Implement a min-heap, Data Structure & Algorithms


A heap is an efficient tree-based data structure that can be used as a priority queue. Recall that the abstract data type of a priority queue has the following operations

  • size, isEmpty, min
  • insert
  • removeMin

We can describe the priority queue ADT using the following Java Entry class and interface:

1 import java.lang.Comparable;


3 /**

4 * When items are added to the heap, you should create an Entry object

5 * to hold the key and value and store this in the appropriate node

6 */

7 public class Entryextends Comparable,V> {

8 protected K key;

9 protected V value;

10 public MyEntry(K k, V v) { key = k; value = v; }

11 public K getKey() { return key; }

12 public V getValue() { return value; }

13 public String toString() { return "(" + key + "," + value + ")"; }

14 }


16 public interface PriorityQueueextends Comparable,V> {

17 /** Returns the number of items in the priority queue. */

18 public int size();

19 /** Returns whether the priority queue is empty. */

20 public boolean isEmpty();

21 /** Returns but does not remove an entry with minimum key. */

22 public Entry min();

23 /** Inserts a key-value pair and return the entry created. */

24 public Entry insert(K key, V value);

25 /** Removes and returns an entry with minimum key. */

26 public Entry removeMin();

27 }


The main operations (insert, removeMin) can be done in O(log n) with a heap, while the other operations of the priority queue ADT (isEmpty, size, or look up the min value) are constant time. In lectures we have seen how to implement a heap using an array-based implementation.

58_Implement a min-heap.png

Figure 1: 3-way heap example

For this assignment you must implement a min-heap using a using a tree-based implementation (similar to the binary tree class we have used in tutorials). This tree should be 3-way tree, where each node needs to have (at most) three children

Note that the definition of a 3-way heap is identical to that of a binary heap, except for allowing at most three children (see Figure ). As with a binary tree, every node must have all of its children, except for the nodes at the last levels of the tree. In more detail, your task is to

1. Design a 3-way tree structure that you will use for building your heap. You can use code provided in the book. You can use any helper data structures that you need (linked lists, arrays etc.), but you must implement the tree structure yourself.

2. Implement your design for a generic 3-way heap in a class called ThreewayHeap. You will need to implement all operations (insert, removeMin, isEmpty, etc.) in the supplied interface and skeleton for the 3-way heap. In most cases the extension is straightforward from binary heaps, with certain extra cases that you need to check.

3. Include a method in your heap to print out a visual representation in DOT format (helpful for testing/debugging purposes).

4. Design test cases for your new heap structure, used as a priority queue

5. Use the provided test code on your implementation

Posted Date: 2/28/2013 3:10:39 AM | Location : United States

Related Discussions:- Implement a min-heap, Assignment Help, Ask Question on Implement a min-heap, Get Answer, Expert's Help, Implement a min-heap Discussions

Write discussion on Implement a min-heap
Your posts are moderated
Related Questions

what is far and near procedures in system programming?

The algorithm to delete any node having key from a binary search tree is not simple where as several cases has to be considered. If the node to be deleted contains no sons,

Linked list representations contain great advantages of flexibility on the contiguous representation of data structures. However, they contain few disadvantages also. Data structur

Write a program to create a hashed file that stores the records currently in the file " data_2013 ". Records should use the same fixed-length schema given previously, and should ag

Q. Illustrate the result of running BFS and DFS on the directed graph given below using vertex 3 as source.  Show the status of the data structure used at each and every stage.

Program segment for the deletion of any element from the queue delmq(i)  /* Delete any element from queue i */ { int i,x; if ( front[i] == rear[i]) printf("Queue is

When there is requirement to access records sequentially by some key value and also to access records directly by the similar key value, the collection of records may be organized

Efficiency of Linear Search How much number of comparisons is there in this search in searching for a particular element? The number of comparisons based upon where the reco

Binary: Each node has one, zero, or two children. This assertion creates many tree operations efficient and simple. Binary Search : A binary tree where each and every left