addition and multiplication for polynomials

gistfile1.c

typedef struct termNode {
  int coef;
  int deg;
  struct termNode* greater;
  struct termNode* lesser;
} termNode;

termNode* make_term(int coef, int deg) {
  termNode* p = malloc(sizeof(termNode));
  p->coef = coef;
  p->deg = deg;
  p->greater = NULL;
  p->lesser = NULL;
  return p;
}

void free_polynomial(termNode* p) {
  while (p != NULL) {
    termNode* del = p;
    p = p->lesser;
    free(del);
  }
}

termNode* link_polynomials(termNode* head,
                           termNode* last,
                           termNode* p) {
  if (p != NULL) {
    p->greater = last;
  }
  if (last != NULL) {
    last->lesser = p;
  }
  if (head == NULL) {
    head = p;
  }
  return head;
}

termNode* copy_polynomial(termNode* head,
                          termNode* last,
                          termNode* p) {
  if (p == NULL) {
    return head;
  }

  termNode* n = make_term(p->coef, p->deg);
  head = link_polynomials(head, last, n);
  return copy_polynomial(head, n, p->lesser);
}

termNode* add_polynomials_(termNode* head,
                           termNode* last,
                           termNode* p1,
                           termNode* p2) {
  if (p1 == NULL) {
    head = copy_polynomial(head, last, p2);
    return head;
  }
  if (p2 == NULL) {
    head = copy_polynomial(head, last, p1);
    return head;
  }

  termNode* p = NULL;
  if (p1->deg < p2->deg) {
    p = make_term(p2->coef, p2->deg);
    p2 = p2->lesser;
  } else if (p1->deg > p2->deg) {
    p = make_term(p1->coef, p1->deg);
    p1 = p1->lesser;
  } else {
    p = make_term(p1->coef + p2->coef, p1->deg);
    p1 = p1->lesser;
    p2 = p2->lesser;
  }

  head = link_polynomials(head, last, p);
  return add_polynomials_(head, p, p1, p2);
}

termNode* add_polynomials(termNode* p1, termNode* p2) {
  return add_polynomials_(NULL, NULL, p1, p2);
}

termNode* mul_polynomials(termNode* p1, termNode* p2) {
  if (p1 == NULL || p2 == NULL) {
    return NULL;
  }

  termNode* mul = NULL;
  while (p1 != NULL) {
    termNode* p = p2;
    while (p != NULL) {
      termNode* n = make_term(p1->coef * p->coef,
                              p1->deg + p->deg);
      termNode* new_mul = add_polynomials(mul, n);
      free_polynomial(mul);
      free_polynomial(n);
      mul = new_mul;
      p = p->lesser;
    }
    p1 = p1->lesser;
  }

  return mul;
}