Final answer:
The number of elementary operations (specifically multiplications) performed by the algorithm segment with nested loops depends on whether n is odd or even. It requires a summing process over all iterations of the loops, different for even and odd values of n. An exact formula would need in-depth mathematical analysis.
Step-by-step explanation:
To determine the actual number of elementary operations performed by the algorithm segment provided, we need to analyze the nested for loops. The inner loop starts at floor((i+1)/2) and goes up to n, and within it, the algorithm performs a multiplication for each iteration, which is an elementary operation. We can break down the calculation of the total number of operations into two cases based on whether n is odd or even.
For odd n:
The inner loop will run n - floor((i+1)/2) + 1 times for each i. Since i goes from 1 to n, we must sum this expression over all possible values of i. The formula becomes complex as we need to account for every odd and even i differently.
For even n:
The calculation is similar to the odd n case, but since n itself is even, it might offer some simplifications in the formula. Again, we must consider how many times the inner loop runs for each value of i and sum it over the range of i.
As the question requests to ignore comparisons in the for-next loops and only look at comparisons within if-then statements - and since there are no if-then statements specified - we are not counting any comparison operations. Therefore, we only focus on the multiplications that take place within the inner loop.
To provide an exact formula, we require a more in-depth mathematical analysis which involves considering different scenarios and potentially using tools like summation formulas or even programming counting simulations. Nonetheless, we should emphasize that the answer should be expressed as a function of n, reflecting the total number of multiplications.