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Applications of Linked Lists

1. Polynomial Representation and operation on Polynomials

Ex: 10 X 6 +20 X 3 + 55

2. Sparse Matrix Representation

0 0 11

22 0 0

0 0 66

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typedef struct poly_node *poly_pointer;

typedef struct poly_node {

int coef;int expon;poly_pointer next;

};poly_pointer a, b, c;

A x a x a x a xm

e

m

e em m( ) . . .= + + +

1 2 0

1 2 0

Representation

Polynomials

coef expon link

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3 14 2 8 1 0a

8 14 -3 10 10 6b

a x x= + +3 2 11 4 8

b x x x= +8 3 1 014 10 6

null

null

Example

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Polynomial Operation

1. Addition2. Subtraction

3. Multiplication

4. Scalar Division

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3 14 2 8 1 0a

8 14 -3 10 10 6

b

11 14

d

a->expon == b->expon

3 14 2 8 1 0

a

8 14 -3 10 10 6

b

11 14

d

a->expon < b->expon-3 10

Polynomial Addition

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3 14 2 8 1 0

a

8 14 -3 10 10 6

b11 14

a->expon > b->expon

-3 10

d

2 8

Polynomial Addition

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3 14 2 8

1 0

a

8 14 -3 10 10 6

b11 14

a->expon > b->expon

3 10

d

2 8

Polynomial Addition (contd)

10 6

1 0

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poly_pointer padd(poly_pointer a, poly_pointer b){

poly_pointer front, rear, temp;int sum;rear =(poly_pointer)malloc(sizeof(poly_node));if (IS_FULL(rear)) {

fprintf(stderr, The memory is full\n);exit(1);

}front = rear;

while (a && b) {switch (COMPARE(a->expon, b->expon)) {

Adding Polynomials (Pseudocode)

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case -1: /* a->expon < b->expon */attach(b->coef, b->expon, &rear);b= b->next;break;

case 0: /* a->expon == b->expon */sum = a->coef + b->coef;if (sum) attach(sum,a->expon,&rear);

a = a->next; b = b->next;break;case 1: /* a->expon > b->expon */

attach(a->coef, a->expon, &rear);a = a->next;

}

}for (; a; a = a->next)attach(a->coef, a->expon, &rear);

for (; b; b=b->next)attach(b->coef, b->expon, &rear);

rear->next = NULL;temp = front; front = front->next; free(temp);return front;

}

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3 142 8

1 0a

8 14 -3 10 10 6

b

-5 14

d

a->expon == b->expon

3 14 2 8 1 0

a

8 14 -3 10 10 6

b

-5 14

d

a->expon < b->expon3 10

Polynomial Subtraction

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3 14 2 8 1 0

a

8 14 -3 10 10 6

b-5 14

a->expon > b->expon

3 10

d

2 8

Polynomial Subtraction (contd)

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3 14 2 8 1 0

a

8 14 -3 10 10 6

b-5 14

a->expon > b->expon

3 10

d

2 8

Polynomial Subtraction (contd)

-10 6

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3 14 2 8

1 0

a

8 14 -3 10 10 6

b-5 14

a->expon > b->expon

3 10

d

2 8

Polynomial Subtraction (contd)

-10 6

1 0

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poly_pointer padd(poly_pointer a, poly_pointer b){

poly_pointer front, rear, temp;int sum;rear =(poly_pointer)malloc(sizeof(poly_node));if (IS_FULL(rear)) {

fprintf(stderr, The memory is full\n);exit(1);

}front = rear;while (a && b) {

switch (COMPARE(a->expon, b->expon)) {

Polynomial Subtraction(Pseudo code)

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case -1: /* a->expon < b->expon */attach(-b->coef, b->expon, &rear);

b= b->next;break;

case 0: /* a->expon == b->expon */sum = a->coef - b->coef;if (sum) attach(sum,a->expon,&rear);

a = a->next; b = b->next;break;case 1: /* a->expon > b->expon */

attach(a->coef, a->expon, &rear);a = a->next;

}

}for (; a; a = a->next)attach(a->coef, a->expon, &rear);

for (; b; b=b->next)attach(-b->coef, b->expon, &rear);

rear->next = NULL;temp = front; front = front->next; free(temp);

return front;}

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Sparse MatrixA sparse matrix is a very large

matrix that contains lot of zeros. Inorder to save storage space, a

sparse matrix stores only thenonzero elements.

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Linked list representationSparse Matrix

m n -- i j val i j val Null

=

0830

0000

9072

0500

A

4 4 -- 0 2 5 3 2 8 Null

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Linked list representationSparse Matrix

aij

i j

ROWLINK

COLLINK

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Linked list representationSparse Matrix

=

0830

0000

9072

0500

A

0

1

2

3

5 2

2 0 7 1 9 3

3 1 8 2