3. Assume that we can find the product of two n-digit-numbers using some number of multi- plications of n/3-digit numbers (plus some additions, subtractions and shifts). What is the largest number of n/3-digit number multiplications that leads to an asymptotically faster algorithm than the n/2 divide-and-conquer algorithm discussed in the lecture? Provide and solve the recurrence equations. 4. Describe the differences in solution strategies between the Knapsack variant in which a fraction of an object is allowed to be packed in comparison to the variant in which only entire objects of integer weight are allowed to be packed. Be prepared to derive the com- putational complexity of the two algorithms