Getting different output on each execution - c++

Question

I tried to implement number of inversions in an array, using merge sort.
Every time I execute this code, I get different value of the number of inversions. I am not able to figure out the reason for this. Please have a look at the code and tell me the mistake.
#include<stdio.h>
#include<iostream>
using namespace std;
int count =0;
void merge(int A[],int start,int mid,int end)
{
int size1 = mid-start+1;
int size2 = end-(mid+1)+1;
int P[size1];
int Q[size2];
for(int i=0;i<size1;i++)
P[i]=A[start+i];
for(int j=0;j<size2;j++)
Q[j]=A[mid+j+1];
int k = 0;
int l = 0;
int i =0;
while(k<mid && l<end)
{
if(P[k]>Q[l])
{
A[i] = Q[l];
l++; i++;
count++;
}
else
{
A[i] = P[k];
k++; i++;
}
}
}
void inversions(int A[],int start,int end)
{
if(start!=end)
{
int mid = (start+end)/2;
inversions(A,start,mid);
inversions(A,mid+1,end);
merge(A,start,mid,end);
}
}
int main()
{
int arr[] = {4,3,1,2,7,5,8};
int n = (sizeof(arr) / sizeof(int));
inversions(arr,0,n-1);
cout<<"The number of inversions is:: "<<count<<endl;
return 0;
}

Answer 1

int k = 0;
int l = 0;
int i =0;
while(k<mid && l<end)
{
if(P[k]>Q[l])
{
A[i] = Q[l];
l++; i++;
count++;
}
else
{
A[i] = P[k];
k++; i++;
}
}
Few mistakes here, i starts from start and not 0. k must loop from 0 till size1 and not till mid. Similarly, l must loop from 0 till size2 and not till end. You are incrementing count by 1 when P[k] > Q[l] but this is incorrect. Notice that all the elements in array P following the element P[k] are greater than Q[l]. Hence they also will form an inverted pair. So you should increment count by size1-k.
Also, the merge procedure should not only count the inversions but also merge the two sorted sequences P and Q into A. The first while loop while(k<size1 && l<size2) will break when either k equals size1 or when l equals size2. Therefore you must make sure to copy the rest of the other sequence as it is back into A.
I have made the appropriate changes in merge and pasted it below.
void merge(int A[],int start,int mid,int end)
{
int size1 = mid-start+1;
int size2 = end-(mid+1)+1;
int P[size1];
int Q[size2];
for(int i=0;i<size1;i++)
P[i]=A[start+i];
for(int j=0;j<size2;j++)
Q[j]=A[mid+j+1];
int k = 0;
int l = 0;
int i = start;
while(k<size1 && l<size2)
{
if(P[k]>Q[l])
{
A[i] = Q[l];
l++; i++;
count += size1-k;
}
else
{
A[i] = P[k];
k++; i++;
}
}
while (k < size1)
{
A[i] = P[k];
++i, ++k;
}
while (l < size2)
{
A[i] = Q[l];
++i, ++l;
}
}

Answer 2

int P[size1];
int Q[size2];
VLA (Variable length arrays) are not supported by C++. size1 and size2 are unknown during compile time. So, each time they get a different value and hence the difference in output.
Use std::vector instead
std::vector<int> P(size1, 0); //initialize with size1 size
std::vector<int> Q(size2, 0); //initialize with size2 size