杭电 1082【矩阵乘法次数的运算】

最新推荐文章于 2022-04-04 15:41:41 发布

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最新推荐文章于 2022-04-04 15:41:41 发布 · 856 阅读

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探讨了杭电1082题目的解决方案，专注于矩阵链乘法的运算次数优化，旨在降低计算复杂度。

Matrix Chain Multiplication

Problem Description

Matrix multiplication problem is a typical example of dynamical programming.
Suppose you have to evaluate an expression like A*B*C*D*E where A,B,C,D and E are matrices. Since matrix multiplication is associative, the order in which multiplications are performed is arbitrary. However, the number of elementary multiplications needed strongly depends on the evaluation order you choose.
For example, let A be a 50*10 matrix, B a 10*20 matrix and C a 20*5 matrix.
There are two different strategies to compute A*B*C, namely (A*B)*C and A*(B*C).
The first one takes 15000 elementary multiplications, but the second one only 3500.
Your job is to write a program that determines the number of elementary multiplications needed for a given evaluation strategy.

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