# 0.6 Sorting  (Page 7/20)

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Selection sort can be implemented as a stable sort . If, rather than swapping in step 2, the minimum value is inserted into the first position (that is, all intervening items moved down), the algorithm is stable. However, this modification leads to Θ(n2 ) writes, eliminating the main advantage of selection sort over insertion sort, which is always stable.

## 6.1.3. bubble sort

Bubble sort is a simple sorting algorithm . It works by repeatedly stepping through the list to be sorted, comparing two items at a time and swapping them if they are in the wrong order. The pass through the list is repeated until no swaps are needed, which means the list is sorted. The algorithm gets its name from the way smaller elements "bubble" to the top (i.e. the beginning) of the list via the swaps. (Another opinion: it gets its name from the way greater elements "bubble" to the end.) Because it only uses comparisons to operate on elements, it is a comparison sort . This is the easiest comparison sort to implement.

A simple way to express bubble sort in pseudocode is as follows:

procedure bubbleSort( A : list of sortable items ) defined as:

do

swapped := false

for each i in 0 to length( A ) - 2 do:

if A[ i ]>A[ i + 1 ] then

swap( A[ i ], A[ i + 1 ])

swapped := true

end if

end for

while swapped

end procedure

The algorithm can also be expressed as:

procedure bubbleSort( A : list of sortable items ) defined as:

for each i in 1 to length(A) do:

for each j in length(A) downto i + 1 do:

if A[ j ]<A[ j - 1 ] then

swap( A[ j ], A[ j - 1 ])

end if

end for

end for

end procedure

This difference between this and the first pseudocode implementation is discussed later in the article .

## Best-case performance

Bubble sort has best-case complexity Ω (n). When a list is already sorted, bubblesort will pass through the list once, and find that it does not need to swap any elements. Thus bubble sort will make only n comparisons and determine that list is completely sorted. It will also use considerably less time than О(n²) if the elements in the unsorted list are not too far from their sorted places. MKH...

## Rabbits and turtles

The positions of the elements in bubble sort will play a large part in determining its performance. Large elements at the top of the list do not pose a problem, as they are quickly swapped downwards. Small elements at the bottom, however, as mentioned earlier, move to the top extremely slowly. This has led to these types of elements being named rabbits and turtles, respectively.

Various efforts have been made to eliminate turtles to improve upon the speed of bubble sort. Cocktail sort does pretty well, but it still retains O(n2) worst-case complexity. Comb sort compares elements large gaps apart and can move turtles extremely quickly, before proceeding to smaller and smaller gaps to smooth out the list. Its average speed is comparable to faster algorithms like Quicksort .

## Alternative implementations

One way to optimize bubble sort is to note that, after each pass, the largest element will always move down to the bottom. During each comparison, it is clear that the largest element will move downwards. Given a list of size n, the nth element will be guaranteed to be in its proper place. Thus it suffices to sort the remaining n - 1 elements. Again, after this pass, the n - 1th element will be in its final place.

find the 15th term of the geometric sequince whose first is 18 and last term of 387
The given of f(x=x-2. then what is the value of this f(3) 5f(x+1)
hmm well what is the answer
Abhi
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20/(×-6^2)
Salomon
okay, so you have 6 raised to the power of 2. what is that part of your answer
I don't understand what the A with approx sign and the boxed x mean
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Salomon
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Salomon
I got X =-6
Salomon
ok. so take the square root of both sides, now you have plus or minus the square root of 20= x-6
oops. ignore that.
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Abhi
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Abhi
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Abhi
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China
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what is system testing
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Stotaw
In this morden time nanotechnology used in many field . 1-Electronics-manufacturad IC ,RAM,MRAM,solar panel etc 2-Helth and Medical-Nanomedicine,Drug Dilivery for cancer treatment etc 3- Atomobile -MEMS, Coating on car etc. and may other field for details you can check at Google
Azam
anybody can imagine what will be happen after 100 years from now in nano tech world
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silver nanoparticles could handle the job?
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not now but maybe in future only AgNP maybe any other nanomaterials
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I'm interested in Nanotube
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this technology will not going on for the long time , so I'm thinking about femtotechnology 10^-15
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