Question: (Matrix Chain Multiplication) Given two matrices A:pq,B:qr,C=AB is a pr matrix, and time to compute C is pqr (calculating by Cij=k=1qAikBkj ). Given three matrices

(Matrix Chain Multiplication) Given two matrices A:pq,B:qr,C=AB is a pr matrix,

(Matrix Chain Multiplication) Given two matrices A:pq,B:qr,C=AB is a pr matrix, and time to compute C is pqr (calculating by Cij=k=1qAikBkj ). Given three matrices A:pq,B:qr,C:rs, though (AB)C=A(BC), the time required to compute in the two cases could vary greatly. (E.g., when p=r=1,q=s, one is 2q and the other is 2q2.) Now, given n matrices Ai,i={1,2,,n}, and Ai has size pipi+1. Find the minimum cost way to compute the multiplication A1A2An. (Dynamic programming) (Matrix Chain Multiplication) Given two matrices A:pq,B:qr,C=AB is a pr matrix, and time to compute C is pqr (calculating by Cij=k=1qAikBkj ). Given three matrices A:pq,B:qr,C:rs, though (AB)C=A(BC), the time required to compute in the two cases could vary greatly. (E.g., when p=r=1,q=s, one is 2q and the other is 2q2.) Now, given n matrices Ai,i={1,2,,n}, and Ai has size pipi+1. Find the minimum cost way to compute the multiplication A1A2An. (Dynamic programming)

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