A) this formula states that optimal number of multiplication required to for Matrix Ai, j = Multiplication required for matrix Ai, k + A k+1, j and the number of multiplication required to multplity these two matrices. And we find the matrix which produces the minimum number of multiplication from all matrices
b) Number of multiplication required will be 2280
parenthetization will be as follows
((10x 8, 8 x 6 ) , (6x 15, 15 x 12))
10×8,8×6,6×15,15×12 4. [15] Dynamic Programming. We are given a set of matrices Ap.A1, A2. .. .An-1....
10×8,8×6,6×15,15×12 4. [15] Dynamic Programming. We are given a set of matrices Ap.A1, A2. .. .An-1. which we must multiply in this order. We let (d, dira) be the dimension of matrix A. The minimal number Nij of operations required to multiply matrices (A, Ati .. A) is defined by: a. Explain this formula. Apply this formula to compute the optimal parenthetization of the product of matrices Ao-A1,Az,A3, where the dimensions of these matrices are, respectively: 6x15, and 15x12. b....
15] Dynamic Programming a. We are given a set of matrices Ao.A1, A2.. An-1. which we must multiply in this order. We let (di, di+1) be the dimension of matrix Ai. The minimal number Nuj of operations required to multiply matrices (Ai,Ai+ Aj) is defined by: Explain this formula. 15] Dynamic Programming a. We are given a set of matrices Ao.A1, A2.. An-1. which we must multiply in this order. We let (di, di+1) be the dimension of matrix Ai....
Find an optimal parenthesizing to multiply the following matrices. Apply dynamic programming and show your work: A1 x A2 x A3 x A4 x A5 x A6 Size of A1 : 30 x 80 Size of A2 : 80 x 100 Size of A3 : 100 x 5 Size of A4 : 5 x 200 Size of A5 :200 x 7 Size of A6: 7 x 7
Use the dynamic programming technique to find an optimal parenthesization of a matrix-chain product whose sequence of dimensions is <5, 8, 40, 10, 20, 6>. Matrix Dimension A1 5 * 8 A2 8*40 A3 40*10 A4 10*20 A5 20*6
5. Dynamic Programming (a) Given a set of four matrices for the following dimensions: We need to compute Al* A2 A3 A4 Al=2X3; A2=3X5; A3=5X2: A4=2X4 Find the order in which the matrix pairs should be multiplied to produce the optimum number of operations. Show all your steps (10) (b) For the problems given below, determine whether it is more efficient to use a divide and conquer strategy or a dynamic programming strategy. Give the reasons for your choice (5*3=15)...
Use the dynamic programming technique to find an optimal parenthesization of a matrix-chain product whose sequence of dimensions is <5, 8, 4, 10, 7, 50, 6>. Matrix Dimension A1 5*8 A2 8*4 A3 4*10 A4 10*7 A5 7*50 A6 50*6 You may do this either by implementing the MATRIX-CHAIN-ORDER algorithm in the text or by simulating the algorithm by hand. In either case, show the dynamic programming tables at the end of the computation. Using Floyd’s algorithm (See Dynamic Programming...
READ CAREFULLY AND CODE IN C++ Dynamic Programming: Matrix Chain Multiplication Description In this assignment you are asked to implement a dynamic programming algorithm: matrix chain multiplication (chapter 15.2), where the goal is to find the most computationally efficient matrix order when multiplying an arbitrary number of matrices in a row. You can assume that the entire input will be given as integers that can be stored using the standard C++ int type and that matrix sizes will be at...