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DATASTRUCTURES

MAHESH GOYANI

MAHATMAGANDHI INSTITUE OF TECHNICALEDUCATION & RESEARCH CENTER

mgoyani@rediffmail.com

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HEAP SORT

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HEAP SORT

A heap is defined as an almost complete binary tree of n nodes such that thevalue of each node is less than or equal to its father.

A [j]

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33

42

33

42

33

42

67

67

42

67

2323

44

44

33

4449

49

42

49

7474

49

74

67

74

Heap Is : 74, 44, 67, 23, 33, 42, 49

HEAP CREATION Input Is : 33, 42, 67, 23, 44, 49, 74

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Input n Element in Heap H

Add new node by incrementing size of heap H: n = n + 1 & LOC = n

While (LOC < 1), Repeat step 4 to 7

PAR = LOC / 2

If (DATA < HA [PAR])

HA [LOC] = DATA

Exit

HA [LOC] = HAP [PAR]

HA [1] = DATA

Exit

INSERT NODE

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996040

8020

10

50 700

85

65

996040

8020

10

50 700

85

65 15

MIN HEAP

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996040

8020

10

50 700

85

65 15

992040

8015

10

50 700

85

65 60

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16

5 11

3 18 16

18 11

3 5 18

16 11

3 5

MAX HEAP

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996040

8020

10

50 700

85

65

DELETE ROOT

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996040

8020

10

50 700

85

65

996040

8020

65

50 700

85

65

DELETE ROOT

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996040

8020

65

700 50

85 996050

8040

20

700 65

85

DELETE ROOT

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Forming the heap from an unsorted arrayForming the heap from an unsorted array

11 26 14 2 19 32 7

32

214711

1926

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Populating the new arrayPopulating the new array

32

214711

1926

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Reforming the heapReforming the heap

32

19

2711

1426

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Repeat the processRepeat the process

32 26

2711

1419

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32 26

14

711

219

Repeat the processRepeat the process

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32 26

19

711

214

Repeat the processRepeat the process

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32 26 19

711

214

Repeat the processRepeat the process

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COMPLEXITY

The heap sort is the slowest of the O(nlog n) sorting algorithms

But unlike the merge and quick sorts it doesn't require massive recursion ormultiple arrays to work. This makes it the most attractive option for very largedata sets of millions of items.