Ultraviolet A 442 matrix chain multiplication (matrix chain multiplication, simulation stack)

The number of times the given matrix chain multiplication expression needs to be calculated. The number of columns in the current matrix is equal to the number of rows in the next matrix. The result is an invalid error.

The input is strictly legal. Even if only two characters are multiplied, the input is enclosed in parentheses. If there are at most two characters in the brackets, it is very easy. When a letter is entered directly into the stack, the result is obtained after calculation by the parentheses. now

#include<cstdio>#include<cctype>#include<cstring>using namespace std;const int N = 1000;int st[N], row[N], col[N], r[N], c[N];int main(){    int n, ans, top;    scanf("%d", &n);    char na[3], s[N];    for(int i = 1; i <= n; ++i)    {        scanf("%s", na);        int j = na[0] - 'A';        scanf("%d%d", &row[j], &col[j]);    }    while(~scanf("%s", &s))    {        int i;        for(i = 0 ; i < 26; ++i)            c[i] = col[i], r[i] = row[i];        ans = top = 0;        for(i = 0; s[i] != '\0'; ++i)        {            if(isalpha(s[i]))            {                int j = s[i] - 'A';                st[++top] = j;            }            else if(s[i] == ')')            {                if(r[st[top]] != c[st[top - 1]])  break;                else                {                    --top;                    c[st[top]] = c[st[top + 1]];                    ans += (r[st[top]] * c[st[top]] * r[st[top + 1]]);                }            }        }        if(s[i] == '\0') printf("%d\n", ans);        else printf("error\n");    }    return 0;}

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 stronugly 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 integerN(), Representing the number of matrices in the first part. The nextNLines 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 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

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))

Sample output

000error10000

Ultraviolet A 442 matrix chain multiplication (matrix chain multiplication, simulation stack)