Sorting Techniques
– Insertion Sort
– Shell Sort
What is sorting?
 Sorting means “Putting things in Order” or
“arranging”
 Arranging can be done in two ways
 Ascending Order ( Smallest to Largest )
 Descending Order ( Largest to Smallest )
 In default Sorting Means arranging in ascending
order
 There are many algorithms for sorting, some
simple but perhaps inefficient others complicated
but efficient.
• We will look at seven algorithms for sorting
Insertion Sorting
Working:
 This is the way that most people sort
playing cards
 The cards are picked up one by one
and put in the proper place.
•The Elements are Picked one by one
and put into the Proper Place
#define MAX 5
void main()
{
int A[MAX],i,j,current;
cout<<"Enter "<<MAX<<"
elements to be sorted:"<<endl;
for (i=0;i<MAX;i++) cin>>A[i];
for (i=1;i<MAX;i++)
{
current= A[i]; //33
j=i;
//1
while ((j>0)&&(current<A[j-1]))
{
// 1>0 && 33 < 67
A[j]= A[j-1]; // 67 moved to next
j--;
A[j]= current; //33 moved to previous
}}cout<<"The elements after Sort"<<endl;
for (i=0;i<MAX;i++)
cout<<A[i]<<endl;
}
67 33 21
84
49
50
75
67
33
67
21
33
67
21
33
67 84
21
33
49 67 84
21 33 49 50 67 84
21
33
49 50 67 75 84
Shell Sort
designed by Shell, is an improvement on the
insertion sort.
drawbacks of insertion sort :
The exchanging was done with adjacent
elements.
Improvement
If exchanging is done with elements that are
further apart then the algorithm would be more
efficient.
Method:
Find an appropriate increment size
(e.g. n/3 + 1)
• Now do insertion sort on the elements separated by this
increment.
67
S 67
h
e 33
l
l 21
S
o
r 67
t
33
21
33
84
21
75
49
67
75
49
50
49
67
75
Insertion Sort
33
49
21
50
33
84
50
33
75
Insertion Sort
Insertion Sort
50
21
84
49
21
75
49
50
IS
21
49
67
IS
33
50
75
50
67
75
84
84
84
84
Inc=n/3+1
7/3+1=3
3/3+1=2
Shell Sort
void SortInterval(int start,int
increment,int a[])
{
int i,j,current;
i=start+increment; // I =3
while (i<MAX) // 3<7
{
current=a[i]; //84
j=i;
//j=3
while ((j>start) && (current<a[jincrement]))
{
// 3 >0 && 84 <67
a[j]=a[j-increment];
j=j-increment;
a[j]= current;
}
i=i+increment;
// I =6
}
}
void main()
{int A[MAX],i,increment,start;
cout<<"Enter "<<MAX<<" elements to
be sorted:"<<endl;
for (i=0;i<MAX;i++) cin>>A[i];
increment=MAX;
do
{increment=increment/3+1;
for (start=0;start<increment;start++)
SortInterval(start,increment,A);
}while (increment>1);
cout<<"The elements after Shell
Sort"<<endl;
for (i=0;i<MAX;i++)
cout<<A[i]<<endl;
}