Write a program to implement the following strategy for multiplying two sparse polynomials...

Write a program to implement the following strategy for multiplying two sparse polynomials P1, P2 of size M and N, respectively. Each polynomial is represented as a linked list of objects consisting of a coefficient and an exponent (Exercise). We multiply each term in P1 by a term in P2 for a total of MN operations. One method is to sort these terms and combine like terms, but this requires sorting MN records, which could be expensive, especially in small-memory environments. Alternatively, we could merge terms as they are computed and then sort the result.

a. Write a program to implement the alternative strategy.

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b. If the output polynomial has about O(M + N) terms, what is the running time of both methods?

Exercise

Rehashing requires recomputing the hash function for all items in the hash table. Since computing the hash function is expensive, suppose objects provide a hash member function of their own, and each object stores the result in an additional data member the first time the hash function is computed for it. Show how such a scheme would apply for the Employee class in Figure, and explain under what circumstances the remembered hash value remains valid in each Employee.

Figure Example of Employee class that can be in a hash table