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.

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.