Matrix Chain Multiplication UVA 442

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

#include <iostream>
#include <cstdio>
#include <stack>
#include <bits/stdc++.h>
using namespace std;
struct matrix
{
    int a,b;
    matrix(int a=0,int b=0):a(a),b(b) {}
}m[26];
stack <matrix> s;
int main()
{
    int n;
    cin>>n;
    for(int i=0;i<n;i++)
    {
        string name;
        cin>>name;
        int k = name[0] - 'A';
        cin>>m[k].a>>m[k].b;
    }
    string expr;
    while(cin>>expr)
    {
        int len = expr.length();
        bool error = false;
        int ans = 0;
        for(int i = 0;i<len;i++)
        {
            if(isalpha(expr[i])) s.push(m[expr[i]-'A']);
            else if(expr[i]==')')
            {
                matrix m2 = s.top();s.pop();
                matrix m1 = s.top();s.pop();
                if(m1.b!=m2.a) {error = true;break;}
                ans += m1.a*m1.b*m2.b;
                s.push(matrix(m1.a,m2.b));
            }
        }
        if(error) printf("error\n");
        else printf("%d\n",ans);
    }
    return 0;
}