Matrix Chain Multiplication
Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 65536/32768 K (Java/Others)
Total Submission(s): 1066    Accepted Submission(s): 719


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.



Input
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 <= n <= 26), representing the number of matrices in the first 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 } <EOF>
Line = Expression <CR>
Expression = Matrix | "(" Expression Expression ")"
Matrix = "A" | "B" | "C" | ... | "X" | "Y" | "Z"



Output
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


Source
University of Ulm Local Contest 1996

<span style="color:#330099;">/************************************************
    author    :   Grant Yuan
    time      :   2014.8.4
    algorithm :   栈的运用
    source    ;   HDU 1082
************************************************/

#include<iostream>
#include<cstdio>
#include<cstdlib>
#include<cstring>
#include<queue>
#include<stack>
#include<algorithm>

using namespace std;
char s[1000];
struct node{
  char c;
  int num1;
  int num2;
};
stack<node>q;
int n,ans;
int sta[26],fin[26];

int main()
{
     char c1;int aa,bb;
     scanf("%d",&n);
     for(int i=0;i<n;i++)
     {
         getchar();
         scanf("%c%d%d",&c1,&aa,&bb);
         sta[c1-'A']=aa;fin[c1-'A']=bb;
     }
     while(~scanf("%s",s)){
            ans=0;
            int flag=1;
        while(!q.empty()) q.pop();
        int l=strlen(s);
        for(int i=0;i<l;i++)
        {
            if(s[i]==')'){
                node n1,n2,n3;
                n1=q.top();q.pop();
                n2=q.top();q.pop();
                if(n2.num2!=n1.num1){flag=0;break;}
                ans+=n2.num1*n2.num2*n1.num2;
                q.pop();
                n3.num1=n2.num1;n3.num2=n1.num2;
                q.push(n3);
            }
            else if(s[i]>='A'&&s[i]<='Z'){
                node n1;
                n1.c=s[i];n1.num1=sta[s[i]-'A'];
                n1.num2=fin[s[i]-'A'];
                q.push(n1);
            }
            else if(s[i]=='('){
                node n1;
                n1.c=s[i];
                n1.num1=0;n1.num2=0;
                q.push(n1);
            }
        }
        if(flag==0) printf("error\n");
        else printf("%d\n",ans);
     }
     return 0;
}
</span>