Implement the algorithm for an optimal parenthesization of a matrix chain product as dis-cussed in the class.Use the following recursive function as part of your program to print the outcome, assumethe matrixes are namedA1, A2, ..., An.PRINT-OPTIMAL-PARENS(s, i, j){if (i=j) thenprint “A”i else{print “(”PRINT-OPTIMAL-PARENS(s,i,s[i, j])PRINT-OPTIMAL-PARENS(s, s[i, j] + 1, j)print “)”} }a- Test your algorithm for the following cases:1. Find and print an optimal parenthesization of a matrix-chain product whose sequenceof dimensions is<5,10,3, X,12,5,50, Y,6>.2. Find and print an optimal parenthesization of a matrix-chain product whose sequenceof dimensions is<5,10,50,6, X,15,40,18, Y,30,15, Z,3,12,5>.

The support functions For the next few questions, we'll be working on finding the roots for the following quadratic equation: f(x)=x²-1.5 which has the derivative: f'(x)=2r Before we get started on the root-finding, however, you are to write two functions that will come in handy later: f(x), which takes a number or numpy array x and returns f(x) as defined above. f_prine(x), which takes a number or numpy array x and returns f'(x) as defined above. Paste these two functions into the answer box below. Note: Each function can easily be written using just a return statement. If you're doing more than this, you're probably overthinking it. For example: Test x = 2 print (f(x)) print(f_prine(x)) Result 2.5 4 Answer: (penalty regime: 0, 10, 20, ... %)

Please provide a solution for the Knapsack Problem using Genetic Algorithm: