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>. 3. Find and print an optimal parenthesization of a matrix-chain product whose sequenceof dimensions is<50,6, X,15,40,18, Y,5,10,3,12,5, Z,40,10,30,5>. X=10Y=20Z=30 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 named A1, A, ., 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 >.3. Find and print an optimal parenthesization of a matrix-chain product whose sequenceof dimensions is < 50, 6, X, 15, 40, 18, Y, 5, 10, 3, 12, 5, Z, 40, 10, 30, 5 >.

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>.

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>.

Operations Research : Applications and Algorithms

4th Edition

ISBN:9780534380588

Author:Wayne L. Winston

Publisher:Wayne L. Winston

Chapter14: Game Theory

Section14.3: Linear Programming And Zero-sum Games

Problem 9P

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