Dynamic Programming and Matrix Chain Multiplication

These flashcards cover key concepts and details regarding Dynamic Programming and the Matrix Chain Multiplication problem.

What is Dynamic Programming primarily used for?

Solving complex problems by breaking them down into simpler subproblems.

What does the recursive algorithm for the nth Fibonacci number return when n=0?

Returns 0.

What is the base case for Fib(n) when n=1?

Returns 1.

In a matrix chain multiplication problem, what is the cost of multiplying matrices of size p, q, r?

The cost is pqr.

What does the subproblem R[i, j] represent in optimal parenthesization?

It represents the optimal solution for the multiplication of matrices Ai to Aj.

What is the optimal substructure property in dynamic programming?

An optimal solution can be constructed from optimal solutions of its subproblems.

What does the recursive formula m[i, j] represent in matrix chain multiplication?

The cost of the optimal solution for multiplying matrices Ai to Aj.

How do you determine the optimal cost for matrix multiplication involving multiple matrices?

Calculate all possible costs and take the minimal one.

What values do you initialize m[i,i] to in matrix chain multiplication?

Initialize m[i,i] to 0.

What does m[1,5] represent in the context of matrix chain multiplication?

The minimum cost of multiplying matrices from A1 to A5.

What should a new table keep track of when providing an optimal solution?

It should keep track of the 'k' values where the minimum is taken.

What is the final outcome of a dynamic programming approach to matrix chain multiplication?

Identifying the optimal order of multiplications to minimize cost.