Skip to main content

Inserting an element into a heap

Image
By

Inserting an element into a heap     

In this article we examine the idea laying in the foundation of the heap data structure. We call it sifting, but you also may meet another terms, like "trickle", "heapify", "bubble" or "percolate".

Insertion algorithm

Now, let us phrase general algorithm to insert a new element into a heap.

  1. Add a new element to the end of an array;
  2. Sift up the new element, while heap property is broken. Sifting is done as following: compare node's value with parent's value. If they are in wrong order, swap them.

Example

Insert -2 into a following heap:

Insert a new element to the end of the array:

In the general case, after insertion, heap property near the new node is broken:

To restore heap property, algorithm sifts up the new element, by swapping it with its parent:

Now heap property is broken at the root node:

Keep sifting:

Heap property is fulfilled, sifting is over.

Source heap

After -2 insertion

Complexity analysis

Complexity of the insertion operation is O(h), where h is heap's height. Taking into account completeness of the tree, O(h) = O(log n), where n is number of elements in a heap.

Code snippets

Java implementation

public class BinaryMinHeap {     

public void insert(int value) {

            if (heapSize == data.length)

                  throw new HeapException("Heap's underlying storage is overflow");

            else {

                  heapSize++;

                  data[heapSize - 1] = value;

                  siftUp(heapSize - 1);

            }

      }    

 

      …

     

private void siftUp(int nodeIndex) {

            int parentIndex, tmp;

            if (nodeIndex != 0) {

                  parentIndex = getParentIndex(nodeIndex);

                  if (data[parentIndex] > data[nodeIndex]) {

                        tmp = data[parentIndex];

                        data[parentIndex] = data[nodeIndex];

                        data[nodeIndex] = tmp;

                        siftUp(parentIndex);

                  }

            }

      }

}

C++ implementation

void BinaryMinHeap::siftUp(int nodeIndex) {

      int parentIndex, tmp;

      if (nodeIndex != 0) {

            parentIndex = getParentIndex(nodeIndex);

            if (data[parentIndex] > data[nodeIndex]) {

                  tmp = data[parentIndex];

                  data[parentIndex] = data[nodeIndex];

                  data[nodeIndex] = tmp;

                  siftUp(parentIndex);

            }

      }

}

 

void BinaryMinHeap::insert(int value) {

      if (heapSize == arraySize)

            throw string("Heap's underlying storage is overflow");

      else {

            heapSize++;

            data[heapSize - 1] = value;

            siftUp(heapSize - 1);

      }

}

DISCLAIMER ========== This e-mail may contain privileged and confidential information which is the property of Persistent Systems Ltd. It is intended only for the use of the individual or entity to which it is addressed. If you are not the intended recipient, you are not authorized to read, retain, copy, print, distribute or use this message. If you have received this communication in error, please notify the sender and delete all copies of this message. Persistent Systems Ltd. does not accept any liability for virus infected mails.

Labels:

Comments

Post a Comment

Popular posts from this blog

WPF-MVVM: RelayCommand Implementation

By
In WPF if we are implementing MVVM pattern then we need to play with Command rather than Events. You can use ICommand interface to create each command class. Implementation of ICommand in a class gives you CanExecute(), Execute() methods which take part in the action performed by Command.   Rather than making Command Class for each Command we can implement a generic Relay Command to get Command. Below is a RelayCommand class that we will implement.   ///   <summary>      ///  To register commands in MMVM pattern      ///   </summary>      class   RelayCommands  :  ICommand     {          readonly   Action < object > _execute;          readonly   Predicate < object > _canExecute;  ...
Post a Comment
Read more

.Net List with Changed event

By
Sometimes we need a List which can notify user when an item is added. Here is the way that you can implement a generic ArrayList which notifies user at the time of an element is added.   using  System; using  System.Collections; namespace  ArchiveData.Logging {    // A delegate type for hooking up change notifications.    public   delegate   void   ChangedEventHandler ( object  sender,  EventArgs  e);    public   class   ListWithChangedEvent  :  ArrayList   {      // An event that clients can use to be notified whenever the      // elements of the list change.      public   event   ChangedEventHandler  Changed;      public   object  NewlyAddedItem {...
Post a Comment
Read more

What is DispatcherTimer in wpf?

By
DispatcherTimer When you want to set a timer working with GUI, you always come across threading problem. The problem is that if you want to send some changes to UI that is constantly/continuously changing then that will make your UI unresponsive or in other words it will hang your UI.   To overcome from this situation, WPF gives us DispatcherTimer threading functionality that will take care of such continuously changing processing on UI thread and that will not hang your UI. We can accomplish same scenario in Win Form , through System.Windows.Forms.Timer and in WPF it is System.Windows.Threading.DispatcherTimer .   Difference between DispatcherTimer and Regular timer (System.Timers.Timer) DispatcherTimer is the regular timer. It fires its Tick event on the UI thread, you can do anything you want with the UI. System.Timers.Timer is an asynchronous timer, its Elapsed event runs on a thread pool thread. You have to be very careful in your event handler...
Post a Comment
Read more