Sorting techniques
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Insertion sort works by scanning an array from left to right and inserting each element into its sorted position in the previously sorted left portion. Quicksort works by partitioning the array around a pivot value, recursively sorting the left and right partitions, and combining the results. It chooses a pivot element and rearranges the array such that all elements smaller than the pivot are to its left and larger elements to its right.
![An Insertion sort is one that sorts a set of
values by inserting values into an existing
sorted List.
Suppose an array a with n elements
a[1],a[2]…a[n] is in memory. The insertion
algo scans a from a[1] to a[n], inserting each
element a[k] into its proper position in the
previously sorted sub Array. That is..](https://image.slidesharecdn.com/sortingtechniques-140910122314-phpapp01/85/Sorting-techniques-2-320.jpg)
![Pass 1. a[1] by itself is trivially sorted
Pass 2. a[2] is inserted either before or after
a[1] so that a[1],a[2] is sorted.
Pass 3. a[3] is inserted into its proper place
in a[1],a[2], that is before a[1],
between a[1] and a[2], or after a[2],
so that they placed in sorted manner.
And so on.](https://image.slidesharecdn.com/sortingtechniques-140910122314-phpapp01/85/Sorting-techniques-3-320.jpg)
![1. Repeat For J = 2 to N
2. Set TEMP = A[J]
3. Set K = J – 1
4. Repeat While (K>=1) and (A[k]>TEMP)
5. Set A[K+1] = A [K]
6. Set K = K – 1
[End of while loop]
7. Set A[K+1] = TEMP
[End of For Loop]
8. Exit](https://image.slidesharecdn.com/sortingtechniques-140910122314-phpapp01/85/Sorting-techniques-5-320.jpg)
![This sorting technique works by partitioning the
array to be sorted. And each partition is in turn
sorted recursively. In partition, one of the array
elements is chosen as a key value. This key value
can be the first element of an array. That is, if a
is an array then key = a[0]. And rest of the array
elements are grouped into two partition such
that
One partition contains elments smaller than the
key value
Another partition contains elements larger than
the key value.](https://image.slidesharecdn.com/sortingtechniques-140910122314-phpapp01/85/Sorting-techniques-6-320.jpg)
![1. If (BEG < END) then
2. Find the element that divides the array into
two parts using subfunction Partition().
3. Quick Sort(Left Half)
4. Quick Sort(Right Half)
[End of If]
5. Exit](https://image.slidesharecdn.com/sortingtechniques-140910122314-phpapp01/85/Sorting-techniques-9-320.jpg)
Sorting techniques
- 1. Prepared By: Er. Sukhvinder Singh
- 2. An Insertion sort is one that sorts a set of values by inserting values into an existing sorted List. Suppose an array a with n elements a[1],a[2]…a[n] is in memory. The insertion algo scans a from a[1] to a[n], inserting each element a[k] into its proper position in the previously sorted sub Array. That is..
- 3. Pass 1. a[1] by itself is trivially sorted Pass 2. a[2] is inserted either before or after a[1] so that a[1],a[2] is sorted. Pass 3. a[3] is inserted into its proper place in a[1],a[2], that is before a[1], between a[1] and a[2], or after a[2], so that they placed in sorted manner. And so on.
- 5. 1. Repeat For J = 2 to N 2. Set TEMP = A[J] 3. Set K = J – 1 4. Repeat While (K>=1) and (A[k]>TEMP) 5. Set A[K+1] = A [K] 6. Set K = K – 1 [End of while loop] 7. Set A[K+1] = TEMP [End of For Loop] 8. Exit
- 6. This sorting technique works by partitioning the array to be sorted. And each partition is in turn sorted recursively. In partition, one of the array elements is chosen as a key value. This key value can be the first element of an array. That is, if a is an array then key = a[0]. And rest of the array elements are grouped into two partition such that One partition contains elments smaller than the key value Another partition contains elements larger than the key value.
- 7. n Partition 1 Partition 2 Values < Key Key Values > Key
- 8. In-place partition in action on a small list. The boxed element is the pivot element, blue elements are less or equal, and red elements are larger.
- 9. 1. If (BEG < END) then 2. Find the element that divides the array into two parts using subfunction Partition(). 3. Quick Sort(Left Half) 4. Quick Sort(Right Half) [End of If] 5. Exit
- 10. 1. Set LEFT = BEG, RIGHT = END and LOC = BEG 2. Beginning with the element pointed by RIGHT, scan the array from right to left, comparing each element with the element pointed by LOC until: 1. Element smaller than the element pointed by LOC is found. 2. Interchange elements pointed by LOC and RIGHT 3. If RIGHT becomes equal to LOC, terminate the subfunction partion().
- 11. 3. Beginning with the element pointed by LEFT, scan the array from left to right, comparing each element with the element pointed by LOC until: 1. Element grater than the element pointed by LOC is found. 2. Interchange elements pointed by LOC and LEFT. 3. If LEFT becomes equal to LOC, terminate the subfunction Partion(). 4. Exit
- 12. Full example of quicksort on a random set of numbers. The shaded element is the pivot. It is always chosen as the last element of the partition. However, always choosing the last element in the partition as the pivot in this way results in poor performance () on already sorted lists, or lists of identical elements. Since sub-lists of sorted / identical elements crop up a lot towards the end of a sorting procedure on a large set, versions of the quicksort algorithm which choose the pivot as the middle element run much more quickly than the algorithm described in this diagram on large sets of numbers.