Application of linked list

1. Application of linked list Geletaw S.

2. Linked list can be used in various environment. Some of the common examples are • Creation of a polynomial • Polynomial manipulation • Sorting • Creation of a tree • Tree Traversals • Multilist Organization

3. Creation of a Polynomial • A node is used to create a list which consist of various components of the polynomial • Example of a polynomial 4x^3 + 3x^2 + 2x + 1 Node1 Node2 Node3 Node4

4. The List contain node that has information about the polynomial degrees and coefficients Example4x^3 Co-eff Power PointerField 4 3 .

5. Similarly for the polynomial 4x^3 + 3x^2 + 2x + 1, the linked list created is as follows Structure used to create a node: Struct node { int power; int coeff; struct node * next; // to point the next node in the list } 4 3 3 2 2 1 1 0

6. Procedure to create a polynomial Void create( ) { int s,c1; Struct node * p1, *n; root = p1 = NULL; cout<<“ enter the higher degree”; cin>>deg; s = sizeof ( struct node *); for (I = deg; i>+0;I - - ) { cout<<“co-efficient :”; cin>> c1; n=(struct node *) new(s); n -> coeff = c1; n -> pow = I; n -> next = NULL; if (root = = NULL) root = n; else p1 -> next = n; p1=n; } }

7. Algorithm to create a polynomial • The highest degree of the polynomial is obtained first • Based on the degree the node is created • The co-efficient and the corresponding power value is stored in the node • The NEXT pointer is updated accordingly

8. Type declaration for array implementation of the polynomial ADT Typedefstruct { intcoeffarray[ Maxdegree + 1 ]; intHighpower; } *Polynomial; Procedure to initialize a polynomial to zero Void zeroPolynomial( Polynomial Poly ) { int i; for( i=0; i<=Maxdegree; i++ ) Poly -> CoeffArray[ i ] = o Poly -> HighPower = o; }

9. Procedure to add two Polynomials Void AddPolynomial( const Polynomial Poly1, const Polynomial Poly2, Polynomail PolySum) { int i; zeroPolynomial( PolySum ); Polysum -> HighPower = Max( Poly1 -> HighPower,Poly2 -> Highpower); for( i= PolySum -> HighPower; i>=0; i++) PolySum ->CoeffArray[ i ] = Poly1 -> coeffArray [ i ] + Poly2 ->coeffArray[ i ]; }

10. PolySum Poly 1 4x^3 + 3x^2 + 2x + 1 Poly 2 5x^2 + 6x + 3 ( + ) ----------------------------------- PolySum 4x^3 + 8X^2 + 8x + 4

11. Procedure to Multiply 2 Polynomials Void MultPolynomial( const Polynomial Poly1, const Polynomial Poly2, Polynomial PolyProd) { int i,j; zeroPolynomial( PolyProd ); PolyProd -> HighPower = Poly1 -> highPower + Poly2 ->HighPower; if( PolyProd -> HighPower > MaxDegree) error( “ Exceeded array Size”); else for( i=0; i<= Poly1 -> highPower; i++) for( j=0; j<= Poly2 -> HighPower; J++) PolyProd -> coeffArray [ i+j ] = Poly1 -> coeffArray [i] * Poly2 -> coeffArray [j]; }

12. PolyProd Poly 1 4x^3 + 3x^2 + 2x + 1 Poly 2 5x^2 + 6x + 3 ( * ) ----------------------------------- 20x^5 + 24x^4 + 12x^3 + 15x^4 + 18x^3 + 6x^2 + 10x^3 + 12x^2 + 6x + 5x^2 + 6x + 3 PolyProd 20x^5 + 39x^4 + 40x^3 + 23x^2 + 12x + 3

13. Radix Sort • It is performed using buckets from 0 to 9 • The digit position of a number is used to perform sorting • The number of passes in a radix sort depends on the number of digits in the given number • It is also called as Card Sort

14. Example 42, 24, 11, 36, 54, 10, 19, 27, 45. The number of digits n the numbers are 2, hence the number of passes are 2 Pass 1

15. The number has been placed in their corresponding pockets based on their unit digit. 10 is placed in pocket 0 27 is placed in pocket 7 Collect back all the nos from the pockets 10,11,42,32,24,54,45,36,27,19

16. Now place all the nos in the pockets based on tenth digit position. 10 is placed in pocket 1 27 is placed in pocket 2