Polynomial Expression
- 1. Data Stucture Unit II POLYNOMIAL EXPRESSION USING LINKED LIST
- 2. Polynomial Expression using Linked List • linked list is a data structure that stores each element as an object in a node of the list. • Polynomial is a mathematical expression that consists of variables and coefficients. • For example: 5x^2 - 4x + 7 • 3x+ 3 • result = 5x^2-x+10
- 3. Polynomial Expression using Linked List • In the Polynomial linked list, the coefficients and exponents of the polynomial are defined as the data node of the list. • Implementation of polynomial Expression, struct node { int power; float coef; struct node *next; };
- 4. Example
- 5. Adding two polynomials using Linked List Input: • 1st number = 5x^2 + 4x^1 + 2x^0 • 2nd number = 5x^1 + 5x^0 Output: 5x^2 + 9x^1 + 7x^0
- 6. Adding two polynomials using Linked List
- 7. Adding two polynomials using Linked List Algorithm: • Create Linked polynomials • Read the co-efficient and exponent values • Set the pointers list1 and list2 to both the polynomials to traverse them. • Start from the first node and compare the exponent of polynomials. • If(list1->exp == list2-> exp) list1->coef= list1->coef + list2->coef list3->exp= list1->exp (move your pointer to next node)
- 8. Adding two polynomials using Linked List Algorithm: • If(list1->exp == list2-> exp) list1->coef= list1->coef + list2->coef list3->exp= list1->exp (move both the pointer to next node) • If(list1->exp > list2-> exp) list3->coef= list1->coef list3->exp= list1->exp (move list1 pointer to next node) • If(list1->exp < list2-> exp) list3->coef= list2->coef list3->exp= list2->exp (move list2 pointer to next node)
- 9. Josephus Circle using circular linked list • There are n people standing in a circle waiting to be executed. • The counting out begins at some point in the circle and proceeds around the circle in a fixed direction. • In each step, a certain number of people are skipped and the next person is executed. • The elimination proceeds around the circle (which is becoming smaller and smaller as the executed people are removed), until only the last person remains, who is given freedom. • Given the total number of persons n and a number m which indicates that m-1 persons are skipped and m-th person is killed in circle. • The task is to choose the place in the initial circle so that you are the last one remaining and so survive. .
- 10. Josephus Circle using circular linked list Algorithm: 1) Create a circular linked list of size n. 2) Traverse through linked list and one by one delete every m-th node until there is one node left. 3) Return value of the only left node.
- 11. Josephus Circle using circular linked list Description: • The Josephus problem involves n people standing in a circle. Each person kills the next person until there is only one person remaining. We will use a circular linked list to solve the Josephus problem. For example: n = 6, 1 -> 2 -> 3 -> 4 -> 5 -> 6 -> 1 • Node 1 kills node 2. Node 3 kills node 4. Node 5 kills node 6. 1 -> 3 -> 5 -> 1 • Node 1 kills node 3. Node 5 kills node 1. 5 -> • Therefore 5 is the last person remaining.
- 12. Josephus Circle using circular linked list Example 1: n = 10, Rotate the list to the left by one position and then delete the first element. Find who is the lone survivor. 1 -> 2 -> 3 -> 4 -> 5 -> 6 -> 7-> 8 -> 9 -> 10
- 13. Josephus Circle using circular linked list Example 1: n = 10 1 -> 2 -> 3 -> 4 -> 5 -> 6 -> 7-> 8 -> 9 -> 10