count swap/comparisons numbers of merge sort algorithm

Question

I need to count how many swaps and comparisons happened during merge sorting, I think my comparison number counting is fine, just due recursion I get as much numbers as my array length, somehow i need to store those numbers to variable in merge sort function?Also would love to know ideas on how to count total swaps

    void merge(double arr[], int l, int m, int r)
    {
        int counter = 0;//number of comparisons
        int i, j, k;
        int n1 = m - l + 1;
        int n2 =  r - m;
        int cc;
        /* create temp arrays */
        double L[n1], R[n2];
        /* Copy data to temp arrays L[] and R[] */
        for (i = 0; i < n1; i++)
            L[i] = arr[l + i];
        for (j = 0; j < n2; j++)
            R[j] = arr[m + 1+ j];
        /* Merge the temp arrays back into arr[l..r]*/
        i = 0; // Initial index of first subarray
        j = 0; // Initial index of second subarray
        k = l; // Initial index of merged subarray
        while (i < n1 && j < n2)
            {

                if (L[i] <= R[j])
                {
                    arr[k] = L[i];
                    i++;
                }
                else
                {
                    arr[k] = R[j];
                    j++;
                }
                k++;
                counter++;
        }
        cout << counter << endl;
    /* Copy the remaining elements of L[], if there
       are any */
        while (i < n1)
        {
            arr[k] = L[i];
            i++;
            k++;
        }
    /* Copy the remaining elements of R[], if there
       are any */
        while (j < n2)
        {
            arr[k] = R[j];
            j++;
            k++;
              }
    }
    void mergeSort(double arr[], int l, int r)
         {
          if (l < r)
         {
            // Same as (l+r)/2, but avoids overflow for
        // large l and h
        int m = l+(r-l)/2;
        // Sort first and second halves
        mergeSort(arr, l, m);
        mergeSort(arr, m+1, r);
        merge(arr, l, m, r);
        }
    }

Answer 1

This is similar to the answer given by @JerryCoffin, but maybe a little bit simpler for you to digest.

A simple solution is to place this code in a class and have a member variable, maybe called int swapcount, that will increment for each swap done. This alleviates having to maintain a local swap counter variable.

class MergeSorter
{
   int swapCount;
   void merge(double arr[], int l, int m, int r);
   void mergeSort(double arr[], int l, int r);

   public:
       MergeSorter() : swapCount(0) { }
       void startSort(double arr[], int l, int r);
       int getSwapCount() const { return swapCount; }
};

void MergeSorter::merge(double arr[], int l, int m, int r)
{
   // code here to merge.  In here, you increment swapCount
}

void MergeSorter::mergeSort(double arr[], int l, int r)
{
    if (l < r)
    {
        int m = l+(r-l)/2;
        mergeSort(arr, l, m);
        mergeSort(arr, m+1, r);
        merge(arr, l, m, r);
    }    
}

void MergeSorter::startSort(double arr[], int l, int r)
{
  swapCount = 0;  // start at 0
  mergeSort(arr, l, r);
}

int main()
{
   double arr[] = {1, 2, 3, 45, 5, 7};
   MergeSorter ms;
   ms.startSort(arr, 0, 5); // or whatever the arguments are
   std::cout << "The number of swaps is " << ms.getSwapCount();
}

Note that we have a function startSort that starts the sort within the class. In the merge function, the swapCount is incremented as needed. At the end, we just output the value of ms.swapCount.

Answer 2

If I understand correctly a swap happens when the original array is altered in merging steps. So in each call of merge I look at the value in original index and compared it with the newly formed value corresponding to that index. If they are different I incremented swap.

int swap=0;

int index(std::vector<double> v,double val){

auto match = std::find(v.begin(), v.end(), val);
return match-v.begin();

}

std::vector<double> merge(std::vector<double> v1,std::vector<double> v2,std::vector<double>& v,int start){

auto it1=std::begin(v1);
auto it2=std::begin(v2);

std::vector<double> newvec;

while(it1!=v1.end() && it2!=v2.end()){

    if(*it1<=*it2){

        newvec.push_back(*it1);

        const FloatingPoint<double> l1(*it1), r1(v.at(index(newvec,*it1)+start));

        if (!l1.AlmostEquals(r1)) swap++;

        it1++;

    }

    else{

        newvec.push_back(*it2);

        const FloatingPoint<double> l2(*it2), r2(v.at(index(newvec,*it2)+start));

        if (!l1.AlmostEquals(r1)) swap++;

        it2++;

    }

}

while(it1!=v1.end()){

    newvec.push_back(*(it1++));

    const FloatingPoint<double> l3(*it1), r3(v.at(index(newvec,*it1)+start));

    if (!l3.AlmostEquals(r3)) swap++;

}

while(it2!=v2.end()){

   newvec.push_back(*(it2++));

    const FloatingPoint<double> l4(*it2), r4(v.at(index(newvec,*it2)+start));

    if (!l4.AlmostEquals(r4)) swap++;


}

return newvec;

} 


 std::vector<double> merge_sort(std::vector<double> v,int start){ // start=0 when it is first called

int size=v.size();

if(size==1) return v;

std::vector<double> merged1,merged2;

auto it=v.begin();

merged1.assign(it,it+(size+1)/2);
merged2.assign(it+(size+1)/2,v.end());

std::vector<double> v1=merge_sort(merged1,start);
std::vector<double> v2=merge_sort(merged2,start+(size+1)/2);

v=merge(v1,v2,v,start);

return v; 

}

Answer 3

I would do the job rather differently.

Instead of trying to instrument the sort itself to track the number or comparisons and swaps, I'd create a type that keeps track of the number of times it's compared and/or swapped. I was too lazy to write a whole merge sort to demonstrate it, but here's one doing a bubble sort:

#include <algorithm>
#include <iostream>
#include <vector>

namespace instrumented {

    template <class T>
    class wrapper {
        T value;
    public:
        static std::size_t comparisons;
        static std::size_t swaps;
        wrapper(T val) : value(val) {}
        bool operator<(wrapper const &other) { ++comparisons; return value < other.value; }
        operator T() const { return value; }

        static void reset() { comparisons = swaps = 0; }

        static std::ostream &report(std::ostream &os) {
            os << "comparisons: " << comparisons << "\n";
            os << "swaps: " << swaps << "\n";
            comparisons = 0;
            swaps = 0;
            return os;
        }
    };

    template <class T>
    std::size_t wrapper<T>::comparisons;

    template <class T>
    std::size_t wrapper<T>::swaps;

    template <class T>
    void swap(wrapper<T> &a, wrapper<T> &b) {
        ++wrapper<T>::swaps;
        auto temp{ a };
        a = b;
        b = temp;
    }
}

template <class T>
void sort(std::vector<T> &input) {
    std::vector<instrumented::wrapper<T>> values;

    for (auto const & i : input)
        values.push_back(i);

    for (auto i = 0; i < values.size() - 1; i++)
        for (auto j = i + 1; j < values.size(); j++)
            if (values[j] < values[i])
                swap(values[i], values[j]);

    values[0].report(std::cout);
}

int main() {
    std::vector<int> inputs1{ 5, 4, 3, 2, 1 };
    sort(inputs1);
    std::cout << "\n";

    std::vector<int> inputs2{ 10, 9, 7, 8, 5, 100, 2, 3, 1, 17, 6 };
    sort(inputs2);
}

Note that with this, you should be able to (for example) get results for std::sort, std::partial_sort, and so on, not just your own sort functions.