GATE | GATE CS 2011 | Question 38

Four matrices M1, M2, M3 and M4 of dimensions pxq, qxr, rxs and sxt respectively can be multiplied is several ways with different number of total scalar multiplications. For example, when multiplied as ((M1 X M2) X (M3 X M4)), the total number of multiplications is pqr + rst + prt. When multiplied as (((M1 X M2) X M3) X M4), the total number of scalar multiplications is pqr + prs + pst.

If p = 10, q = 100, r = 20, s = 5 and t = 80, then the number of scalar multiplications needed is:
(A) 248000
(B) 44000
(C) 19000
(D) 25000


Answer: (C)

Explanation: We get minimum number of multiplications using ((M1 X (M2 X M3)) X M4).

Total number of multiplications = 100x20x5 (for M2 x M3) + 10x100x5 + 10x5x80 = 19000.

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