(Min-heap) The heap presented in the text is also known as a max-heap, in which each node is greater than or equal to any of its children

/*********************************************************************************
* (Min-heap) The heap presented in the text is also known as a max-heap, in      *
* which each node is greater than or equal to any of its children. A min-heap is *
* a heap in which each node is less than or equal to any of its children.        *
* Min-heaps are often used to implement priority queues. Revise the Heap class   *
* in Listing 23.9 to implement a min-heap.                                       *
*********************************************************************************/

public class Exercise_23_07 {
	/** Heap sort method */
	public  static <E extends Comparable<E>> void heapSort(E[] list) {
		// Create a Heap of integers
		Heap<E> heap = new Heap<>();

		// Add elements to the heap
		for (int i = 0; i < list.length; i++) 
			heap.add(list[i]);
		
		// Remove elements from the heap
		for (int i = list.length - 1; i >= 0; i--)
			list[i] = heap.remove();
	}

	/** A test method */
	public static void main(String[] args) {
		Integer[] list = {-44, -5, -3, 3, 3, 1, -4, 0, 1, 2, 4, 5, 53};
		heapSort(list);
		for (int i = 0; i < list.length; i++)
			System.out.print(list[i] + " ");
		System.out.println();
	}
}

Heap.java

public class Heap<E extends Comparable<E>> {
	private java.util.ArrayList<E> list = new java.util.ArrayList<>();

	/** Create a default heap */
	public Heap() {
	}

	/** Create a heap from an array of objects */
	public Heap(E[] objects) {
		for (int i = 0; i < objects.length; i++)
			add(objects[i]);
	}

	/** Add a new object into the heap */
	public void add(E newObject) {
		list.add(newObject); // Append to the heap
		int currentIndex = list.size() - 1; // The index of the last node

		while (currentIndex > 0) {
			int parentIndex = (currentIndex - 1) / 2;
			// Swap if the current object is less than its parent
			if (list.get(currentIndex). compareTo(
				 list.get(parentIndex)) < 0) {
				E temp = list.get(currentIndex);
				list.set(currentIndex, list.get(parentIndex));
				list.set(parentIndex, temp);
			}
			else
				break; // The tree is a heap now

			currentIndex = parentIndex;
		}
	}

	/** Remove the root from the heap */
	public E remove() {
		if (list.size() == 0) return null;

		E removedObject = list.get(0);
		list.set(0, list.get(list.size() - 1));
		list.remove(list.size() - 1);

		int currentIndex = 0;
		while (currentIndex < list.size()) {
			int leftChildIndex = 2 * currentIndex + 1;
			int rightChildIndex = 2 * currentIndex + 2;

			// Find the maximum between two children
			if (leftChildIndex >= list.size()) break; // The tree is a heap
			int maxIndex = leftChildIndex;
			if (rightChildIndex < list.size()) {
				if (list.get(maxIndex).compareTo(
					 list.get(rightChildIndex)) > 0) {
					maxIndex = rightChildIndex;
				}
			}

			// Swap if the current node is greater than the maximum
			if (list.get(currentIndex).compareTo(
				 list.get(maxIndex)) > 0) {
				E temp = list.get(maxIndex);
				list.set(maxIndex, list.get(currentIndex));
				list.set(currentIndex, temp);
				currentIndex = maxIndex;
			}
			else
				break; // The tree is a heap
		}

		return removedObject;
	}

	/** Get the number of nodes in the tree */
	public int getSize() {
		return list.size();
	}
}