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Heaps. A heap is a binary tree. A heap is best implemented in sequential representation (using an array). Two important uses of heaps are: (i) efficient implementation of priority queues (ii) sorting -- Heapsort. 10. 30. 20. 40. 50. 25. 55. 52. 42. A Heap. Any node’s key value is

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Heaps

Heaps

  • A heap is a binary tree.

  • A heap is best implemented in sequential representation (using an array).

  • Two important uses of heaps are:

    • (i) efficient implementation of priority queues

    • (ii) sorting -- Heapsort.


A heap

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42

A Heap

Any node’s key value is

less than its children’s.


Sequential representation of trees

Sequential Representation of Trees

  • There are three methods of representing a binary tree using array representation.

    1. Using index values to represent edges:

    class Node {

    Dataelt;

    intleft;

    intright;

    } Node;

    Node[] BinaryTree[TreeSize];


Method 1 example

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B

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I

Method 1: Example


Method 2

Method 2

2. Store the nodes in one of the natural traversals:

class Node {

Dataelt;

booleanleft;

booleanright;

};

Node[] BinaryTree[TreeSize];


Method 2 example

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B

C

D

E

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Method 2: Example

Elements stored in Pre-Order traversal


Method 3

Method 3

3. Store the nodes in fixed positions: (i) root goes into first index, (ii) in general left child of tree[i] is stored in tree[2i] and right child in tree[2i+1].


Method 3 example

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Method 3: Example


Heaps1

Heaps

  • Heaps are represented sequentially using the third method.

  • Heap is a complete binary tree: shortest-path length tree with nodes on the lowest level in their leftmost positions.

  • Complete Binary Tree:let h be the height of the heap

    • for i= 0, … , h - 1, there are 2i nodes of depth i

    • at depth h- 1, the internal nodes are to the left of the external nodes


Heaps cont

Heaps (Cont.)

  • Max-Heap has max element as root. Min-Heap has min element as root.

  • The elements in a heap satisfy heap conditions: for Min-Heap: key[parent] < key[left-child] or key[right-child].

  • The last node of a heap is the rightmost node of maximum depth

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last node

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7


Heap an example

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Heap: An example

All the three arrangements

satisfy min heap conditions


Heap an example1

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Heap: An example

All the three arrangements

satisfy min heap conditions


Heap an example2

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25

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55

Heap: An example

All the three arrangements

satisfy min heap conditions


Constructing heaps

Constructing Heaps

  • There are two methods of constructing heaps:

    • Using SiftDown operation.

    • Using SiftUp operation.

  • SiftDown operation inserts a new element into the Heap from the top.

  • SiftUp operation inserts a new element into the Heap from the bottom.


Adt heap

ADT Heap

Elements: The elements are called HeapElements.

Structure: The elements of the heap satisfy the heap conditions.

Domain: Bounded. Type name: Heap.


Adt heap1

ADT Heap

Operations:

  • Method SiftUp (int n)

    requires: Elements H[1],H[2],…,H[n-1] satisfy heap conditions.

    results: Elements H[1],H[2],…,H[n] satisfy heap conditions.

  • Method SiftDown (int m,n)

    requires: Elements H[m+1],H[m+2],…,H[n] satisfy the heap conditions.

    results: Elements H[m],H[m+1],…,H[n] satisfy the heap conditions.

  • Method Heap (int n) // Constructor

    results: Elements H[1],H[2],….H[n] satisfy the heap conditions.


Adt heap element

ADT Heap: Element

public class HeapElement<T> {

T data;

Priority p;

public HeapElement(T e, Priority pty) {

data = e;

p = pty;

}

// Setters/Getters...

}


Insertion into a heap

Method insertItem of the priority queue ADT corresponds to the insertion of a key k to the heap

The insertion algorithm consists of three steps

Find the insertion node z (the new last node)

Store k at z

Restore the heap-order property (discussed next)

Insertion into a Heap

Heaps


Upheap

Upheap

  • After the insertion of a new key k, the heap-order property may be violated

  • Algorithm upheap restores the heap-order property by swapping k along an upward path from the insertion node

  • Upheap terminates when the key k reaches the root or a node whose parent has a key smaller than or equal to k

  • Since a heap has height O(log n), upheap runs in O(log n) time

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z

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insertion node

Heaps


Upheap1

Upheap

  • After the insertion of a new key k, the heap-order property may be violated

  • Algorithm upheap restores the heap-order property by swapping k along an upward path from the insertion node

  • Upheap terminates when the key k reaches the root or a node whose parent has a key smaller than or equal to k

  • Since a heap has height O(log n), upheap runs in O(log n) time

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5

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9

7

Heaps


Upheap2

Upheap

  • After the insertion of a new key k, the heap-order property may be violated

  • Algorithm upheap restores the heap-order property by swapping k along an upward path from the insertion node

  • Upheap terminates when the key k reaches the root or a node whose parent has a key smaller than or equal to k

  • Since a heap has height O(log n), upheap runs in O(log n) time

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1

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9

7

Heaps


Upheap3

Upheap

  • After the insertion of a new key k, the heap-order property may be violated

  • Algorithm upheap restores the heap-order property by swapping k along an upward path from the insertion node

  • Upheap terminates when the key k reaches the root or a node whose parent has a key smaller than or equal to k

  • Since a heap has height O(log n), upheap runs in O(log n) time

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2

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9

7

Heaps


Upheap4

Upheap

  • After the insertion of a new key k, the heap-order property may be violated

  • Algorithm upheap restores the heap-order property by swapping k along an upward path from the insertion node

  • Upheap terminates when the key k reaches the root or a node whose parent has a key smaller than or equal to k

  • Since a heap has height O(log n), upheap runs in O(log n) time

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z

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9

7

insertion node

Heaps


Upheap5

Upheap

  • After the insertion of a new key k, the heap-order property may be violated

  • Algorithm upheap restores the heap-order property by swapping k along an upward path from the insertion node

  • Upheap terminates when the key k reaches the root or a node whose parent has a key smaller than or equal to k

  • Since a heap has height O(log n), upheap runs in O(log n) time

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7

Heaps


Upheap6

Upheap

  • After the insertion of a new key k, the heap-order property may be violated

  • Algorithm upheap restores the heap-order property by swapping k along an upward path from the insertion node

  • Upheap terminates when the key k reaches the root or a node whose parent has a key smaller than or equal to k

  • Since a heap has height O(log n), upheap runs in O(log n) time

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z

Heaps

insertion node


Upheap7

Upheap

  • After the insertion of a new key k, the heap-order property may be violated

  • Algorithm upheap restores the heap-order property by swapping k along an upward path from the insertion node

  • Upheap terminates when the key k reaches the root or a node whose parent has a key smaller than or equal to k

  • Since a heap has height O(log n), upheap runs in O(log n) time

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5

2

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10

9

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4

Heaps


Upheap8

Upheap

  • After the insertion of a new key k, the heap-order property may be violated

  • Algorithm upheap restores the heap-order property by swapping k along an upward path from the insertion node

  • Upheap terminates when the key k reaches the root or a node whose parent has a key smaller than or equal to k

  • Since a heap has height O(log n), upheap runs in O(log n) time

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9

Heaps


Upheap9

Upheap

  • After the insertion of a new key k, the heap-order property may be violated

  • Algorithm upheap restores the heap-order property by swapping k along an upward path from the insertion node

  • Upheap terminates when the key k reaches the root or a node whose parent has a key smaller than or equal to k

  • Since a heap has height O(log n), upheap runs in O(log n) time

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Heaps


Removal from a heap 7 3 3

Removal from a Heap (§ 7.3.3)

2

  • Method removeMin of the priority queue ADT corresponds to the removal of the root key from the heap

  • The removal algorithm consists of three steps

    • Replace the root key with the key of the last node w

    • Remove w

    • Restore the heap-order property (discussed next)

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last node

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new last node

Heaps


Downheap

Downheap

  • After replacing the root key with the key k of the last node, the heap-order property may be violated

  • Algorithm downheap restores the heap-order property by swapping key k along a downward path from the root

  • Upheap terminates when key k reaches a leaf or a node whose children have keys greater than or equal to k

  • Since a heap has height O(log n), downheap runs in O(log n) time

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w

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last node

Heaps


Downheap1

Downheap

  • After replacing the root key with the key k of the last node, the heap-order property may be violated

  • Algorithm downheap restores the heap-order property by swapping key k along a downward path from the root

  • Upheap terminates when key k reaches a leaf or a node whose children have keys greater than or equal to k

  • Since a heap has height O(log n), downheap runs in O(log n) time

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w

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last node

Heaps


Downheap2

Downheap

  • After replacing the root key with the key k of the last node, the heap-order property may be violated

  • Algorithm downheap restores the heap-order property by swapping key k along a downward path from the root

  • Upheap terminates when key k reaches a leaf or a node whose children have keys greater than or equal to k

  • Since a heap has height O(log n), downheap runs in O(log n) time

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w

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delete last node

Heaps


Downheap3

Downheap

  • After replacing the root key with the key k of the last node, the heap-order property may be violated

  • Algorithm downheap restores the heap-order property by swapping key k along a downward path from the root

  • Upheap terminates when key k reaches a leaf or a node whose children have keys greater than or equal to k

  • Since a heap has height O(log n), downheap runs in O(log n) time

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5

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9

DownHeap/SiftDown

Heaps


Downheap4

Downheap

  • After replacing the root key with the key k of the last node, the heap-order property may be violated

  • Algorithm downheap restores the heap-order property by swapping key k along a downward path from the root

  • Upheap terminates when key k reaches a leaf or a node whose children have keys greater than or equal to k

  • Since a heap has height O(log n), downheap runs in O(log n) time

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9

Heaps


Downheap5

Downheap

  • After replacing the root key with the key k of the last node, the heap-order property may be violated

  • Algorithm downheap restores the heap-order property by swapping key k along a downward path from the root

  • Upheap terminates when key k reaches a leaf or a node whose children have keys greater than or equal to k

  • Since a heap has height O(log n), downheap runs in O(log n) time

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w

9

last node

Heaps


Downheap6

Downheap

  • After replacing the root key with the key k of the last node, the heap-order property may be violated

  • Algorithm downheap restores the heap-order property by swapping key k along a downward path from the root

  • Upheap terminates when key k reaches a leaf or a node whose children have keys greater than or equal to k

  • Since a heap has height O(log n), downheap runs in O(log n) time

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7

6

w

9

last node

Heaps


Downheap7

Downheap

  • After replacing the root key with the key k of the last node, the heap-order property may be violated

  • Algorithm downheap restores the heap-order property by swapping key k along a downward path from the root

  • Upheap terminates when key k reaches a leaf or a node whose children have keys greater than or equal to k

  • Since a heap has height O(log n), downheap runs in O(log n) time

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7

6

w

delete last node

Heaps


Downheap8

Downheap

  • After replacing the root key with the key k of the last node, the heap-order property may be violated

  • Algorithm downheap restores the heap-order property by swapping key k along a downward path from the root

  • Upheap terminates when key k reaches a leaf or a node whose children have keys greater than or equal to k

  • Since a heap has height O(log n), downheap runs in O(log n) time

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7

6

DownHeap/SiftDown

Heaps


Downheap9

Downheap

  • After replacing the root key with the key k of the last node, the heap-order property may be violated

  • Algorithm downheap restores the heap-order property by swapping key k along a downward path from the root

  • Upheap terminates when key k reaches a leaf or a node whose children have keys greater than or equal to k

  • Since a heap has height O(log n), downheap runs in O(log n) time

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7

9

Heaps


Downheap10

Downheap

  • After replacing the root key with the key k of the last node, the heap-order property may be violated

  • Algorithm downheap restores the heap-order property by swapping key k along a downward path from the root

  • Upheap terminates when key k reaches a leaf or a node whose children have keys greater than or equal to k

  • Since a heap has height O(log n), downheap runs in O(log n) time

6

w

7

9

last node

Heaps


Downheap11

Downheap

  • After replacing the root key with the key k of the last node, the heap-order property may be violated

  • Algorithm downheap restores the heap-order property by swapping key k along a downward path from the root

  • Upheap terminates when key k reaches a leaf or a node whose children have keys greater than or equal to k

  • Since a heap has height O(log n), downheap runs in O(log n) time

9

w

7

9

last node

Heaps


Downheap12

Downheap

  • After replacing the root key with the key k of the last node, the heap-order property may be violated

  • Algorithm downheap restores the heap-order property by swapping key k along a downward path from the root

  • Upheap terminates when key k reaches a leaf or a node whose children have keys greater than or equal to k

  • Since a heap has height O(log n), downheap runs in O(log n) time

9

w

7

delete last node

Heaps


Downheap13

Downheap

  • After replacing the root key with the key k of the last node, the heap-order property may be violated

  • Algorithm downheap restores the heap-order property by swapping key k along a downward path from the root

  • Upheap terminates when key k reaches a leaf or a node whose children have keys greater than or equal to k

  • Since a heap has height O(log n), downheap runs in O(log n) time

9

7

DownHeap/SiftDown

Heaps


Downheap14

Downheap

  • After replacing the root key with the key k of the last node, the heap-order property may be violated

  • Algorithm downheap restores the heap-order property by swapping key k along a downward path from the root

  • Upheap terminates when key k reaches a leaf or a node whose children have keys greater than or equal to k

  • Since a heap has height O(log n), downheap runs in O(log n) time

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9

Heaps


Updating the last node

Updating the Last Node

  • The insertion node can be found by traversing a path of O(log n) nodes

    • Go up until a left child or the root is reached

    • If a left child is reached, go to the right child

    • Go down left until a leaf is reached

  • Similar algorithm for updating the last node after a removal

Heaps


Heap sort

Consider a priority queue with n items implemented by means of a heap

the space used is O(n)

methods insert and removeMin take O(log n) time

methods size, isEmpty, and min take time O(1) time

Using a heap-based priority queue, we can sort a sequence of n elements in O(n log n) time

The resulting algorithm is called heap-sort

Heap-sort is much faster than quadratic sorting algorithms, such as insertion-sort and selection-sort

Heap-Sort

Heaps


Vector based heap implementation

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Vector-based Heap Implementation

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  • We can represent a heap with n keys by means of a vector of length n +1

  • For the node at rank i

    • the left child is at rank 2i

    • the right child is at rank 2i +1

  • Links between nodes are not explicitly stored

  • The cell of at rank 0 is not used

  • Operation insert corresponds to inserting at rank n +1

  • Operation removeMin corresponds to removing at rank n

  • Yields in-place heap-sort

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Heaps


Bottom up heap construction

2i -1

2i -1

Bottom-up Heap Construction

  • We can construct a heap storing n given keys in using a bottom-up construction with log n phases

  • In phase i, pairs of heaps with 2i -1 keys are merged into heaps with 2i+1-1 keys

2i+1-1

Heaps


Example

Example

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Heaps


Example contd

Example (contd.)

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Heaps


Example contd1

Example (contd.)

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Heaps


Example end

Example (end)

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Heaps


Merging two heaps

Merging Two Heaps

  • We are given two two heaps and a key k

  • We create a new heap with the root node storing k and with the two heaps as subtrees

  • We perform downheap to restore the heap-order property

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Heaps


Merging two heaps1

Merging Two Heaps

  • We are given two two heaps and a key k

  • We create a new heap with the root node storing k and with the two heaps as subtrees

  • We perform downheap to restore the heap-order property

k

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Heaps


Merging two heaps2

Merging Two Heaps

  • We are given two two heaps and a key k

  • We create a new heap with the root node storing k and with the two heaps as subtrees

  • We perform downheap to restore the heap-order property

k

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Merge

Heaps


Merging two heaps3

Merging Two Heaps

  • We are given two two heaps and a key k

  • We create a new heap with the root node storing k and with the two heaps as subtrees

  • We perform downheap to restore the heap-order property

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Downheap/SiftDown

Heaps


Merging two heaps4

Merging Two Heaps

  • We are given two two heaps and a key k

  • We create a new heap with the root node storing k and with the two heaps as subtrees

  • We perform downheap to restore the heap-order property

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Downheap/SiftDown

Heaps


Merging two heaps5

Merging Two Heaps

  • We are given two two heaps and a key k

  • We create a new heap with the root node storing k and with the two heaps as subtrees

  • We perform downheap to restore the heap-order property

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Downheap/SiftDown

Heaps


Heaps and priority queues

Heaps and Priority Queues

  • We can use a heap to implement a priority queue

  • We store a (key, element) item at each internal node

  • We keep track of the position of the last node

(2, Sue)

(5, Pat)

(6, Mark)

(9, Jeff)

(7, Anna)

Heaps


Priority queue as heap

Priority Queue as Heap

Representation as a Heap

public class HeapPQ<T> {

Heap<T> pq;

/** Creates a new instance of HeapPQ */

public HeapPQ() {

pq = new Heap(10);

}


Priority queue as heap1

Priority Queue as Heap

Representation as a Heap

public class HeapPQ<T> {

Heap<T> pq;

/** Creates a new instance of HeapPQ */

public HeapPQ() {

pq = new Heap(10);

}

Create new heap (maxsize=10)


Priority queue as heap2

Priority Queue as Heap

public void enqueue(T e, Priority pty){

HeapElement<T> x = new HeapElement<T>(e, pty);

pq.SiftUp(x);

}

public T serve(Priority pty){

T e;

Priority p;

e = pq.heap[1].get_data();

p = pq.heap[1].get_priority();

pty.set_value(p.get_value());

pq.heap[1] = pq.heap[pq.size];

pq.size--;

pq.SiftDown(1);

return e;

}


Priority queue as heap3

Priority Queue as Heap

public void enqueue(T e, Priority pty){

HeapElement<T> x = new HeapElement<T>(e, pty);

pq.SiftUp(x);

}

public T serve(Priority pty){

T e;

Priority p;

e = pq.heap[1].get_data();

p = pq.heap[1].get_priority();

pty.set_value(p.get_value());

pq.heap[1] = pq.heap[pq.size];

pq.size--;

pq.SiftDown(1);

return e;

}

Create new heap element (data/priority)


Priority queue as heap4

Priority Queue as Heap

public void enqueue(T e, Priority pty){

HeapElement<T> x = new HeapElement<T>(e, pty);

pq.SiftUp(x);

}

public T serve(Priority pty){

T e;

Priority p;

e = pq.heap[1].get_data();

p = pq.heap[1].get_priority();

pty.set_value(p.get_value());

pq.heap[1] = pq.heap[pq.size];

pq.size--;

pq.SiftDown(1);

return e;

}

Insert the element at the end of heap, and SiftUp


Priority queue as heap5

Priority Queue as Heap

public void enqueue(T e, Priority pty){

HeapElement<T> x = new HeapElement<T>(e, pty);

pq.SiftUp(x);

}

public T serve(Priority pty){

T e;

Priority p;

e = pq.heap[1].get_data();

p = pq.heap[1].get_priority();

pty.set_value(p.get_value());

pq.heap[1] = pq.heap[pq.size];

pq.size--;

pq.SiftDown(1);

return e;

}

Each enqueue is inserted in the heap and Sifted Up.

This ensures the element with the lowest priority (min-heap)

or the highest priority (max-heap) is at the top of the heap (index 1).


Priority queue as heap6

Priority Queue as Heap

public void enqueue(T e, Priority pty){

HeapElement<T> x = new HeapElement<T>(e, pty);

pq.SiftUp(x);

}

public T serve(Priority pty){

T e;

Priority p;

e = pq.heap[1].get_data();

p = pq.heap[1].get_priority();

pty.set_value(p.get_value());

pq.heap[1] = pq.heap[pq.size];

pq.size--;

pq.SiftDown(1);

return e;

}

Get data of the root of the heap (index 1) and store it in e


Priority queue as heap7

Priority Queue as Heap

public void enqueue(T e, Priority pty){

HeapElement<T> x = new HeapElement<T>(e, pty);

pq.SiftUp(x);

}

public T serve(Priority pty){

T e;

Priority p;

e = pq.heap[1].get_data();

p = pq.heap[1].get_priority();

pty.set_value(p.get_value());

pq.heap[1] = pq.heap[pq.size];

pq.size--;

pq.SiftDown(1);

return e;

}

Get priority of the root of the heap (index 1)


Priority queue as heap8

Priority Queue as Heap

public void enqueue(T e, Priority pty){

HeapElement<T> x = new HeapElement<T>(e, pty);

pq.SiftUp(x);

}

public T serve(Priority pty){

T e;

Priority p;

e = pq.heap[1].get_data();

p = pq.heap[1].get_priority();

pty.set_value(p.get_value());

pq.heap[1] = pq.heap[pq.size];

pq.size--;

pq.SiftDown(1);

return e;

}

Set “pty” value to the root’s priority value


Priority queue as heap9

Priority Queue as Heap

public void enqueue(T e, Priority pty){

HeapElement<T> x = new HeapElement<T>(e, pty);

pq.SiftUp(x);

}

public T serve(Priority pty){

T e;

Priority p;

e = pq.heap[1].get_data();

p = pq.heap[1].get_priority();

pty.set_value(p.get_value());

pq.heap[1] = pq.heap[pq.size];

pq.size--;

pq.SiftDown(1);

return e;

}

Copy the last node into the root (delete root)


Priority queue as heap10

Priority Queue as Heap

public void enqueue(T e, Priority pty){

HeapElement<T> x = new HeapElement<T>(e, pty);

pq.SiftUp(x);

}

public T serve(Priority pty){

T e;

Priority p;

e = pq.heap[1].get_data();

p = pq.heap[1].get_priority();

pty.set_value(p.get_value());

pq.heap[1] = pq.heap[pq.size];

pq.size--;

pq.SiftDown(1);

return e;

}

Update the size to delete last node (delete duplicate node)


Priority queue as heap11

Priority Queue as Heap

public void enqueue(T e, Priority pty){

HeapElement<T> x = new HeapElement<T>(e, pty);

pq.SiftUp(x);

}

public T serve(Priority pty){

T e;

Priority p;

e = pq.heap[1].get_data();

p = pq.heap[1].get_priority();

pty.set_value(p.get_value());

pq.heap[1] = pq.heap[pq.size];

pq.size--;

pq.SiftDown(1);

return e;

}

SiftDown the copied last element from the root

down the tree until it satisfies the heap conditions


Priority queue as heap12

Priority Queue as Heap

public void enqueue(T e, Priority pty){

HeapElement<T> x = new HeapElement<T>(e, pty);

pq.SiftUp(x);

}

public T serve(Priority pty){

T e;

Priority p;

e = pq.heap[1].get_data();

p = pq.heap[1].get_priority();

pty.set_value(p.get_value());

pq.heap[1] = pq.heap[pq.size];

pq.size--;

pq.SiftDown(1);

return e;

}

Return e (the deleted root)


Priority queue as heap13

Priority Queue as Heap

public intlength(){

return pq.size;

}

public booleanfull(){

return false;

}


Heapsort

HeapSort

  • Heap can be used for sorting. Two step process:

    • Step 1: the data is put in a heap.

    • Step 2: the data are extracted from the heap in sorted order.

  • HeapSort based on the idea that heap always has the smallest or largest element at the root.


Adt heap implementation

ADT Heap: Implementation

//This method extracts elements in sorted order from the heap. Heap size becomes 0.

public void HeapSort(){

while(size > 1){

swap(heap, 1, size);

size--;

SiftDown(1);

}

//Display the sorted elements.

for(inti = 1; i <= maxsize; i++){

System.out.println(heap[i].get_priority().get_value());

}

}


Adt heap implementation1

ADT Heap: Implementation

//This method extracts elements in sorted order from the heap. Heap size becomes 0.

public void HeapSort(){

while(size > 1){

swap(heap, 1, size);

size--;

SiftDown(1);

}

//Display the sorted elements.

for(inti = 1; i <= maxsize; i++){

System.out.println(heap[i].get_priority().get_value());

}

}

Loop the number of elements in the array


Adt heap implementation2

ADT Heap: Implementation

//This method extracts elements in sorted order from the heap. Heap size becomes 0.

public void HeapSort(){

while(size > 1){

swap(heap, 1, size);

size--;

SiftDown(1);

}

//Display the sorted elements.

for(inti = 1; i <= maxsize; i++){

System.out.println(heap[i].get_priority().get_value());

}

}

Swap first element (root) with last element

In the heap array


Adt heap implementation3

ADT Heap: Implementation

//This method extracts elements in sorted order from the heap. Heap size becomes 0.

public void HeapSort(){

while(size > 1){

swap(heap, 1, size);

size--;

SiftDown(1);

}

//Display the sorted elements.

for(inti = 1; i <= maxsize; i++){

System.out.println(heap[i].get_priority().get_value());

}

}

Each time reduce the size

(size define last element which will be used with swap/SiftDown)


Adt heap implementation4

ADT Heap: Implementation

//This method extracts elements in sorted order from the heap. Heap size becomes 0.

public void HeapSort(){

while(size > 1){

swap(heap, 1, size);

size--;

SiftDown(1);

}

//Display the sorted elements.

for(inti = 1; i <= maxsize; i++){

System.out.println(heap[i].get_priority().get_value());

}

}

SiftDown the swapped element (last element) from the rootdown the heap until it satisfies heap conditions.


Adt heap implementation5

ADT Heap: Implementation

//This method extracts elements in sorted order from the heap. Heap size becomes 0.

public void HeapSort(){

while(size > 1){

swap(heap, 1, size);

size--;

SiftDown(1);

}

//Display the sorted elements.

for(inti = 1; i <= maxsize; i++){

System.out.println(heap[i].get_priority().get_value());

}

}

Repeat until the entire heap array is sorted

If it is min-heap, it will be sorted in descending order

If it is max-heap, it will be sorted in ascending order


Adt heap implementation6

ADT Heap: Implementation

//This method extracts elements in sorted order from the heap. Heap size becomes 0.

public void HeapSort(){

while(size > 1){

swap(heap, 1, size);

size--;

SiftDown(1);

}

//Display the sorted elements.

for(inti = 1; i <= maxsize; i++){

System.out.println(heap[i].get_priority().get_value());

}

}

Print the sorted array

(print priorities values)


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