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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.
SecondPart = Line { Line }Line = Expression Expression = Matrix | "(" Expression Expression ")"Matrix = "A" | "B" | "C" | ... | "X" | "Y" | "Z"
9A 50 10B 10 20C 20 5D 30 35E 35 15F 15 5G 5 10H 10 20I 20 25ABC(AA)(AB)(AC)(A(BC))((AB)C)(((((DE)F)G)H)I)(D(E(F(G(HI)))))((D(EF))((GH)I))
000error10000error3500150004050047500 15125 需要对字符进行处理 如果是'('就跳过 如果是')'就将)前的两个矩阵取出 判断先前的矩阵的行数与后一个的矩阵的列数是否相同 如果不同就输出error 再将乘之后的矩阵继续放回栈中 #include#include #include #include #include
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