This document discusses using linked lists to represent polynomials and perform operations like addition and subtraction on them. It also discusses radix sort, which sorts integers based on their digits, and multi-linked lists, which have multiple links between nodes allowing for multiple lists to be embedded in a single data structure. Linked lists allow storing polynomial terms with coefficient and power, and traversing the lists to add/subtract terms with the same power and output a new polynomial list. Radix sort requires as many passes as the largest number's digits, sorting based on each digit place value. Multi-lists generalize linked lists by having nodes with multiple pointers connecting separate embedded lists.

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