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Java heap sorting questions

Posted on 2010-11-27
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Last Modified: 2012-05-10
Could anyone please help me to understand this code:
That is java class which sorts array.
Questions:
1) What are the numbers of steps you needed to build the heap, and to destroy the heap?
2) How to get the sum of the construction and destruction steps?


Website: http://www.iti.fh-flensburg.de/lang/algorithmen/sortieren/heap/heapen.htm

public class HeapSorter 
{
    private static int[] a;
    private static int n;

    public static void sort(int[] a0)
    {
        a=a0;
        n=a.length;
        heapsort();
    }

    private static void heapsort()
    {
        buildheap();
        while (n>1)
        {
            n--;
            exchange (0, n);
            downheap (0);
        } 
    }

    private static void buildheap()
    {
        for (int v=n/2-1; v>=0; v--)
            downheap (v);
    }

    private static void downheap(int v)
    {
        int w=2*v+1;    // first descendant of v
        while (w<n)
        {
            if (w+1<n)    // is there a second descendant?
                if (a[w+1]>a[w]) w++;
            // w is the descendant of v with maximum label

            if (a[v]>=a[w]) return;  // v has heap property
            // otherwise
            exchange(v, w);  // exchange labels of v and w
            v=w;        // continue
            w=2*v+1;
        }
    }

    private static void exchange(int i, int j)
    {
        int t=a[i];
        a[i]=a[j];
        a[j]=t;
    }

}    // end class HeapSorter

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Question by:prog458
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Expert Comment

by:TommySzalapski
ID: 34224072
Since this is most likely a school assignment of some kind, we can't just give out answers but I can sure point you to how to solve it.

I don't see any destruction code, but the entire heap is stored in a single array. So how many steps would it take to 'destroy' that?

Your questions 1 and 2 appear to be the same. This is how you would count the construction steps. Look at how many times the for loop in buildheap runs. So for each of those you do downheap. What is the highest amount of steps that downheap could take? (Hint: the heap is a binary heap so the maximum height is known. You should know what it is too.)

Now just multiply those two numbers together.
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Author Comment

by:prog458
ID: 34228020
Thanks for help i think i am getting there. How can i put those numbers into code. It would be ok with buildheap. How would i do with a downheap?
Theoretically it says h=log(Base2)(N+1)-1 - max hight.The thing is i want to generate that answer from code. Do you have any suggestions.
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Accepted Solution

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TommySzalapski earned 500 total points
ID: 34228044
Are you trying to actually count the instructions? In that case just make a global variable start it at 0 and increment it in the loop in downheap and nowhere else.
If you want the runtime, you don't want or need it in the code. They want the average case runtime which you can see is O(n*lg(n))
The current hight of the heap can be calculated as the number of times the loop in downheap runs.
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