Java: Heap sort Algorithm

Java Sorting Algorithm: Exercise-5 with Solution

Write a Java program to sort an array of given integers using the Heap sort algorithm.

In computer science heapsort (invented by J. W. J. Williams in 1964) is a comparison-based sorting algorithm. Heapsort can be thought of as an improved selection sort: like that algorithm, it divides its input into a sorted and an unsorted region, and it interactively shrinks the unsorted region by extracting the largest element and moving that to the sorted region. The improvement consists of the use of a heap data structure rather than a linear-time search to find the maximum. Although somewhat slower in practice on most machines than a well-implemented quicksort, it has the advantage of a more favorable worst-case O(n log n) runtime. Heapsort is an in-place algorithm, but not a stable sort.

A run of the heapsort algorithm sorting an array of randomly permuted values. In the first stage of the algorithm the array elements are reordered to satisfy the heap property. Before the actual sorting takes place, the heap tree structure is shown briefly for illustration.

Animation credits : RolandH

Pseudocode:

// Ref.: https://bit.ly/2DBQsFI
function heapSort(a, count) is
   input: an unordered array a of length count
 
   (first place a in max-heap order)
   heapify(a, count)
 
   end := count - 1
   while end > 0 do
      (swap the root(maximum value) of the heap with the
       last element of the heap)
      swap(a[end], a[0])
      (decrement the size of the heap so that the previous
       max value will stay in its proper place)
      end := end - 1
      (put the heap back in max-heap order)
      siftDown(a, 0, end)

function heapify(a,count) is
   (start is assigned the index in a of the last parent node)
   start := (count - 2) / 2
   
   while start ≥ 0 do
      (sift down the node at index start to the proper place
       such that all nodes below the start index are in heap
       order)
      siftDown(a, start, count-1)
      start := start - 1
   (after sifting down the root all nodes/elements are in heap order)
 
function siftDown(a, start, end) is
   (end represents the limit of how far down the heap to sift)
   root := start

   while root * 2 + 1 ≤ end do       (While the root has at least one child)
      child := root * 2 + 1           (root*2+1 points to the left child)
      (If the child has a sibling and the child's value is less than its sibling's...)
      if child + 1 ≤ end and a[child] < a[child + 1] then
         child := child + 1           (... then point to the right child instead)
      if a[root] < a[child] then     (out of max-heap order)
         swap(a[root], a[child])
         root := child                (repeat to continue sifting down the child now)
      else
         return

Sample Solution:

Java Code:

public class HeapSort
{
public static void heapSort(int[] a){
	int count = a.length;
	//first place a in max-heap order
	heapify(a, count);
	int end = count - 1;
	while(end > 0){
		//swap the root(maximum value) of the heap with the
		//last element of the heap
		int tmp = a[end];
		a[end] = a[0];
		a[0] = tmp;
		//put the heap back in max-heap order
		siftDown(a, 0, end - 1);
		//decrement the size of the heap so that the previous
		//max value will stay in its proper place
		end--;
	}
}
public static void heapify(int[] a, int count){
	//start is assigned the index in a of the last parent node
	int start = (count - 2) / 2; //binary heap
	while(start >= 0){
		//sift down the node at index start to the proper place
		//such that all nodes below the start index are in heap
		//order
		siftDown(a, start, count - 1);
		start--;
	}
	//after sifting down the root all nodes/elements are in heap order
}
public static void siftDown(int[] a, int start, int end){
	//end represents the limit of how far down the heap to sift
	int root = start;
	while((root * 2 + 1) <= end){      //While the root has at least one child
		int child = root * 2 + 1;           //root*2+1 points to the left child
		//if the child has a sibling and the child's value is less than its sibling's...
		if(child + 1 <= end && a[child] < a[child + 1])
			child = child + 1;           //... then point to the right child instead
		if(a[root] < a[child]){     //out of max-heap order
			int tmp = a[root];
			a[root] = a[child];
			a[child] = tmp;
			root = child;                //repeat to continue sifting down the child now
		}else
			return;
	}
}
// Driver program
	public static void main(String args[])
	{
		int arr[] = {7, -5, 3, 2, 1, 0, 45};
		int n = arr.length;
		HeapSort ob = new HeapSort();
		ob.heapSort(arr);
		System.out.println("Sorted array:");
		 for (int element: arr) {
            System.out.print(" "+element);
        }
	}
}

Sample Output:

Sorted array:
 -5 0 1 2 3 7 45

Flowchart:

Java Code Editor:

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