(Solved): Problem 3. Data Cube Computation (20 points) Assume our data is stored in a d ...

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Problem 3. Data Cube Computation (20 points) Assume our data is stored in a data cube with 3 dimensions A, B and C. We would like to do full cube computation using multi-way array aggregation. The lengths of dimensions A and $$B$$ are 4000 and 400 , respectively. The length of dimension $$\mathrm{C}$$ is an unknown value $$x$$ $$(x>0)$$. We cut each dimension into quarters and get 64 chunks as follows. (1) (4 points) If we follow the scan order $$1?2?3?4?5?6??$$, what is the memory requirement to compute the whole cube? (2) (4 points) If we follow the scan order $$1?5?9?13?2?6??$$, what is the memory requirement to compute the whole cube? (3) (4 points) If we follow the scan order $$1?17?33?49?5?21??$$, what is the memory requirement to compute the whole cube? (4) (4 points) What is the maximum integer value of $$x$$ if (3) is the most memory-saving order among (1), (2) and (3)? (5) (4 points) Besides the scan orders in (1)-(3), are there any other scan orders? If yes, please list all the other scan orders by specifying the first 10 chunks in their orders (you can assume the order always starts from chunk 1). If not, please justify your answer.