all types of Sorting

8/2/2019 all types of Sorting

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SORTING

By:

Name :- Arshpreet Singh

Section: - RK22H1B30

Reg No. 11107537


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Properties

The two Main properties of sorting techniques are:

Stable: If the sorting algorithm preserves

the relative order of any two equal elements, thenthe sorting algorithm is stable.

In Place: If an algorithm does not require an extra

memory space except for few memory units, thenthe algorithm is said to be in place.


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Sorting Algorithms

Various sorting algorithms are

Bubble Sort

Selection Sort

Insertion Sort

Quick Sort Merge Sort


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Bubble Sort

This is one of the most simplest sorting

technique and most straight forward method

of sorting.

In this sorting technique, the adjacent

elements in the list are compared and

exchanged if they are out of order.

This is also called as Sinking Sort


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Time Complexity(Bubble sort)

The time complexity of bubble sort in all

three cases (best, average & worst)is

Which is not efficient compare to other sorting

techniques.

T(n) = (n^2)


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An Animated Example

674523 14 6 3398 42

1 2 3 4 5 6 7 8

to_do

index

7

N 8 did_swap true


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An Animated Example

674523 14 6 3398 42

1 2 3 4 5 6 7 8

to_do

index

7

1

N 8 did_swap false


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An Animated Example

674523 14 6 3398 42

1 2 3 4 5 6 7 8

to_do

index

7

1

N 8

Swap

did_swap false


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An Animated Example

674598 14 6 3323 42

1 2 3 4 5 6 7 8

to_do

index

7

1

N 8

Swap

did_swap true


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An Animated Example

674598 14 6 3323 42

1 2 3 4 5 6 7 8

to_do

index

7

2

N 8 did_swap true


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An Animated Example

674598 14 6 3323 42

1 2 3 4 5 6 7 8

to_do

index

7

2

N 8

Swap

did_swap true


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An Animated Example

679845 14 6 3323 42

1 2 3 4 5 6 7 8

to_do

index

7

2

N 8

Swap

did_swap true


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An Animated Example

679845 14 6 3323 42

1 2 3 4 5 6 7 8

to_do

index

7

3

N 8 did_swap true


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An Animated Example

679845 14 6 3323 42

1 2 3 4 5 6 7 8

to_do

index

7

3

N 8

Swap

did_swap true


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An Animated Example

671445 98 6 3323 42

1 2 3 4 5 6 7 8

to_do

index

7

4

N 8 did_swap true


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An Animated Example

671445 98 6 3323 42

1 2 3 4 5 6 7 8

to_do

index

7

4

N 8

Swap

did_swap true


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An Animated Example

671445 6 98 3323 42

1 2 3 4 5 6 7 8

to_do

index

7

4

N 8

Swap

did_swap true


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An Animated Example

671445 6 98 3323 42

1 2 3 4 5 6 7 8

to_do

index

7

5

N 8 did_swap true


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An Animated Example

671445 6 98 3323 42

1 2 3 4 5 6 7 8

to_do

index

7

5

N 8

Swap

did_swap true


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An Animated Example

981445 6 67 3323 42

1 2 3 4 5 6 7 8

to_do

index

7

5

N 8

Swap

did_swap true


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An Animated Example

981445 6 67 3323 42

1 2 3 4 5 6 7 8

to_do

index

7

6

N 8 did_swap true


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An Animated Example

981445 6 67 3323 42

1 2 3 4 5 6 7 8

to_do

index

7

6

N 8

Swap

did_swap true


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An Animated Example

331445 6 67 9823 42

1 2 3 4 5 6 7 8

to_do

index

7

6

N 8

Swap

did_swap true


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An Animated Example

331445 6 67 9823 42

1 2 3 4 5 6 7 8

to_do

index

7

7

N 8 did_swap true


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An Animated Example

331445 6 67 9823 42

1 2 3 4 5 6 7 8

to_do

index

7

7

N 8

Swap

did_swap true


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An Animated Example

331445 6 67 4223 98

1 2 3 4 5 6 7 8

to_do

index

7

7

N 8

Swap

did_swap true


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After First Pass of Outer Loop

331445 6 67 4223 98

1 2 3 4 5 6 7 8

to_do

index

7

8

N 8

Finished first Bubble Up

did_swap true


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The Second Bubble Up

331445 6 67 4223 98

1 2 3 4 5 6 7 8

to_do

index

6

1

N 8 did_swap false


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331445 6 67 4223 98

1 2 3 4 5 6 7 8

to_do

index

6

1

N 8 did_swap false

No Swap


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331445 6 67 4223 98

1 2 3 4 5 6 7 8

to_do

index

6

2

N 8 did_swap false


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331445 6 67 4223 98

1 2 3 4 5 6 7 8

to_do

index

6

2

N 8 did_swap false

Swap


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334514 6 67 4223 98

1 2 3 4 5 6 7 8

to_do

index

6

2

N 8 did_swap true

Swap


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334514 6 67 4223 98

1 2 3 4 5 6 7 8

to_do

index

6

3

N 8 did_swap true


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334514 6 67 4223 98

1 2 3 4 5 6 7 8

to_do

index

6

3

N 8 did_swap true

Swap


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33614 45 67 4223 98

1 2 3 4 5 6 7 8

to_do

index

6

3

N 8 did_swap true

Swap


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33614 45 67 4223 98

1 2 3 4 5 6 7 8

to_do

index

6

4

N 8 did_swap true

No Swap


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33614 45 67 4223 98

1 2 3 4 5 6 7 8

to_do

index

6

5

N 8 did_swap true


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33614 45 67 4223 98

1 2 3 4 5 6 7 8

to_do

index

6

5

N 8 did_swap true

Swap


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67614 45 33 4223 98

1 2 3 4 5 6 7 8

to_do

index

6

5

N 8 did_swap true

Swap


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67614 45 33 4223 98

1 2 3 4 5 6 7 8

to_do

index

6

6

N 8 did_swap true


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67614 45 33 4223 98

1 2 3 4 5 6 7 8

to_do

index

6

6

N 8 did_swap true

Swap


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42614 45 33 6723 98

1 2 3 4 5 6 7 8

to_do

index

6

6

N 8 did_swap true

Swap


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After Second Pass of Outer Loop

42614 45 33 6723 98

1 2 3 4 5 6 7 8

to_do

index

6

7

N 8 did_swap true

Finished second Bubble Up


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The Third Bubble Up

42614 45 33 6723 98

1 2 3 4 5 6 7 8

to_do

index

5

1

N 8 did_swap false


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The Third Bubble Up

42614 45 33 6723 98

1 2 3 4 5 6 7 8

to_do

index

5

1

N 8 did_swap false

Swap


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The Third Bubble Up

42623 45 33 6714 98

1 2 3 4 5 6 7 8

to_do

index

5

1

N 8 did_swap true

Swap


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The Third Bubble Up

42623 45 33 6714 98

1 2 3 4 5 6 7 8

to_do

index

5

2

N 8 did_swap true


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The Third Bubble Up

42623 45 33 6714 98

1 2 3 4 5 6 7 8

to_do

index

5

2

N 8 did_swap true

Swap


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The Third Bubble Up

42236 45 33 6714 98

1 2 3 4 5 6 7 8

to_do

index

5

2

N 8 did_swap true

Swap


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The Third Bubble Up

42236 45 33 6714 98

1 2 3 4 5 6 7 8

to_do

index

5

3

N 8 did_swap true


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The Third Bubble Up

42236 45 33 6714 98

1 2 3 4 5 6 7 8

to_do

index

5

3

N 8 did_swap true

No Swap


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The Third Bubble Up

42236 45 33 6714 98

1 2 3 4 5 6 7 8

to_do

index

5

4

N 8 did_swap true


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The Third Bubble Up

42236 45 33 6714 98

1 2 3 4 5 6 7 8

to_do

index

5

4

N 8 did_swap true

Swap


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The Third Bubble Up

42236 33 45 6714 98

1 2 3 4 5 6 7 8

to_do

index

5

4

N 8 did_swap true

Swap


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The Third Bubble Up

42236 33 45 6714 98

1 2 3 4 5 6 7 8

to_do

index

5

5

N 8 did_swap true


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The Third Bubble Up

42236 33 45 6714 98

1 2 3 4 5 6 7 8

to_do

index

5

5

N 8 did_swap true

Swap


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The Third Bubble Up

45236 33 42 6714 98

1 2 3 4 5 6 7 8

to_do

index

5

5

N 8 did_swap true

Swap


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After Third Pass of Outer Loop

45236 33 42 6714 98

1 2 3 4 5 6 7 8

to_do

index

5

6

N 8 did_swap true

Finished third Bubble Up


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The Fourth Bubble Up

45236 33 42 6714 98

1 2 3 4 5 6 7 8

to_do

index

4

1

N 8 did_swap false


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45236 33 42 6714 98

1 2 3 4 5 6 7 8

to_do

index

4

1

N 8 did_swap false

Swap


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452314 33 42 676 98

1 2 3 4 5 6 7 8

to_do

index

4

1

N 8 did_swap true

Swap


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452314 33 42 676 98

1 2 3 4 5 6 7 8

to_do

index

4

2

N 8 did_swap true


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452314 33 42 676 98

1 2 3 4 5 6 7 8

to_do

index

4

2

N 8 did_swap true

No Swap


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452314 33 42 676 98

1 2 3 4 5 6 7 8

to_do

index

4

3

N 8 did_swap true


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452314 33 42 676 98

1 2 3 4 5 6 7 8

to_do

index

4

3

N 8 did_swap true

No Swap


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452314 33 42 676 98

1 2 3 4 5 6 7 8

to_do

index

4

4

N 8 did_swap true


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452314 33 42 676 98

1 2 3 4 5 6 7 8

to_do

index

4

4

N 8 did_swap true

No Swap


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After Fourth Pass of Outer Loop

452314 33 42 676 98

1 2 3 4 5 6 7 8

to_do

index

4

5

N 8 did_swap true

Finished fourth Bubble Up


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The Fifth Bubble Up

452314 33 42 676 98

1 2 3 4 5 6 7 8

to_do

index

3

1

N 8 did_swap false


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The Fifth Bubble Up

452314 33 42 676 98

1 2 3 4 5 6 7 8

to_do

index

3

1

N 8 did_swap false

No Swap


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The Fifth Bubble Up

452314 33 42 676 98

1 2 3 4 5 6 7 8

to_do

index

3

2

N 8 did_swap false


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The Fifth Bubble Up

452314 33 42 676 98

1 2 3 4 5 6 7 8

to_do

index

3

2

N 8 did_swap false

No Swap


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The Fifth Bubble Up

452314 33 42 676 98

1 2 3 4 5 6 7 8

to_do

index

3

3

N 8 did_swap false


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The Fifth Bubble Up

452314 33 42 676 98

1 2 3 4 5 6 7 8

to_do

index

3

3

N 8 did_swap false

No Swap

f f f


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After Fifth Pass of Outer Loop

452314 33 42 676 98

1 2 3 4 5 6 7 8

to_do

index

3

4

N 8 did_swap false

Finished fifth Bubble Up


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Selection Sort

In this technique first we find the smallest item in the

list and we exchange it with the first item.

Next, obtain the second smallest item in the list &

exchange it with the second element and so on. Since, the next least item is selected and exchanged

appropriately so that elements are finally sorted ,this

technique is called Selection Sort


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Time Complexity(Selection sort)

The time complexity of selection sort in all

three cases (best, average& worst) is

Which is not efficient compare to other sorting

techniques.

T(n) = (n^2)

S l i S


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Selection Sort

5 1 3 4 6 2

Comparison

Data Movement

Sorted

S l i S


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Selection Sort

5 1 3 4 6 2

Comparison

Data Movement

Sorted

S l i S


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Selection Sort

5 1 3 4 6 2

Comparison

Data Movement

Sorted

S l i S


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Selection Sort

5 1 3 4 6 2

Comparison

Data Movement

Sorted

S l ti S t


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Selection Sort

5 1 3 4 6 2

Comparison

Data Movement

Sorted

S l ti S t


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Selection Sort

5 1 3 4 6 2

Comparison

Data Movement

Sorted

S l ti S t


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Selection Sort

5 1 3 4 6 2

Comparison

Data Movement

Sorted

S l ti S t


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Selection Sort

5 1 3 4 6 2

LargestComparison

Data Movement

Sorted

S l ti S t


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Selection Sort

5 1 3 4 2 6

Comparison

Data Movement

Sorted

S l ti S t


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Selection Sort

5 1 3 4 2 6

Comparison

Data Movement

Sorted

S l ti S t


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Selection Sort

5 1 3 4 2 6

Comparison

Data Movement

Sorted

Selection Sort


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Selection Sort

5 1 3 4 2 6

Comparison

Data Movement

Sorted

Selection Sort


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Selection Sort

5 1 3 4 2 6

Comparison

Data Movement

Sorted

Selection Sort


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Selection Sort

5 1 3 4 2 6

Comparison

Data Movement

Sorted

Selection Sort


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Selection Sort

5 1 3 4 2 6

Comparison

Data Movement

Sorted

Selection Sort


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Selection Sort

5 1 3 4 2 6

Largest

Comparison

Data Movement

Sorted

Selection Sort


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Selection Sort

2 1 3 4 5 6

Comparison

Data Movement

Sorted

Selection Sort


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Selection Sort

2 1 3 4 5 6

Comparison

Data Movement

Sorted

Selection Sort


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Selection Sort

2 1 3 4 5 6

Comparison

Data Movement

Sorted

Selection Sort


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Selection Sort

2 1 3 4 5 6

Comparison

Data Movement

Sorted

Selection Sort


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Selection Sort

2 1 3 4 5 6

Comparison

Data Movement

Sorted

Selection Sort


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Selection Sort

2 1 3 4 5 6

Comparison

Data Movement

Sorted

Selection Sort


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Selection Sort

2 1 3 4 5 6

LargestComparison

Data Movement

Sorted

Selection Sort


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Selection Sort

2 1 3 4 5 6

Comparison

Data Movement

Sorted

Selection Sort


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Selection Sort

2 1 3 4 5 6

Comparison

Data Movement

Sorted

Selection Sort


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Selection Sort

2 1 3 4 5 6

Comparison

Data Movement

Sorted

Selection Sort


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Selection Sort

2 1 3 4 5 6

Comparison

Data Movement

Sorted

Selection Sort


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Selection Sort

2 1 3 4 5 6

Comparison

Data Movement

Sorted

Selection Sort


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Selection Sort

2 1 3 4 5 6

LargestComparison

Data Movement

Sorted

Selection Sort


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Selection Sort

2 1 3 4 5 6

Comparison

Data Movement

Sorted

Selection Sort


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Selection Sort

2 1 3 4 5 6

Comparison

Data Movement

Sorted

Selection Sort


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Selection Sort

2 1 3 4 5 6

Comparison

Data Movement

Sorted

Selection Sort


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Selection Sort

2 1 3 4 5 6

Comparison

Data Movement

Sorted

Selection Sort


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Selection Sort

2 1 3 4 5 6

Largest

Comparison

Data Movement

Sorted


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Selection Sort


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Selection Sort

1 2 3 4 5 6

DONE!ComparisonData Movement

Sorted

Insertion Sort


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se t o So t

In this technique the given list is divided into twoparts:sorted part(left) &unsorted part(right).

The unsorted elements can be placed any of thepositions in the sorted part so that elements towardsleft of boundary are sorted.

As each item is inserted towards the sorted left part,the boundary moves to the right decreasing theunsorted list.

Finally,once the boundary moves to the right most

position,the elements towards the left of boundaryrepresent the sorted list.

l ( )


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Time Complexity(Insertion sort)

The Time complexity of insertion sort is:

Worst case:

Average case:

Best case:

T(n) = (n^2)

T(n) = O(n^2)

T(n) = (n)

Insertion Sort


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Insertion Sort

23 17 45 18 12 22

Insertion Sort


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Insertion Sort

23 17 45 18 12 22

1 2 6543

Insertion Sort


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Insertion Sort

23 17 45 18 12 22

1 2 6543

1 2 6543

Insertion Sort


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Insertion Sort

23

17 45 18 12 22

1 2 6543

1 2 6543

Insertion Sort


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2317

45 18 12 22

1 2 6543

1 2 6543

Insertion Sort


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2317 45

18 12 22

1 2 6543

1 2 6543

Insertion Sort


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2317 4518

12 22

1 2 6543

1 2 6543

Insertion Sort


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2317 4518

12 22

1 2 6543

1 2 6543

Insertion Sort


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2317 451812

22

1 2 6543

1 2 6543

Insertion Sort


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2317 451812

22

1 2 6543

1 2 6543

Insertion Sort


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1812 2217 23 45

1 2 6543

1 2 6543

Merge sort


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g

In merge sort, a given array of elements is dividedinto two parts.

The left part of the array as well as the right part of

the array is sorted recursively.

Later, the sorted left part and the sorted right part

are finally merged into a single sorted vector.

The process of merging of two sorted vectors into

a single sorted vector is called simple merge.

Time complexity(Merge sort)


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Time complexity(Merge sort)

The time complexity of Merge sort in all threecases (best,average&worst) is:

T(n) = (nlog2n)

Merge Sort


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1062 5 3 19 7

1 2 3 4 5 6 7 8

Merge Sort


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1062 5 3 19 7

1 2 3 4 5 6 7 8

Merge Sort


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Greatest Digit comes

first Place

1062 5 3 19 7

2 9

Merge Sort


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1062 5 3 19 7

1 72 9 3 105 6

Merge Sort


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1062 5 3 19 7

1 72 9 3 105 6

2

Greatest Digit comes first Place

Merge Sort


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1062 5 3 19 7

1 72 9 3 105 6

2 5


Merge Sort


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1062 5 3 19 7

1 72 9 3 105 6

2 5 6


Merge Sort


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1062 5 3 19 7

1 72 9 3 105 6

2 5 6 9

Merge Sort


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1062 5 3 19 7

1 72 9 3 105 6

2 5 6 9 1 3 7 10

Merge Sort


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1062 5 3 19 7

1 72 9 3 105 6

2 5 6 9 1 3 7 10

1

Merge Sort


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106

25

3 19 7

1 72 9 3 105 6

2 5 6 9 1 3 7 10

1 2

Merge Sort


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106

25

3 19 7

1 72 9 3 105 6

2 5 6 9 1 3 7 10

1 2 3

Merge Sort


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106

25

3 19 7

1 72 9 3 105 6

2 5 6 9 1 3 7 10

1 2 3 5

Merge Sort


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106

25

3 19 7

1 72 9 3 105 6

2 5 6 9 1 3 7 10

1 2 3 5 6

Merge Sort


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106

25

3 19 7

1 72 9 3 105 6

2 5 6 9 1 3 7 10

1 2 3 5 6 7

Merge Sort


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106

25 3

19

7

1 72 9 3 105 6

2 5 6 9 1 3 7 10

1 2 3 5 6 7 9

Merge Sort


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106

25 3

19

7

1 72 9 3 105 6

2 5 6 9 1 3 7 10

1 2 3 5 6 7 9 10

Conclusion


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Conclusion

By comparing all the sorting techniquesMerge sort time complexity is less in all three

cases (time consuming is less).

So, Merge sort is the most efficient techniquewhen compare to all other sorting techniques.


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THANK YOU

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