Question

4) Which is a more efficient way to determine the optimal number of multiplications in a matrix-chain multiplication problem: enumerating all the ways of parenthesizing the product and computing the number of multiplications for each, or running RECURSIVE-MATRIX-CHAIN? Justify your answer

Answer 1

Answer:

Running RECURSIVE-MATRIX-CHAIN is asymptotically more efficient than enumerating all the ways of parenthesizing the product and computing the number of multiplications of each.

the running time complexity of enumerating all the ways of parenthesizing the product is n*P(n) while in case of RECURSIVE-MATRIX-CHAIN, all the internal nodes are run on all the internal nodes of the tree and it will also create overhead.

Explanation: