14085 Bubble Merge

8/6/2019 14085 Bubble Merge

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Bubble Sort

Merge Sort


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Bubble Sort


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Sorting

Sorting takes an unordered collection and

makes it an ordered one.

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1 2 3 4 5 6

5 12 35 42 77 101

1 2 3 4 5 6


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"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


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512354277 101

1 2 3 4 5 6

Swap

42 77


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512357742 101

1 2 3 4 5 6

Swap

35 77


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512773542 101

1 2 3 4 5 6

Swap12 77


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577123542 101

1 2 3 4 5 6

No need to swap


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577123542 101

1 2 3 4 5 6

Swap5 101


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77123542 5

1 2 3 4 5 6

101

Largest value correctly placed


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The Bubble Up Algorithm

index A[index + 1]) then

Swap(A[index], A[index + 1])

endif

index


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No, Swap isnt built in.

Procedure Swap(a, b isoftype in/outNum)

t isoftypeNum

t


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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


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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.


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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 771 2 3 4 5 6101

4235125 77

1 2 3 4 5 6

101

N

-1


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Reducing the Number of Comparisons

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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


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Reducing the Number of Comparisons

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

For example:

This is the 4th bubble up

MAX is 6

Thus we have 2 comparisons to do

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1 2 3 4 5 6

101


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Putting It All Together


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N is // Size of Array

Arr_Type definesa Array[1..N] of Num

Procedure Swap(n1, n2 isoftype in/out Num)temp isoftype Num

temp


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procedure Bubblesort(A isoftype in/out Arr_Type)

to_do, index isoftype Num

to_do A[index + 1]) then

Swap(A[index], A[index + 1])

endif

index


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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!

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1 2 3 4 5 6

101


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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.


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did_swap isoftype Boolean

did_swap


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An Animated Example

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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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1 2 3 4 5 6 7 8

to_do

index

6

2

N 8 did_swap false


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1 2 3 4 5 6 7 8

to_do

index

6

2

N 8 did_swap false

Swap


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1 2 3 4 5 6 7 8

to_do

index

6

2

N 8 did_swap true

Swap


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1 2 3 4 5 6 7 8

to_do

index

6

3

N 8 did_swap true


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1 2 3 4 5 6 7 8

to_do

index

6

3

N 8 did_swap true

Swap


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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


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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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1 2 3 4 5 6 7 8

to_do

index

6

5

N 8 did_swap true


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1 2 3 4 5 6 7 8

to_do

index

6

5

N 8 did_swap true

Swap


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1 2 3 4 5 6 7 8

to_do

index

6

5

N 8 did_swap true

Swap


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1 2 3 4 5 6 7 8

to_do

index

6

6

N 8 did_swap true


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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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1 2 3 4 5 6 7 8

to_do

index

4

1

N 8 did_swap false


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1 2 3 4 5 6 7 8

to_do

index

4

1

N 8 did_swap false

Swap


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1 2 3 4 5 6 7 8

to_do

index

4

1

N 8 did_swap true

Swap


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1 2 3 4 5 6 7 8

to_do

index

4

2

N 8 did_swap true


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1 2 3 4 5 6 7 8

to_do

index

4

2

N 8 did_swap true

No Swap


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1 2 3 4 5 6 7 8

to_do

index

4

3

N 8 did_swap true

No Swap


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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

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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

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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

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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

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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

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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

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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

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1 2 3 4 5 6 7 8

to_do

index

3

3

N 8 did_swap false

No Swap


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After Fifth Pass of Outer Loop

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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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Finished Early

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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.


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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


98/151

Truth in CS Act

NOBODY EVER USES BUBBLE SORT

NOBODY

NOT EVER

BECAUSE IT IS EXTREMELY INEFFICIENT


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Questions?


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Mergesort


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Sorting

Sorting takes an unordered collection and

makes it an ordered one.

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1 2 3 4 5 6

5 12 35 42 77 101

1 2 3 4 5 6


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M t


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Mergesort

A divide-and-conquer algorithm:

Divide the unsorted array into 2 halves until the

sub-arrays only contain one element

Merge the sub-problem solutions together:

Compare the sub-arrays first elements Remove the smallest element and put it into

the result array

Continue the process until all elements have

been put into the result array

37 23 6 89 15 12 2 19


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Algorithm

Mergesort(Passed an array)if array size > 1

Divide array in half

Call Mergesort on first half.

Call Mergesort on second half.

Merge two halves.

Merge(Passed two arrays)

Compare leading element in each array

Select lower and place in new array.(If one input array is empty then place

remainder of other array in output array)

LB


105/151

More TRUTH in CS

We dont really pass in two arrays!

We pass in one array with indicator variables which

tell us where one set of data starts and finishes and

where the other set of data starts and finishes.

Honest.

s1 f1 s2 f2

LB


106/151

Algorithm

Mergesort(Passed an array)if array size > 1

Divide array in half

Call Mergesort on first half.

Call Mergesort on second half.

Merge two halves.

Merge(Passed two arrays)

Compare leading element in each array

Select lower and place in new array.(If one input array is empty then place

remainder of other array in output array)

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Merge

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Merge

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Merge

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Merge

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14

Merge

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Merge

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Merge

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14

23 45

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Merge

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14 23

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Merge

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14 23 45

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Merge

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4523 1498

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676 33 42

23 98 4514

14 23 45 98

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676 33 42

676

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676

Merge

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676

6

Merge

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14 23 45 98

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676

67

Merge

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14 23 45 98

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676 33 42

23 98 4514 676

14 23 45 98

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Merge

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14 23 45 98

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4523 1498

2398 45 14

676 33 42

676 33 42

Merge

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14 23 45 98

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4523 1498

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676 33 42

676 33 42

Merge

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14 23 45 98

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Merge

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676 33 42

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Merge

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14 23 45 98 6

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Merge

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14 23 45 98 6 33

67 42

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Merge

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14 23 45 98 6 33 42

67

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Merge

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14 23 45 98 6 33 42 67

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Merge

23 98 4514 676 4233

23 45 98 33 42 6714 6

674523 14 6 3398 42


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4523 1498

2398 45 14

676 33 42

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Merge

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23 45 98 6 42 67

6

14 33

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674523 14 6 3398 42

4523 1498

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Merge

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14 45 98 6 42 67

6 14

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676 33 42

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Merge

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14 23 98 6 42 67

6 14 23

45 33


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676 33 42

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Merge

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14 23 98 6 33 42

6 14 23 33 42

45 67

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Merge

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14 23 45 6 33 42

6 14 23 33 42 45

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4523 1498

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Merge

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14 23 45 98 6 33 42 67

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676 33 42

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Merge

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14 23 45 98 6 33 42 67

6 14 23 33 42 45 67 98

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14 23 45 98 6 33 42 67

6 14 23 33 42 45 67 98

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147/151

6 14 23 33 42 45 67 98

Summary


148/151

Summary

Divide the unsorted collection into two

Until the sub-arrays only contain one

element

Then merge the sub-problem solutions

together


149/151

Questions?


150/151

Review?


151/151

14085 Bubble Merge

Documents

Transcript of 14085 Bubble Merge