Linear Data Structures

1. Application of linked list
• Polynomial ADT
• Radix ADT
• Multilist

2. Polynomial ADT:
We can perform the polynomial
manipulations such as addition, subtraction and
differentiation etc,.
Declaration:
struct poly
{
int coeff;
int power;
struct poly *next;
}*list1,*list2,*list3;

3. Creation of the polynomial:
poly create(poly *head1,poly *newnode1)
{
poly *ptr;
if(head1==NULL)
{
head1=newnode1;
}

4. else
{
ptr=head1;
while(ptr->next!=NULL)
ptr=ptr->next;
ptr->next=newnode1;
}
return(head1);
}

5. Linked list based polynomial addition
void add()
{
poly *ptr1,*ptr2, *newnode;
ptr1=list1;
ptr2=list2;
while(ptr1!=NULL && ptr2!=NULL)
{
newnode=malloc(sizeof(struct poly));

6. if(ptr1-> power == ptr2-> power)
{
newnode ->coeff=ptr1->coeff+ ptr2->coeff;
newnode-> power = ptr1-> power;
newnode-> next =NULL;
list 3= create(list3, newnode)
ptr1 = ptr1-> next;
ptr2 = ptr2 -> next;
}

7. else
{
if(ptr1-> power > ptr2--> power)
{
newnode ->coeff=ptr1->coeff;
newnode-> power = ptr1-> power;
newnode-> next =NULL;
list 3= create(list3, newnode)
ptr1 = ptr1-> next;
}

8. else
{
newnode ->coeff=ptr2->coeff;
newnode-> power = ptr2-> power;
newnode-> next =NULL;
list 3= create(list3, newnode)
ptr2 = ptr2-> next;
}
}
}

9. Example
Input: 1st number =
5x^2 + 4x^1 + 2x^0
2nd number =
5x^1 + 5x^0
Output: 5x^2 + 9x^1 + 7x^0
Input: 1st number = 5x^3 +
4x^2 + 2x^0
2nd number = 5x^1 + 5x^0
Output: 5x^3 + 4x^2 + 5x^1
+ 7x^0

10. Linked list based polynomial
Subtraction
void sub()
{
poly *ptr1,*ptr2, *newnode;
ptr1=list1;
ptr2=list2;
while(ptr1!=NULL && ptr2!=NULL)
{
newnode=malloc(sizeof(struct poly));

11. if(ptr1-> power == ptr2-> power)
{
newnode ->coeff=ptr1->coeff - ptr2->coeff;
newnode-> power = ptr1-> power;
newnode-> next =NULL;
list 3= create(list3, newnode)
ptr1 = ptr1-> next;
ptr2 = ptr2 -> next;
}

12. else
{
if(ptr1-> power > ptr2-> power)
{
newnode ->coeff=ptr1->coeff;
newnode-> power = ptr1-> power;
newnode-> next =NULL;
list 3= create(list3, newnode)
ptr1 = ptr1-> next;
}

13. else
{
newnode ->coeff=ptr2->coeff;
newnode-> power = ptr2-> power;
newnode-> next =NULL;
list 3= create(list3, newnode)
ptr2 = ptr2-> next;
}
}
}

14. Poly * multiply()
{
Node *ptr1, *ptr2,*Newnode;
ptr1 = list1;
ptr2 = list2;
while (ptr1 != NULL)
{
while (ptr2 != NULL)
{
Newnode->coeff = ptr1->coeff * ptr2->coeff;

15. Newnode->power = ptr1->power + ptr2->power;
list2=create(list3,Newnode);
ptr2 = ptr2->next;
}
ptr2 = list2;
ptr1 = ptr1->next;
}
}

16. Radix Sort:
• Radix sort is one of the sorting algorithms used
to sort a list of integer numbers in order. In
radix sort algorithm, a list of integer numbers
will be sorted based on the digits of individual
numbers.
• Radix sort algorithm requires the number of
passes which are equal to the number of digits
present in the largest number among the list of
numbers.
• For example, if the largest number is a 3 digit
number then that list is sorted with 3 passes.

18. Multi-Linked Lists
• A multilinked list is a more general linked list
with multiple links from nodes.
• In a general multi-linked list each node can
have any number of pointers to other nodes,
• Multi-lists are essentially the technique of
embedding multiple lists into a single data
structure.
• A multi-list has more than one next pointer,
like a doubly linked list, but the pointers
create separate lists