Most efficient way to implement trickledown operation in a Ternary Heap

Question

Sorry if the terminology in the title was off. I'm trying to better understand the terms by using them more often.

Anyway, I'm currently working on a lab in a data structures class (using C++) where I have to build a Ternary Heap and compare it to a Binary Heap already given to us. Since I have some extra time I wanted to iron out some of the details in my code so that it is running as efficiently as possible.

My greatest concern is the amount of if-else statements that I'm using. I actually had to take ten minutes and organize the layout of them on paper just so I didn't get confused. (I'm not complaining, I just don't know if this is the best way to approach the problem or not.)

template<class T>
void TernaryHeap<T>::trickleDown(int i) {
do {
    int j = -1;

    int r = right(i);
    if (r < n && compare(a[r], a[i]) < 0) {

        int l = left(i);
        if (compare(a[l], a[r]) < 0) {
            j = l;
        } else {
            j = r;
        }

        int m = mid(i);
        if (compare(a[m], a[r]) < 0) {
            j = m;
        } else { 
            j = r; 
        } 

    } else {

        int l = left(i);
        if (l < n && compare(a[l], a[i]) < 0) {

            int m = mid(i);
            if (compare(a[m], a[l]) < 0) {
                j = m;
            } else {
                j = l;
            }
        }
    }
    if (j >= 0) a.swap(i, j);
    i = j;
} while (i >= 0);
}

Answer 1

How would you go about finding the smallest element in a 2-element array? You'll probably find that a single if-else is enough.

Now make the same thing for a 3-element array. Do you just add more conditionals? Or do you just write a generic algorithm that handles arrays of any size?

Your "sift-down" algorithm is done in two steps: find the smallest element, then swap it with the current element. You generalized the binary heap into a ternary heap by simply adding more tests, when you probably should have gone with the more general solution. What if you go to a 4-ary heap? Will you add even more if-else tests?