HEAPS

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HEAPS
Definition A max tree is a tree in which the key
value in each node is no smaller than the key
values in its children (if any). A max heap is
a complete binary tree that is also a max
tree Definition A min tree is a tree in which
the key value in each node is no larger than the
key values in its children (if any). A min heap
is a complete binary tree that is also a min tree.
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Heaps as a Abstract Data Type

• When viewed as an ADT, a max heap is very simple.
  In particular the only basic operations are
• Creation of an empty heap
• Insertion of a new element into the heap
• Deletion of the largest element from the heap

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Samples of Max Heaps
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Samples of Min Heaps
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Example Max Heap Object Methods

• Construct (initialize) a max heap object using
  data elements of an array A
• Build a max heap object from an array A of n
  data elements
• Destroy (delete) a heap object and an array A
• Compare data elements
• Swap data elements
• Rebuild a max heap
• Add/insert an element into a max heap object
• Delete an element from a max heap object
• Do a heap sort for an array A using a max heap
  object
• Display (print) a heap object at each iteration
  of heap sort
• Print a max heap object

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Creation of a Heap

• define MAX_ELEMENTS 200 / maximum heap
  size 1 /
• define HEAP_FULL(n) (n MAX_ELEMENTS 1)
• define HEAP_EMPTY(n) (!n)
• typedef struct (
• int key
• / other fields /
• ) element
• element heap(MAX_ELEMENTS)
• int n 0

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Insertion into a max heap
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(a) Heap before insertion
(b) Initial location of new node
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(c) Insert 5 into heap (a)
(d) Insert 21 into heap (a)
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• Void insert_max_heap(element item, int n) /
  insert item into a max heap of current size n
  / int i if (HEAP_FULL(n)) fprintf(stderr,
  The heap is full. \n) exit(1) i
  (n) while((i ! 1) (item.key gt
  heapi/2.key)) heapi heapi/2
• i / 2 heapi item