Selection Sort and Insertion Sort

SELECTION SORT
AND INSERTION
SORT

SELECTION SORT
› The smallest element is selected from
the unsorted array and swapped with
the leftmost element, and that element
becomes a part of the sorted array. This
process continues moving unsorted
array boundary by one element to the
right.

COMPLEXITY
 Selecting the minimum requires
scanning {displaystyle n} elements
(taking {displaystyle n-
1} comparisons) and then swapping it
into the first position. Finding the next
lowest element requires scanning the
remaining {displaystyle n-1} elements
and so on.

How Selection Sort Works?
Consider the following depicted array as
an example.

For the first position in the sorted list,
the whole list is scanned sequentially.
The first position where 14 is stored
presently, we search the whole list and
find that 10 is the lowest value.

So we replace 14 with 10. After one
iteration 10, which happens to be the
minimum value in the list, appears in
the first position of the sorted list.

For the second position, where 33 is
residing, we start scanning the rest of
the list in a linear manner.

We find that 14 is the second lowest
value in the list and it should appear at
the second place. We swap these
values.

After two iterations, two least values are
positioned at the beginning in a sorted
manner.
The same process is applied to the rest
of the items in the array.

Following is a depiction of the entire sorting process −
SORTED ARRAY

PROGRAM
#include<iostream>
using namespace std;
int main()
{
int elements, arr[10], input, j, temp;
cout<<“How many elements?:”;
cin>>elements;
cout<<“Enter Array Elements:n”;

for(input=0;input<elements;input++)
{
for(j=input+1;j<elements;j++)
{
if(arr[input]>arr[j];
{
temp=arr[input]
arr[input]=arr[j]
arr[j]=temp;
}
}
}
Cout<<“nThe sorted array is:n”;
For(input=0;input<elements;input++)
{
cout<<arr[input]<<“ “;
}
Cout<<“n”;
}

INSERTION SORT
It is a simple Sorting algorithm which sorts
the array by shifting elements one by one.
In 2006 Bender, Martin Farach-Colton, and
Mosteiro published a new variant of insertion
sort called library sort or gapped insertion
sort that leaves a small number of unused
spaces (i.e., "gaps") spread throughout the
array.

 The benefit is that insertions need only
shift elements over until a gap is
reached. The authors show that this
sorting algorithm runs with high
probability in O(n log n) time.

ADVANATAGES OF INSERTION
SORT
 Simple implementation: Jon
Bentley shows a three-line C version,
and a five-line optimized version
 Efficient for (quite) small data sets,
much like other quadratic sorting
algorithms
 More efficient in practice than most
other simple quadratic (i.e., O(n2))
algorithms such as selection
sort or bubble sort.

 Adaptive, i.e., efficient for data sets that
are already substantially sorted: the time
complexity is O(nk) when each element
in the input is no more than k places
away from its sorted position
 Stable; i.e., does not change the relative
order of elements with equal keys
 In-place; i.e., only requires a constant
amount O(1) of additional memory space
 Online; i.e., can sort a list as it receives it

CHARACTERISTICS OF
INSERTION SORT
 It has one of the simplest
implementation
 It is efficient for smaller data sets, but
very inefficient for larger lists.
 Insertion Sort is adaptive, that means
it reduces its total number of steps if
given a partially sorted list, hence it
increases its efficiency.

 It is better than Selection Sort and
Bubble Sort algorithms.
 Its space complexity is less. Like
Bubble Sorting, insertion sort also
requires a single additional memory
space.
 It is a Stable sorting, as it does not
change the relative order of elements
with equal keys.

Consider the following depicted array as
an example.

Insertion sort compares the first two
elements.
It finds that both 14 and 33 are already
in ascending order. For now, 14 is in
sorted sub-list.

Insertion sort moves ahead and
compares 33 with 27.
And finds that 33 is not in the correct
position.
It swaps 33 with 27

It also checks with all the elements of
sorted sub-list. Here we see that the
sorted sub-list has only one element 14,
and 27 is greater than 14. Hence, the
sorted sub-list remains sorted after
swapping.

Next, it compares 33 with 10.
These values are not in a sorted order.

So we swap them.
However, swapping makes 27 and 10
unsorted. Hence, we swap them too.

Again we find 14 and 10 in an unsorted
order.
We swap them again. By the end of
third iteration, we have a sorted sub-list
of 4 items.
This process goes on until all the
unsorted values are covered in a sorted
sub-list.

SIMPLE STEPS OF INSERTION
 Step 1 − If it is the first element, it is
already sorted. return 1;
 Step 2 − Pick next element
 Step 3 − Compare with all elements in
the sorted sub-list
 Step 4 − Shift all the elements in the
sorted sub-list that is greater than the
value to be sorted
 Step 5 − Insert the value
 Step 6 − Repeat until list is sorted

{3, 7, 4, 9, 5, 2, 6, 1}
3 7 4 9 5 2 6 1
3 7 4 9 5 2 6 1
3 7 4 9 5 2 6 1
3 4 7 9 5 2 6 1
3 4 7 9 5 2 6 1
3 4 5 7 9 2 6 1
2 3 4 5 7 9 6 1
2 3 4 5 6 7 9 1
1 2 3 4 5 6 7 9

PROGRAM
#include<iostream>
Using namespace std;
Int main()
{
int i,j,n,temp,a[30];
cout<< “Enter the number of elements:”
cin>>n;
cout<<“Enter the elementn”;
for(i-=1;i<n;i++)
{
cin>>a[i];
}

for(i=1;i<=n-1;i++)
{
temp=a[i];
j=i-1;
while((temp<a[j])&&(j>=0))
{
a[j+1]=a[j]; //moves element forward
j=j-1;
}
a[j+1]=temp; //insert element forward
}
Cout<< “nThe sorted array is:”;
For(i=0;i<n;i++)
{
cout<< a[i]<<“ “;
}
Return 0;
}

Selection Sort and Insertion Sort

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