Problem 55305. Chain multiplication - 02

Asif Newaz

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Following up on the problem in 55295, you found the number of multiplications needed to multiply two matrices.
Now, you are given a sequence of matrices. There are many different ways you can multiply the matrices. For example, 
say, you are given 4 matrix - A, B, C, D. They can be multiplied as follows - A(B(CD)), A((BC)D), ((AB)C)D, (AB)(CD), (A(BC))D.
you have to figure out which is the optimal way of multiplying those matrices based on the mininum number of multiplications required. For example, consider a simple 3 matrix case.
A(1,2), B(2,3), C(3,2)
A(BC) => BC requires 12 multiplications; multiplying A matrix with the result requires 4 multiplications. Total = 12+4= 16.
(AB)C => AB requires 6 multiplications; multiplying the result with the C matrix requires 6 multiplications. Total = 6+6= 12.
Therefore, to multiply ABC - the optimal way is (AB)C requiring 12 multiplications in total.
Here, you will be given an array 'a' containing the size of consequtive matrices. The output is the minimum number of multiplications required to multiply those matrices.
here, a = [2, 4, 6, 1] represents 3 matrices --  A(2,4), B(4,6), and C(6,1)