Design a recursive version of dynamic programming algorithm $($Top$-$down$)$ to construct the actual solution

of the matrix chain multiplication problem $($i$.$e$.,$ the parentheses order$).$ For this problem, please write down

the recursive function in pseudocode and Write down the dynamic table and matrix output on the following

examples:

$($a$)$ Three matrices $($A$,$ B$,$ and C$)$ with dimensions $10505100,$ respectively.

$($b$)$ Four matrices $($A$,$ B$,$ C$,$ and D$)$ with dimensions $205103010,$ respectively.