QuickSort and Hoare Partition

Question

I have a hard time translating QuickSort with Hoare partitioning into C code, and can\'t find out why. The code I\'m using is shown below:

void QuickSort(in         


        

Answer 1

Your final code is wrong, since the initial value of j should be r + 1 instead of r. Otherwise your partition function always ignore the last value.

Actually, HoarePartition works because for any array A[p...r] which contains at least 2 elements(i.e. p < r), every element of A[p...j] is <= every element of A[j+1...r] when it terminates. So the next two segments that the main algorithm recurs on are [start...q] and [q+1...end]

So the right C code is as follows:

void QuickSort(int a[],int start,int end) {
    if (end <= start) return;
    int q=HoarePartition(a,start,end);
    QuickSort(a,start,q);
    QuickSort(a,q + 1,end);
}

int HoarePartition (int a[],int p, int r) {
    int x=a[p],i=p-1,j=r+1;
    while (1) {
        do  j--; while (a[j] > x);
        do  i++; while (a[i] < x);
        if  (i < j) 
            swap(&a[i],&a[j]);
        else 
            return j;
    }
}

More clarifications:

1. partition part is just the translation of the pseudocode. (Note the return value is j)

2. for the recursive part, note that the base case checking (end <= start instead of end <= start + 1 otherwise you will skip the [2 1] subarray )