Binary Heap Implemented via a Binary Tree Structure

Question

For an assignment, we were instructed to create a priority queue implemented via a binary heap, without using any built-in classes, and I have done so successfully by using

Answer 1

A tree implementation of a binary heap uses a complete tree [or almost full tree: every level is full, except the deepest one].
You always 'know' which is the last occupied leaf - where you delete from [and modifying it is O(logn) after it changed so it is not a problem], and you always 'know' which is the first non-occupied leaf, in which you add elements to [and again, modifying it is also O(logn) after it changed].

The algorithm idea is simple:
insert: insert element to the first non-occupied leaf, and use heapify [sift up] to get this element to its correct place in the heap.

delete_min: replace the first element with the last occupied leaf, and remove the last occupied leaf. then, heapify [sift down] the heap.

EDIT: note that delete() can be done to any element, and not only the head, however - finding the element you want to replace with the last leaf will be O(n), which will make this op expensive. for this reason, the delete() method [besides the head], is usually not a part of the heap data structure.

Answer 2

I really wanted to do this for almost a decade.Finally sat down today and wrote it.Anyone who wants it can use it.I got inspired by Quora founder to relearn Heap.Apparently he was asked how would you find K near points in a set of n points in his Google phone screen.Apparently his answer was to use a Max Heap and to store K values and remove the maximum element after the size of the heap exceeds K.The approach is pretty simple and the worst case is nlog K which is better than n^2 in most sorting cases.Here is the code.

import java.util.ArrayList;
import java.util.List;

/**
 * @author Harish R
 */
public class HeapPractise<T extends Comparable<T>> {

    private List<T> heapList;

    public List<T> getHeapList() {
        return heapList;
    }

    public void setHeapList(List<T> heapList) {
        this.heapList = heapList;
    }

    private int heapSize;

    public HeapPractise() {
        this.heapList = new ArrayList<>();
        this.heapSize = heapList.size();
    }

    public void insert(T item) {
        if (heapList.size() == 0) {
            heapList.add(item);
        } else {
            siftUp(item);
        }

    }

    public void siftUp(T item) {
        heapList.add(item);
        heapSize = heapList.size();
        int currentIndex = heapSize - 1;
        while (currentIndex > 0) {
            int parentIndex = (int) Math.floor((currentIndex - 1) / 2);
            T parentItem = heapList.get(parentIndex);
            if (parentItem != null) {
                if (item.compareTo(parentItem) > 0) {
                    heapList.set(parentIndex, item);
                    heapList.set(currentIndex, parentItem);
                    currentIndex = parentIndex;
                    continue;
                }
            }
            break;
        }
    }

    public T delete() {
        if (heapList.size() == 0) {
            return null;
        }
        if (heapList.size() == 1) {
            T item = heapList.get(0);
            heapList.remove(0);
            return item;
        }
        return siftDown();
    }

    public T siftDown() {
        T item = heapList.get(0);
        T lastItem = heapList.get(heapList.size() - 1);
        heapList.remove(heapList.size() - 1);
        heapList.set(0, lastItem);
        heapSize = heapList.size();
        int currentIndex = 0;
        while (currentIndex < heapSize) {
            int leftIndex = (2 * currentIndex) + 1;
            int rightIndex = (2 * currentIndex) + 2;
            T leftItem = null;
            T rightItem = null;
            int currentLargestItemIndex = -1;
            if (leftIndex <= heapSize - 1) {
                leftItem = heapList.get(leftIndex);
            }
            if (rightIndex <= heapSize - 1) {
                rightItem = heapList.get(rightIndex);
            }
            T currentLargestItem = null;
            if (leftItem != null && rightItem != null) {

                if (leftItem.compareTo(rightItem) >= 0) {
                    currentLargestItem = leftItem;
                    currentLargestItemIndex = leftIndex;
                } else {
                    currentLargestItem = rightItem;
                    currentLargestItemIndex = rightIndex;
                }
            } else if (leftItem != null && rightItem == null) {
                currentLargestItem = leftItem;
                currentLargestItemIndex = leftIndex;
            }
            if (currentLargestItem != null) {
                if (lastItem.compareTo(currentLargestItem) >= 0) {
                    break;
                } else {
                    heapList.set(currentLargestItemIndex, lastItem);
                    heapList.set(currentIndex, currentLargestItem);
                    currentIndex = currentLargestItemIndex;
                    continue;
                }
            }
        }
        return item;

    }

    public static void main(String[] args) {
        HeapPractise<Integer> heap = new HeapPractise<>();

        for (int i = 0; i < 32; i++) {
            heap.insert(i);
        }
        System.out.println(heap.getHeapList());
        List<Node<Integer>> nodeArray = new ArrayList<>(heap.getHeapList()
                .size());
        for (int i = 0; i < heap.getHeapList().size(); i++) {
            Integer heapElement = heap.getHeapList().get(i);
            Node<Integer> node = new Node<Integer>(heapElement);
            nodeArray.add(node);
        }
        for (int i = 0; i < nodeArray.size(); i++) {
            int leftNodeIndex = (2 * i) + 1;
            int rightNodeIndex = (2 * i) + 2;
            Node<Integer> node = nodeArray.get(i);
            if (leftNodeIndex <= heap.getHeapList().size() - 1) {
                Node<Integer> leftNode = nodeArray.get(leftNodeIndex);
                node.left = leftNode;
            }
            if (rightNodeIndex <= heap.getHeapList().size() - 1) {
                Node<Integer> rightNode = nodeArray.get(rightNodeIndex);
                node.right = rightNode;
            }
        }
        BTreePrinter.printNode(nodeArray.get(0));
    }
}

public class Node<T extends Comparable<?>> {
    Node<T> left, right;
    T data;

    public Node(T data) {
        this.data = data;
    }
}

import java.util.ArrayList;
import java.util.Collections;
import java.util.List;

class BTreePrinter {

    public static <T extends Comparable<?>> void printNode(Node<T> root) {
        int maxLevel = BTreePrinter.maxLevel(root);

        printNodeInternal(Collections.singletonList(root), 1, maxLevel);
    }

    private static <T extends Comparable<?>> void printNodeInternal(
            List<Node<T>> nodes, int level, int maxLevel) {
        if (nodes.isEmpty() || BTreePrinter.isAllElementsNull(nodes))
            return;

        int floor = maxLevel - level;
        int endgeLines = (int) Math.pow(2, (Math.max(floor - 1, 0)));
        int firstSpaces = (int) Math.pow(2, (floor)) - 1;
        int betweenSpaces = (int) Math.pow(2, (floor + 1)) - 1;

        BTreePrinter.printWhitespaces(firstSpaces);

        List<Node<T>> newNodes = new ArrayList<Node<T>>();
        for (Node<T> node : nodes) {
            if (node != null) {
                String nodeData = String.valueOf(node.data);
                if (nodeData != null) {
                    if (nodeData.length() == 1) {
                        nodeData = "0" + nodeData;
                    }
                }
                System.out.print(nodeData);
                newNodes.add(node.left);
                newNodes.add(node.right);
            } else {
                newNodes.add(null);
                newNodes.add(null);
                System.out.print("  ");
            }

            BTreePrinter.printWhitespaces(betweenSpaces);
        }
        System.out.println("");

        for (int i = 1; i <= endgeLines; i++) {
            for (int j = 0; j < nodes.size(); j++) {
                BTreePrinter.printWhitespaces(firstSpaces - i);
                if (nodes.get(j) == null) {
                    BTreePrinter.printWhitespaces(endgeLines + endgeLines + i
                            + 1);
                    continue;
                }

                if (nodes.get(j).left != null)
                    System.out.print("//");
                else
                    BTreePrinter.printWhitespaces(1);

                BTreePrinter.printWhitespaces(i + i - 1);

                if (nodes.get(j).right != null)
                    System.out.print("\\\\");
                else
                    BTreePrinter.printWhitespaces(1);

                BTreePrinter.printWhitespaces(endgeLines + endgeLines - i);
            }

            System.out.println("");
        }

        printNodeInternal(newNodes, level + 1, maxLevel);
    }

    private static void printWhitespaces(int count) {
        for (int i = 0; i < 2 * count; i++)
            System.out.print(" ");
    }

    private static <T extends Comparable<?>> int maxLevel(Node<T> node) {
        if (node == null)
            return 0;

        return Math.max(BTreePrinter.maxLevel(node.left),
                BTreePrinter.maxLevel(node.right)) + 1;
    }

    private static <T> boolean isAllElementsNull(List<T> list) {
        for (Object object : list) {
            if (object != null)
                return false;
        }

        return true;
    }

}

Please note that BTreePrinter is a code I took somewhere in Stackoverflow long back and I modified to use with 2 digit numbers.It will be broken if we move to 3 digit numbers and it is only for simple understanding of how the Heap structure looks.A fix for 3 digit numbers is to keep everything as multiple of 3. Also due credits to Sesh Venugopal for wonderful tutorial on Youtube on Heap data structure