GATE CSE · 2018 · CS
Question 31: Algorithms
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Question 31
CSMCQ2 marksNeeds review
Assume that multiplying a matrix G_i of dimension p × q with another matrix G_j of dimension q × r requires pqr scalar multiplications. Computing the product of n matrices G_1G_2G_3...G_n can be done by parenthesizing in different ways. Define G_iG_ as an explicitly computed pair for a given parenthesization if they are directly multiplied. For example, in the matrix multiplication chain G_1G_2G_3G_4G_5G_6 using parenthesization (G_1(G_2G_3))(G_4(G_5G_6)), G_2G_3 and G_5G_6 are the only explicitly computed pairs.
Consider a matrix multiplication chain F_1F_2F_3F_4F_5, where matrices F_1, F_2, F_3, F_4 and F_5 are of dimensions 2×25, 25×3, 3×16, 16×1 and 1×1000, respectively. In the parenthesization of F_1F_2F_3F_4F_5 that minimizes the total number of scalar multiplications, the explicitly computed pairs is/are
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2018CS
GATE CSE 2018 · Paper 1
Computer Science and Information Technology · Original paper archive
- Section
- Computer Science and Information Technology
- Question type
- Multiple choice (MCQ)
- Marks
- 2 marks
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