Explain how dynamic programming reduces the complexity of a simple algorithm. Also explain the matrix chain multiplication algorithm in this context.

Explain how dynamic programming reduces the complexity of a  simple algorithm. Also explain the matrix chain multiplication  algorithm in this context. Derive the principle of  optimality for  multiplication of matrix chain. Compute the optimalmultiplications  required following matrices.  A1 of order 30 x 35; A2 of order 35 x 15; A3 of order 15 x 5