UVa 442 矩阵链乘

Posted 2020-08-21 谦谦君子，陌上其华

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 (  ), 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 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

栈的运用。

 1 #include<iostream>
 2 #include<stack>
 3 #include<string>
 4 using namespace std;
 5 
 6 struct Node
 7 {
 8     int m, n;
 9     Node(int m = 0, int n = 0) :m(m), n(n){}
10 }Matrix[30];
11 
12 stack<Node> chain;
13 
14 void clear()
15 {
16     while (!chain.empty())
17         chain.pop();
18 }
19 
20 void Multiplication(string s)
21 {   
22     clear();
23     int count = 0;
24     if (s[0] != \'(\')    {cout << "0" << endl; return;}
25     for (int i = 0; i < s.length(); i++)
26     {
27         if (s[i] == \')\')
28         {
29             Node x2 = chain.top();
30             chain.pop();
31             Node x1 = chain.top();
32             chain.pop();
33             if (x1.n != x2.m)  { cout << "error" << endl; return; }
34             else
35             {
36                 count += x1.m * x1.n * x2.n;
37                 chain.push(Node(x1.m,x2.n));
38             }
39         }
40         else if (s[i] == \'(\')  { ; }
41         else  chain.push(Matrix[s[i]-\'A\']);
42     }
43     cout << count << endl;
44 }
45 
46 int main()
47 {
48     int t, m, n;
49     char name;
50     cin >> t;
51     while (t--)
52     {
53         cin >> name >> m >> n;
54         Matrix[name - \'A\'].m = m;
55         Matrix[name - \'A\'].n = n;
56     }
57     string s;
58     while (cin >> s)
59     {
60         Multiplication(s);
61     }
62     return 0;
63 }