bubblesort.ppt

7/28/2019 bubbleSort.ppt

1/101

How to make a cup of tea


2/101

1. Put a cup of water to boil

2. Take 3/4 piece of ginger

3. Add the ginger to the water4. Then pour over some tea-leaves

5. Wait until leaves are settled at the bottom of the pot.

6. Pour into mug,add sugar and enjoy the tea !


3/101

So.......Algorithm? In simple terms, is a series of instructions to solve a

problem (complete a task)

Problems can be in any form How to go from Curzon Hall to NewMarket

Explain how to tie shoelaces to a five year old child

Find largest number from a set of number

Sort a given set of number


4/101

Remember Computers only

do things that you have told itto do !!!


5/101

Example: Selection Problem

Given a list of N numbers, determine the kth largest,

where k N.

Algorithm 1:

(1) Read N numbers into an array

(2) Sort the array in decreasing order by some

simple algorithm

(3) Return the element in position k


6/101

Bubble Sort


7/101

Sorting

Sorting takes an unordered collection and

makes it an ordered one.

512354277 101

1 2 3 4 5 6

5 12 35 42 77 101

1 2 3 4 5 6


8/101

"Bubbling Up" the Largest Element

Traverse a collection of elements

Move from the front to the end

Bubble the largest value to the end usingpair-wise comparisons and swapping

512354277 101

1 2 3 4 5 6


9/101





512354277 101

1 2 3 4 5 6

Swap42 77


10/101





512357742 101

1 2 3 4 5 6

Swap35 77


11/101





512773542 101

1 2 3 4 5 6

Swap12 77


12/101





577123542 101

1 2 3 4 5 6

No need to swap


13/101





577123542 101

1 2 3 4 5 6

Swap5 101


14/101





77123542 5

1 2 3 4 5 6

101

Largest value correctly placed


15/101

Items of Interest

Notice that only the largest value is

correctly placed

All other values are still out of order

So we need to repeat this process

77123542 5

1 2 3 4 5 6

101

Largest value correctly placed


16/101

Repeat Bubble Up How Many Times?

If we have N elements

And if each time we bubble an element,

we place it in its correct location

Then we repeat the bubble upprocess N 1 times.

This guarantees well correctlyplace all N elements.


17/101

Bubbling All the Elements

77123542 5

1 2 3 4 5 6

101

5421235 77

1 2 3 4 5 6

101

4253512 77

1 2 3 4 5 6

101

4235512 77

1 2 3 4 5 6

101

4235125 77

1 2 3 4 5 6

101

N-

1


18/101

The Bubble Up Algorithm

n = totalData

for i=1 to i=n-1

for j=1 to j=n-1

if number[j]>number[j+1]

swap(number[j],number[j+1])


19/101

No, Swap isnt built in.

Procedure Swap(a, b)

t = a

a = bb = t

LB


20/101

Reducing the Number of Comparisons

12354277 101

1 2 3 4 5 6

5

77123542 5

1 2 3 4 5 6

101

5421235 77

1 2 3 4 5 6

101

4253512 77

1 2 3 4 5 6

101

4235512 77

1 2 3 4 5 6

101


21/101

Reducing the Number of Comparisons

On the Nthbubble up, we only need todo MAX-N comparisons.

For example:

This is the 4thbubble up

MAX is 6

Thus we have 2 comparisons to do

4253512 771 2 3 4 5 6

101


22/101

Putting It All Together


23/101

The Bubble Up Algorithm (Extended

)n = totalData

for i=1 to i=n-1

for j=1 to j=n-1-iif number[j]>number[j+1]



24/101

Already Sorted Collections?

What if the collection was already sorted?

What if only a few elements were out of place and

after a couple of bubble ups, the collection was

sorted?

We want to be able to detect this

and stop early!

4235125 77

1 2 3 4 5 6

101


25/101

Using a Boolean Flag

We can use a boolean variable to determine if any

swapping occurred during the bubble up.

If no swapping occurred, then we know that the

collection is already sorted!

This boolean flag needs to be reset after eachbubble up.


26/101

The Bubble Up Algorithm (Extended

)n = totalData

finish = false

for i=1 to i=n-1

if finish

break

finish = true

for j=1 to j=n-1-iif number[j]>number[j+1]


finish = false


27/101

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


28/101

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


29/101

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


30/101

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


31/101

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


32/101

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


33/101

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


34/101

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


35/101

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


36/101

An Animated Example

671445 98 6 3323 42

1 2 3 4 5 6 7 8

to_do

index

7

3

N 8

Swap

did_swap true


37/101

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


38/101

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


39/101

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


40/101

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


41/101

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


42/101

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


43/101

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


44/101

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


45/101

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


46/101

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


47/101

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


48/101

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


49/101

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


50/101

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


51/101


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


52/101


331445 6 67 4223 98

1 2 3 4 5 6 7 8

to_do

index

6

2

N 8 did_swap false


53/101


331445 6 67 4223 98

1 2 3 4 5 6 7 8

to_do

index

6

2

N 8 did_swap false

Swap


54/101


334514 6 67 4223 98

1 2 3 4 5 6 7 8

to_do

index

6

2

N 8 did_swap true

Swap


55/101


334514 6 67 4223 98

1 2 3 4 5 6 7 8

to_do

index

6

3

N 8 did_swap true


56/101


334514 6 67 4223 98

1 2 3 4 5 6 7 8

to_do

index

6

3

N 8 did_swap true

Swap


57/101


33614 45 67 4223 98

1 2 3 4 5 6 7 8

to_do

index

6

3

N 8 did_swap true

Swap


58/101


33614 45 67 4223 98

1 2 3 4 5 6 7 8

to_do

index

6

4

N 8 did_swap true


59/101


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


60/101


33614 45 67 4223 98

1 2 3 4 5 6 7 8

to_do

index

6

5

N 8 did_swap true


61/101


33614 45 67 4223 98

1 2 3 4 5 6 7 8

to_do

index

6

5

N 8 did_swap true

Swap


62/101


67614 45 33 4223 98

1 2 3 4 5 6 7 8

to_do

index

6

5

N 8 did_swap true

Swap


63/101


67614 45 33 4223 98

1 2 3 4 5 6 7 8

to_do

index

6

6

N 8 did_swap true


64/101


67614 45 33 4223 98

1 2 3 4 5 6 7 8

to_do

index

6

6

N 8 did_swap true

Swap


65/101


42614 45 33 6723 98

1 2 3 4 5 6 7 8

to_do

index

6

6

N 8 did_swap true

Swap


66/101

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


67/101

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


68/101

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


69/101

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


70/101

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


71/101

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


72/101

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


73/101

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


74/101

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


75/101

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


76/101

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


77/101

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


78/101

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


79/101

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


80/101

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


81/101

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


82/101

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


83/101


45236 33 42 6714 98

1 2 3 4 5 6 7 8

to_do

index

4

1

N 8 did_swap false

Swap


84/101


452314 33 42 676 98

1 2 3 4 5 6 7 8

to_do

index

4

1

N 8 did_swap true

Swap


85/101


452314 33 42 676 98

1 2 3 4 5 6 7 8

to_do

index

4

2

N 8 did_swap true


86/101


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


87/101


452314 33 42 676 98

1 2 3 4 5 6 7 8

to_do

index

4

3

N 8 did_swap true


88/101


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


89/101


452314 33 42 676 98

1 2 3 4 5 6 7 8

to_do

index

4

4

N 8 did_swap true


90/101


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


91/101

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


92/101

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


93/101

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


94/101

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


95/101

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


96/101

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


97/101

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


98/101

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


99/101

Finished Early

452314 33 42 676 98

1 2 3 4 5 6 7 8

to_do

index

3

4

N 8 did_swap false

We didnt do any swapping,

so all of the other elements

must be correctly placed.

We can skip the last two

passes of the outer loop.


100/101

Summary

Bubble Up algorithm will move largestvalue to its correct location (to the right)

Repeat Bubble Up until all elements are

correctly placed:

Maximum of N-1 times

Can finish early ifno swapping occurs

We reduce the number of elements we

compare each time one is correctly placed

LB


101/101

Truth in CS Act

NOBODY EVER USES BUBBLE SORT

NOBODY

NOT EVER

BECAUSE IT IS EXTREMELY INEFFICIENT

bubblesort.ppt

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