在openmp中对数组进行排序-关键部分

Question

Quite similar to that question Sorting an array in openmp which has several hundred views but no correct answer. Therefore I give it another try asking here again. I am aware of the overhead and uselessness of this regarding speedup or performance. It simply is a small example to get into openMP. The fact that is is insertSort is given by my courseinstructor.

Here is my code:

std::vector<int> insertionSort(std::vector<int> a) {
    int i, j, k;
    #pragma omp parallel for private(i,j,k)
    for(i = 0; i < a.size(); i++) {
    #pragma omp critical
        k = a[i];
        for (j = i; j > 0 && a[j-1] > k; j--)

        #pragma omp critical
        {
            a[j] = a[j-1];
            a[j] = k;
        }
    }
 return a;
 }

I understand that the critical aspect is the race-condition between threads accessing (reading and writing) elements of a - that is, why I put a critical section arround all of them. That does not seem to be sufficient. What am I missing here. Without the pragmas, the sorting is correct.