Count the number of component wise comparisons in quicksort algorithm.

Question

I'm trying to count the number of comparisons my quicksort algorithm makes for an array size of 500. I know that the best case for quicksort with partition is nlogn-n+1. So for an array size of 500, the best case number of component wise comparisons would be about 3983. However, when I run my code, I'm getting 2400 comparisons or so, depending on the array the random function generates. Am I counting the number of component wise comparisons wrong? Please help.

#include <iostream>
    #include <string>
    #include <stdlib.h>
    using namespace std;


    int count_500 = 0;

    int partition(int *S,int l, int u);
    void swap(int &val1, int &val2);
    void Quicksort(int S[],int low, int hi);
    void exchange(int list[], int p, int q);
    int median_of_3(int list[], int p, int r);
    void Quicksort_M3(int S[], int low, int hi);





    int main()
    {
            int S1_500[500];
            int S2_500[500];
            int S3_500[500];

            int S1_200[200];
            int S2_200[200];
            int S3_200[200];

            int S1_8[8];
            int S2_8[8];
            int S3_8[8];

            srand ( time(NULL) );



            for(int i=0; i<500; i++)
            {
                    S1_500[i] = rand()%1000;
                    S2_500[i] = rand()%1000;
                    S3_500[i] = rand()%1000;
            }

            for(int i=0; i<200; i++)
            {
                    S1_200[i] = rand()%500;
                    S2_200[i] = rand()%500;
                    S3_200[i] = rand()%500;
            }

            for(int i=0; i<8; i++)
            {
                    S1_8[i] = rand()%100;
                    S2_8[i] = rand()%100;
                    S3_8[i] = rand()%100;
            }

            Quicksort(S1_500,0,499);
            for(int i=0; i<500; i++)
            {
                    cout << S1_500[i] << endl;
            }

            cout << "Number of component wise comparisons is: " << count_500 << endl;





    }


    int partition(int *S,int l, int u)
    {
            int x = S[l];
            int j = l;
            for(int i=l+1; i<=u; i++)
            {
                    if(S[i] < x)
                    {       
                            count_500++; // Count the component wise comparison
                            j++;
                            swap(S[i],S[j]);
                    }
            }
            int p = j;
            swap(S[l],S[p]);
            return p;
    }

    void swap(int &val1, int &val2)
    {
            int temp = val1;
            val1 = val2;
            val2 = temp;
    }

    void Quicksort(int S[],int low, int hi)
    {
            if (low < hi)
            {
                    int p = partition(S,low,hi);
                    Quicksort(S,low,p-1);
                    Quicksort(S,p+1,hi);
            }
    }

Answer 1

You want the count_500++; outside the if statement. You're only counting the comparisons, where the result is true .

Change

                if(S[i] < x) 
                {        
                        count_500++; // Count the component wise comparison 
                ...
                }

to

                count_500++; // Count the component wise comparison 
                if(S[i] < x) 
                {        
                ...
                }