Heapify 方法对于最大堆无法正常工作

Question

I am preparing for a data structures and algorithms final exam. I am trying to work through all of the data structures we have learnt this semester and program them by my self to help prepare me for the final. I am working on the max heap right now which includes a inserting (with a heapify) and a retrieve max. I am stuck on the heapifying/swapping of the parent and the child. It seems that the heapify is not working as I get back an array in the order of the way the numbers were inserted. Here is what I have so far.

private int getLeftChildIndex(int index)
    {
        return (2*index + 1);
    }
    private int getLeftChildValue(int index)
    {
        return heap[2*index + 1];
    }


    private int getRightChildIndex(int index)
    {
        return (2*index + 2);
    }
    private int getRightChildValue(int index)
    {
        return heap[2*index + 2];
    }

    private int getParentIndex(int index)
    {
        return ((int) Math.ceil((index - 2)/2));
    }

    private void swap(int child, int parent)
    {
        int temp = heap[parent];
        heap[parent] = heap[child];
        heap[child] = temp;
    }

    private void insert(int num)
    {
        heap[heapSize] = num;
        heapSize++;
        int index = heapSize - 1;
        while (getParentIndex(index) > 0 && heap[index] > heap[getParentIndex(index)])
        {
            swap(index, getParentIndex(index));
            index = getParentIndex(index);
        }
    }

 public static void main(String[] args)
    {
        HeapTest heap = new HeapTest();
        heap.insert(15);
        heap.insert(5);
        heap.insert(10);
        heap.insert(30);
    }

which just gives an array of the form [15,5,10,30] for example. This array for a max heap should be of the form [30,15,10,5]

Im expecting this: [15,5,10,30] -> [15,30,10,5] -> [30,15,10,5]

Could any one provide some insight as to why the heapify part of insert is not working?

Thanks!!

Answer 1

There are a couple of issues I can see.

1. consider what Math.ceil((index - 2)/2) would return for index 3. This would return 0 rather than 1 because the /2 is an integer operation. Changing that to /2.0 will fix it. Or even simpler would be to make use of integer arithmetic with (index - 1) / 2 which is clearer and more efficient.

2. getParentIndex(index) > 0 means that you are ignoring the root node at index 0 - currently your code will never swap that item. changing to >= will fix it.

There could well be other issues but those are 2 I can see by inspection. Either unit testing or interactive debugging would have uncovered those issues.