Pieces in Parentheses

Computer Science Level 3

A 1 : 5 × 10 A 2 : 10 × 3 A 3 : 3 × 12 A 4 : 12 × 5 A_1 : 5 \times 10 \\ A_2 : 10 \times 3 \\ A_3 : 3 \times 12 \\ A_4 : 12 \times 5

Consider the following matrices, along with their dimensions as described above.

What would be the best way of arranging the parentheses for multiplying A 1 . . A 4 A_1 .. A_4 such that it needs a minimal number of scalar multiplications?

( A 1 × A 2 × A 3 ) × A 4 ( A_1 \times A_2 \times A_3) \times A_4 ( A 1 × A 2 ) × ( A 3 × A 4 ) (A_1\times A_2)\times(A_3 \times A_4) A 1 × ( A 2 × A 3 × A 4 ) A_1 \times ( A_2 \times A_3 \times A_4 ) ( A 1 × A 2 ) × A 3 × A 4 (A_1 \times A_2) \times A_3 \times A_4

Thaddeus Abiy by Thaddeus Abiy , 25, Ethiopia

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