What is matrix chain multiplication with examples?

For example, suppose A is a 10 × 30 matrix, B is a 30 × 5 matrix, and C is a 5 × 60 matrix. Then, (AB)C = (10×30×5) + (10×5×60) = 1500 + 3000 = 4500 operations A(BC) = (30×5×60) + (10×30×60) = 9000 + 18000 = 27000 operations. Clearly the first parenthesization requires less number of operations.

What is correct option for matrix chain multiplication?

1. Which of the following methods can be used to solve the matrix chain multiplication problem? Explanation: Dynamic Programming, Brute force, Recursion methods can be used to solve the matrix chain multiplication problem.

What does matrix chain multiplication mean?

Matrix chain multiplication (or the matrix chain ordering problem) is an optimization problem concerning the most efficient way to multiply a given sequence of matrices. The problem is not actually to perform the multiplications, but merely to decide the sequence of the matrix multiplications involved.

What is the time complexity of matrix chain multiplication?

O(n^3)
So it is O(n^3).

How do you find the optimal Parenthesization in a matrix chain multiplication?

Step1: Structure of an optimal parenthesization: Our first step in the dynamic paradigm is to find the optimal substructure and then use it to construct an optimal solution to the problem from an optimal solution to subproblems. Ai Ai+1…. Aj. If i < j then any parenthesization of the product Ai Ai+1 ……

What is time complexity of matrix chain multiplication?

As before, if we have n matrices to multiply, it will take O(n) time to generate each of the O(n2) costs and entries in the best matrix for an overall complexity of O(n3) time at a cost of O(n2) space.

What is the objective of matrix chain multiplication problem?

Matrix chain multiplication (or Matrix Chain Ordering Problem, MCOP) is an optimization problem that to find the most efficient way to multiply a given sequence of matrices. The problem is not actually to perform the multiplications but merely to decide the sequence of the matrix multiplications involved.

What is the running time of matrix chain order algorithm?

MATRIX-CHAIN-ORDER (p) 1. n length[p]-1 2.