A data cube \(πΆ\), has π dimensions, and each dimensions has exactly \(π\)β¦
2015
A data cube \(πΆ\),Β hasΒ πΒ dimensions, and each dimensions has exactlyΒ \(π\)Β distinct values in the base cuboid. Assume that there are no concept hierarchies associated with the dimensions. What is the maximum number of cells possible in the data cube,Β \(πΆ\)?
- A.
\(p^n\) - B.
\(π\) - C.
\((2^n-1)(p+1)\) - D.
\((p+1)^n\)
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Correct answer: D
Each dimension has p distinct base values, and when forming the full data cube each dimension can additionally be aggregated using the value ALL. Therefore each dimension effectively has p+1 possible settings (the p concrete values or ALL).
Counting combinations across the n dimensions:
Direct reasoning: with p+1 choices per dimension, the total number of possible cells is (p+1)^n.
Equivalent binomial expansion: sum over the number of aggregated dimensions k gives Sum_{k=0}^n C(n,k) p^{n-k} = (p+1)^n, which matches the direct count.
Therefore the maximum number of cells possible in the data cube C is (p+1)^n.