Ultraviolet A Matrix Chain Multiplication

The questions are as follows:

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 saved med 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 ")"
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

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

I used this question to practice map and pair in the STL library, and I felt familiar with it a lot. I directly simulate it. When there are two letters in the brackets, we use rappers to form a new matrix (in lower case) and add the number of multiplication to count, when the Left row is not equal to the right column, an error is output in the loop.

The AC code is as follows: