題目如下：
Matrix Chain Multiplication
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.
Input Specification
Input consists of two parts: a list of matrices and a list of expressions.
The first line of the input file contains one integer n ( 1=
part. The next n lines each contain one capital letter, specifying the name of the matrix, and two integers, specifying
the number of rows and columns of the matrix.
The second part of the input file strictly adheres to the following syntax (given in EBNF):
SecondPart = Line { Line }
Line = Expression
Expression = Matrix | "(" Expression Expression ")"
Matrix = "A" | "B" | "C" | ... | "X" | "Y" | "Z"
Output Specification
For each expression found in the second part of the input file, print one line containing the word "error" if evaluation
of the expression leads to an error due to non-matching matrices. Otherwise print one line containing the number of
elementary multiplications needed to evaluate the expression in the way specified by the parentheses.
Sample Input
9
A 50 10
B 10 20
C 20 5
D 30 35
E 35 15
F 15 5
G 5 10
H 10 20
I 20 25
A
B
C
(AA)
(AB)
(AC)
(A(BC))
((AB)C)
(((((DE)F)G)H)I)
(D(E(F(G(HI)))))
((D(EF))((GH)I))
Sample Output
0
0
0
error
10000
error
3500
15000
40500
47500
15125
我用這道題練了練STL庫中的map和pair，感覺熟悉了許多，一遍AC了。我是直接模擬的，遇到括號內有兩個字母的情況，直接raplace成一個新矩陣（用小寫表示），並給count加上乘法的數目，遇到左行不等於右列的情況，跳出循環，輸出error。
AC的代碼如下：
