;
        }
      }
    void quick_recurse(int left, int right) 
      {  
      int l = left, r = right, tmp;
      int pivot = array[(left + right) / 2];
      while (l <= r)
        {
        while (array[l] < pivot)l++;
        while (array[r] > pivot)r--;
        if (l <= r) 
          {
          tmp = array[l];
          array[l] = array[r];
          array[r] = tmp;
          l++;
          r--;
          }
        }
      if (left < r)quick_recurse(left, r);
      if (l < right)quick_recurse(l, right);
      }  
    void quick_sort()
      {
      quick_recurse(0,size);
      }
    void rand_to_array()
      {
      srand(time(NULL));
      int* k;
      for (k = array; k != array + size; ++k)                                             
        { 
        *k=rand();                                      
        } 
      }
    void order_to_array()
      {
      int* k;
      int i = 0;
      for (k = array; k != array + size; ++k)                                             
        { 
        *k=i;
        ++i;        
        } 
      }
    void rorder_to_array()
      {
      int* k;
      int i = size;
      for (k = array; k != array + size; ++k)                                             
        { 
        *k=i;
        --i;        
        } 
      }
  };
int main()
  {
  dynamic_array<int> d1(1000000);
  d1.order_to_array();
  clock_t time_start=clock();
  d1.merge_sort(); 
  clock_t time_end=clock();
  double result = (double)(time_end - time_start) / CLOCKS_PER_SEC; 
  cout << result;
  }

Answer 1

Worst case for quick sort is when the pivot element is the largest or smallest element in the array on every recursion. In that case you will have to do n-1 recursions (one of the arrays you split always only has one element) which gives you an O(n²) overall.

You can reproduce the worst case for quick sort if you use an already sorted array and pick the first or last element as pivot element.