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Saturday, 25 May 2013

Polynomial Multiplication Using Linked List

A polynomial expression can be represent as linked list.   4X^4 + 3x^2 + 7X is a polynomial expression and its linked list representation is as follows.

+------------+      +-----------+      +---------------+
| 4 | 4  |  -|--->| 3 | 2 |   -|--->| 7 | 1 | NULL|
+------------+      +-----------+      +----------------+

Here, each node composed of co-efficient, exponent and a pointer to the next node.

Multiplication of polynomial expressions:
3X^3 + 4x^2 + 5X
X^4

Output is 3x^7 + 4X^6 + 5X^4

See Also:


Example Program To Multiply Two Polynomial Expressions Using Linked List (in C):



  #include<stdio.h>
  #include<stdlib.h>

  struct node {
        int coefficient, exponent;
        struct node *next;
  };

  struct node *hPtr1, *hPtr2, *hPtr3;
  /*
   * creates new node and fill the given data
   */
  struct node * buildNode(int coefficient, int exponent) {
        struct node *ptr = (struct node *) malloc(sizeof (struct node));
        ptr->coefficient = coefficient;
        ptr->exponent = exponent;
        ptr->next = NULL;
        return ptr;
  }

  /* insert data in decending order - based on exponent value */
  void polynomial_insert(struct node ** myNode, int coefficient, int exponent) {
        struct node *lPtr, *pPtr, *qPtr = *myNode;
        lPtr = buildNode(coefficient, exponent);

        /* inserting new node at appropriate position */
        if (*myNode == NULL || (*myNode)->exponent < exponent) {
                *myNode = lPtr;
                (*myNode)->next = qPtr;
                return;
        }

        /* placing new node between two nodes or end of node */
        while (qPtr) {
                pPtr = qPtr;
                qPtr = qPtr->next;
                if (!qPtr) {
                        pPtr->next = lPtr;
                        break;
                } else if ((exponent < pPtr->exponent) &&
                                (exponent > qPtr->exponent)) {
                        lPtr->next = qPtr;
                        pPtr->next = lPtr;
                        break;
                }
        }
        return;
  }

  /* inserting new node with resultant data into the output list (n1) */
  void polynomial_add(struct node **n1, int coefficient, int exponent) {
        struct node *x = NULL, *temp = *n1;
        if (*n1 == NULL || (*n1)->exponent < exponent) {
                /* adding at the front */
                *n1 = x = buildNode(coefficient, exponent);
                (*n1)->next = temp;
        } else {
                while (temp) {
                        if (temp->exponent == exponent) {
                                /* updating the co-efficient value  alone */
                                temp->coefficient = temp->coefficient + coefficient;
                                return;
                        }
                        if (temp->exponent > exponent && (!temp->next ||
                                temp->next->exponent < exponent)) {
                                /* inserting in the middle or end */
                                x = buildNode(coefficient, exponent);
                                x->next = temp->next;
                                temp->next = x;
                                return;
                        }
                        temp = temp->next;
                }
                x->next = NULL;
                temp->next = x;
        }
  }

  void polynomial_multiply(struct node **n1, struct node *n2, struct node *n3) {
        struct node * temp;
        int coefficient, exponent;

        temp = n3;

        /* if both input list are absent, then output list is NULL */
        if (!n2 && !n3)
                return;

        /* input list 1(n2) is absent, then output list is input list2 (n3) */
        if (!n2) {
                *n1 = n3;
        } else if (!n3) {

                /*
                 * list n3 is absent, then o/p list is n2
                 */
                *n1 = n2;
        } else {
                while (n2) {
                        while (n3) {
                                /* multiply coefficient & add exponents */
                                coefficient = n2->coefficient * n3->coefficient;
                                exponent = n2->exponent + n3->exponent;
                                n3 = n3->next;
                                /* insert the above manipulated data to o/p list */
                                polynomial_add(n1, coefficient, exponent);
                        }
                        n3 = temp;
                        n2 = n2->next;
                }
        }
        return;
  }

  /* delete the given input list */
  struct node * polynomial_deleteList(struct node *ptr) {
        struct node *temp;
        while (ptr){
                temp = ptr->next;
                free(ptr);
                ptr = temp;
        }
        return NULL;
  }

  void polynomial_walkList(struct node *ptr) {
        int i = 0;
        while (ptr) {
                printf("%dX^%d %c ", ptr->coefficient,
                        ptr->exponent, ptr->next?'+':'\0');
                ptr = ptr->next;
                i++;
        }
        printf("\n");
        return;
  }

  int main (int argc, char *argv[]) {
        int coefficient, exponent, i, n;
        FILE *fp1, *fp2;
        fp1 = fopen(argv[1], "r");
        fp2 = fopen(argv[2], "r");

        if (!fp1 || !fp2) {
                printf("Unable to open file\n");
                fcloseall();
                exit(0);
        }

        /* scan co-eff & exponent from input file 1 */
        while (fscanf(fp1, "%d%d", &coefficient, &exponent) != EOF) {
                polynomial_insert(&hPtr1, coefficient, exponent);
        }

        /* scan co-eff and exponent from input file 2 */
        while (fscanf(fp2, "%d%d", &coefficient, &exponent) != EOF) {
                polynomial_insert(&hPtr2, coefficient, exponent);
        }
        printf("Polynomial Expression 1: ");
        polynomial_walkList(hPtr1);
        printf("Polynomial Expression 2: ");
        polynomial_walkList(hPtr2);

        polynomial_multiply(&hPtr3, hPtr1, hPtr2);

        printf("Output:");
        polynomial_walkList(hPtr3);

        hPtr1 = polynomial_deleteList(hPtr1);
        hPtr2 = polynomial_deleteList(hPtr2);
        hPtr3 = polynomial_deleteList(hPtr3);

        return 0;
  }



First column in the input file represents co-efficient and the second column represents exponent.


  Output: (C Program Multiply Two Polynomial Expressions Using Linked List)
  jp@jp-VirtualBox:~/$ cat input1.txt 
  6 5
  7 4
  8 2
  jp@jp-VirtualBox:~/$ cat input2.txt 
  7 5
  3 4
  5 3
  jp@jp-VirtualBox:~/$ ./a.out input1.txt input2.txt 
  Polynomial Expression 1: 6X^5 + 7X^4 + 8X^2  
  Polynomial Expression 2: 7X^5 + 3X^4 + 5X^3  
  Output:42X^10 + 67X^9 + 51X^8 + 91X^7 + 24X^6 + 40X^5  



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